aainstitutetext: Department of Physics, Arizona State University, AZ 85287,
United Statesbbinstitutetext: Beyond: Center for Fundamental Concepts in
Science, Arizona State University, Tempe, Arizona 85287, USA

# Graviton Noise Correlation in Nearby Detectors

Maulik Parikh a Francesco Setti<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We consider quantum gravity fluctuations in a pair of nearby gravitational
wave detectors. Quantum fluctuations of long-wavelength modes of the
gravitational field induce coherent fluctuations in the detectors, leading to
correlated noise. We determine the variance and covariance in the lengths of
the arms of the detectors, and thereby obtain the graviton noise correlation.
We find that the correlation depends on the angle between the detector arms as
well as their separation distance.

##  1 Introduction

It is widely expected on theoretical grounds that gravity must ultimately obey
the laws of quantum mechanics Feynman:1963ax ; Weinberg:1964kqu ; Deser:1969wk
; Boulware:1974sr . By contrast there is, as yet, no compelling experimental
evidence for the quantization of gravity. Smoking-gun proofs of the
quantization of gravity are remarkably challenging to find Carney:2023nzz .
Indeed, it is challenging enough to find any distinctive observational
signature of quantum gravity, smoking-gun or otherwise. In particular, it has
been argued by Dyson that single-graviton detection is virtually impossible
Dyson:2013hbl ; Rothman:2006fp ; Boughn:2006st . However, it is not necessary
to detect individual gravitons to detect observational signatures of quantum
gravity: just as Brownian noise can be observed even when collisions with
individual molecules cannot, it can be that graviton noise is observable even
when individual gravitons are not. In a series of papers, Parikh, Wilczek, and
Zahariade (PWZ) calculated the effect of a quantized spacetime metric on a
pair of free-falling particles Parikh:2020fhy ; Parikh:2020kfh ;
Parikh:2020nrd ; they found that quantum-gravitational fluctuations induce
stochastic fluctuations (i.e. noise) in the separation of the particles. The
particle separation, which in classical general relativity would be governed
by the geodesic deviation equation, now obeys a Langevin-like stochastic
equation, a kind of quantum geodesic deviation equation. These results, which
were extended by Cho and Hu Cho:2021gvg  and obtained by a different approach
by Kanno et al Kanno:2020usf ; Kanno:2021gpt , are exciting because they
indicate the presence of quantum-gravitational fluctuations (“the noise of
gravitons”) in the separation of the mirrors of a gravitational wave
interferometer. The statistical properties of the noise depend on the quantum
state of the gravitational field and can be greatly enhanced for certain
classes of states, notably squeezed states. These results have been
corroborated by several other authors Guerreiro:2021qgk ; Haba:2020jqs ;
Haba:2021esn ; Haba:2022rpu ; Nandi:2021xtr ; Sen:2023ksj ; Moreira:2023hpj ;
Abrahao:2023lle . In addition, PWZ’s work has inspired much theoretical effort
to better understand the behavior of the noise due to gravitons. For example,
researchers have calculated the quantum corrections to the trajectory of a
free-falling particle Chawla:2021lop , and the quantum corrections in the
Raychaudhuri equation Bak:2022oyn ; Cho:2023dmh ; newPaper . Furthermore,
PWZ’s formalism has been used to study the quantization of cylindrical
gravitational waves He:2022tvk , and the interest in squeezed states has led
to a study on whether Virgo-LIGO data could be compatible with a gravitational
field in such a quantum state Hertzberg:2021rbl .

These calculations are the beginning of attempts to extract a precise
observational signature of the quantization of gravity that experimentalists
could search for. In order for the noise to be observable, however, two
requirements need to be met. First, the amplitude of the noise must be large
enough to be observable. As mentioned, this requires the gravitational field
to be in an especially noisy state, such as a squeezed state; an open
theoretical problem is determining whether there are realistic astrophysical
scenarios that might give rise to such states. Second, the noise needs to be
distinguishable from the numerous other sources of noise that gravitational
wave interferometers are subject to.

Although graviton noise has a characteristic spectrum (depending on the
state), it can nevertheless be challenging to distinguish it from the many
other types of noise present in gravitational wave detectors, such as thermal
noise, seismic noise, electronic noise, and photon shot noise, among others
LIGOScientific:2019hgc . To address this problem PWZ suggested that the
quantum noise due to gravitons might be correlated in different detectors.
This would help in the isolation of graviton noise because other types of
noise are generically uncorrelated between different detectors. Intuitively,
quantum fluctuations in long-wavelength modes of the gravitational field have
the same coupling to nearby detectors and therefore lead to correlated
stochastics. In this paper, we analyze the correlations in graviton noise,
deriving the noise covariance, the standard deviation, and the correlation. We
predict the existence of correlated quantum-gravitational noise between nearby
detector arms, with the correlation dependent on the angle between the arms
and their separation distance. Based on the angular dependence of the graviton
noise correlation, we suggest a configuration of gravitational wave
interferometers to distinguish quantum-gravitational noise from environmental
noise.

##  2 Derivation of the Correlation

###  2.1 Obtaining the Equations of Motion

Consider a system with four masses $m_{0}$, $m_{1}$, $m_{2}$, and $m_{3}$. Let
$m_{0}$ and $m_{1}$ be the mirrors of the first detector, and let $m_{2}$ and
$m_{3}$ be the mirrors of the second detector. Let the metric be
$g_{\mu\nu}=\eta_{\mu\nu}+\kappa h_{\mu\nu}$ where $\kappa^{2}=16\pi G$ and
$h_{\mu\nu}$ is the metric perturbation due to gravitons.

We set up Fermi normal coordinates at the origin, so that $m_{0}$ is
stationary. In addition, let $\xi^{i}$ be the vector from $m_{0}$ to $m_{1}$,
$\eta^{i}$ be the vector from $m_{0}$ to $m_{2}$, and $\zeta^{i}$ be the
vector from $m_{0}$ to $m_{3}$. Since we are in Fermi normal coordinates, the
components of these vectors are proper lengths. In addition,
$\xi=\sqrt{\delta_{ij}\xi^{i}\xi^{j}}=\xi^{3}$, is the arm length of the first
detector, while we define the arm length of the second detector to be
$\rho=\sqrt{\delta_{ij}\rho^{i}\rho^{j}}$, where
$\rho^{i}=\zeta^{i}-\eta^{i}$.

Figure 1: In the above image, $m_{0}$ and $m_{1}$ are the mirrors of the first
detector, while $m_{2}$ and $m_{3}$ are the mirrors of the second detector.
$\vec{\xi}$ and $\vec{\rho}$, shown in red, are the arms of the two detectors
while $\vec{\eta}$ and $\vec{\zeta}$, shown in blue, are the positions of the
mirrors of the second detector. Since we are working in Fermi normal
coordinates, all lengths are proper lengths.

Working in linearized gravity, it is straightforward to show that the
classical action for the system is

$\displaystyle\begin{split}S_{\text{total}}=&\,S_{\text{grav}}+S_{m_{0}}+S_{m_{1}}+S_{m_{2}}+S_{m_{3}}\\\
=&\,-\frac{1}{4}\int
d^{4}x\,\partial_{\alpha}h_{\mu\nu}(x)\partial^{\alpha}h^{\mu\nu}(x)+\int
dt\,\frac{\delta_{ij}}{2}[m_{1}\dot{\xi}^{i}\dot{\xi}^{j}+m_{2}\dot{\eta}^{i}\dot{\eta}^{j}+m_{3}\dot{\zeta}^{i}\dot{\zeta}^{j}]\\\
&+\frac{\kappa}{4}\ddot{h}_{ij}(x)[m_{1}\xi^{i}\xi^{j}+m_{2}\eta^{i}\eta^{j}+m_{3}\zeta^{i}\zeta^{j}],\end{split}$
(1)

where the metric perturbation can be decomposed into modes using the following
equation

$h_{\mu\nu}(x)=\int
dk^{3}\sum_{s=+,\crossproduct}\epsilon_{\mu\nu}^{(s)}(\vec{k})\,h^{(s)}(\vec{k},t)\,e^{i\vec{k}\cdot\vec{x}}$
(2)

Notice that in equation (1) we implicitly applied a dipole approximation in
order to factor out the second time derivative of the metric perturbation in
the last line. This dipole approximation is needed because we are only
interested in the modes that are correlated in the two detectors. Because of
this approximation, the integral in equation (2) is only over the modes that
have a wavelength much larger than the dimensions of the system.

Now, suppose that the masses are initially in a quantum state $|A\rangle$ and
that the gravitational field is initially in a state $|\Psi\rangle$. Then, the
probability that the system is in final state $|B\rangle$ is given by the
following path integral

$\begin{split}P_{\Psi}(A\to
B)\sim\int\mathcal{D}\xi\,\mathcal{D}\xi^{\prime}\,\mathcal{D}\eta\,\mathcal{D}\eta^{\prime}\mathcal{D}\zeta\,\mathcal{D}\zeta^{\prime}\Bigr{\\{}&e^{\frac{i}{\hbar}\int
dt\frac{1}{2}[m_{1}(\dot{\xi}^{2}-\dot{\xi}^{\prime
2})+m_{2}(\dot{\eta}^{2}-\dot{\eta}^{\prime
2})+m_{3}(\dot{\zeta}^{2}-\dot{\zeta}^{\prime 2})]}\\\
&F_{\Psi}[\xi,\xi^{\prime},\eta,\eta^{\prime},\zeta,\zeta^{\prime}]\Bigl{\\}}\end{split}$
(3)

where $F_{\Psi}$ is the Feynman-Vernon influence functional Feynman:1963fq .
Generalizing Cho and Hu’s calculations Cho:2021gvg  to the case of 4
stationary masses, we find that the influence functional can be written in
terms of the noise kernel

$K^{\Psi}_{ijkl}(t,t^{\prime})=\frac{1}{2}\frac{d^{2}}{dt^{2}}\frac{d^{2}}{dt^{\prime
2}}\int d^{3}k\,d^{3}k^{\prime}\int
d^{3}x\,d^{3}x^{\prime}\,e^{-i\vec{k}\cdot\vec{x}}e^{-i\vec{k}^{\prime}\cdot\vec{x}^{\prime}}\sum_{s}\epsilon_{ij}^{(s)}(\vec{k})\epsilon_{kl}^{(s)}(\vec{k}^{\prime})G_{\Psi}^{(1)}(x,x^{\prime})$
(4)

with

$G_{\Psi}^{(1)}(x,x^{\prime})=\langle\Psi|\\{h(x),h(x^{\prime})\\}|\Psi\rangle$
(5)

Next, it is possible to rewrite the part of the influence functional that
involves the noise kernel using a trick due to Feynman and Vernon. As
discussed in Parikh:2020fhy ; Cho:2021gvg , this introduces in the action a
stochastic tensor $\mathcal{N}_{ij}$ that has the following properties

$\displaystyle
P\left[\mathcal{N}\right]=\,\mathcal{C}e^{-\frac{1}{2}\int\mathcal{N}_{ij}[(K^{\Psi})^{-1}]^{ijkl}\mathcal{N}_{kl}}$
(6)
$\displaystyle\expectationvalue{\mathcal{N}_{ij}(t)}_{s}=\int\mathcal{D}\mathcal{N}\,P\left[\mathcal{N}\right]\mathcal{N}_{ij}(t)=\,0$
(7)
$\displaystyle\expectationvalue{\mathcal{N}_{ij}(t)\mathcal{N}_{kl}(t^{\prime})}_{s}=\int\mathcal{D}\mathcal{N}\,P\left[\mathcal{N}\right]\mathcal{N}_{ij}(t)\mathcal{N}_{kl}(t^{\prime})=K^{\Psi}_{ijkl}(t,t^{\prime}),$
(8)

where (6) is a Gaussian probability density, and the subscript $s$ in (7) and
(8) denotes a statistical average. Using the new form of the action that
contains the stochastic tensor, we can obtain the equations of motion by
evaluating the saddle point of the path integral, which is obtained by taking
a derivative of the above action with respect to $\xi$, $\eta$, or $\zeta$,
and setting it equal to zero. By taking another derivative with respect to
time, and dropping the radiation reaction terms, we obtain

$\begin{split}&\ddot{\xi}^{i}(t)-2\alpha\delta^{ip}\mathcal{N}_{pj}(t)\xi^{j}(t)=0\\\
&\ddot{\eta}^{i}(t)-2\alpha\delta^{ip}\mathcal{N}_{pj}(t)\eta^{j}(t)=0\\\
&\ddot{\zeta}^{i}(t)-2\alpha\delta^{ip}\mathcal{N}_{pj}(t)\zeta^{j}(t)=0\end{split}$
(9)

where $\alpha=\kappa/2\sqrt{2}(2\pi)^{3}$. These are Langevin-like equations
in which the arm length of the detectors is affected by the stochastic tensor.
Notice that the equations of motion are uncoupled. This means that the motion
of one mass does not influence the motion of the other mass. This is what we
expect since, by ignoring the radiation reaction terms, we made the
approximation that the masses emit no gravitational waves when they move, and
so they have no way of interacting with one another. Also, this implies that
any correlation in the motion of the masses is indeed due to the background
gravitons.

###  2.2 Solving the Equations of Motion to Obtain the 2-point Functions

Hi by Following Bak:2022oyn , we will solve the equations of motion
perturbatively. Let us begin by solving the equation of motion for $m_{1}$.
The equations of motion for the other masses are solved in an analogous way.

Let $\xi^{i}(t)=\xi_{0}^{i}(t)+\xi_{1}^{i}(t)+\xi_{2}^{i}(t)+\dots$, where the
superscript indicates the spatial vector component and the subscripts indicate
the order, which corresponds to the number of stochastic tensor factors. Then,
the equation for $\xi$ becomes

$\displaystyle\ddot{\xi}^{i}_{0}(t)$ $\displaystyle=0\,,$ (10)
$\displaystyle\ddot{\xi}^{i}_{1}(t)$
$\displaystyle=2\alpha\,\delta^{ij}\mathcal{N}_{jk}(t)\,\xi^{k}_{0}(t)\,,$
(11) $\displaystyle\ddot{\xi}^{i}_{2}(t)$
$\displaystyle=2\alpha\,\delta^{ij}\mathcal{N}_{jk}(t)\,\xi^{k}_{1}(t)\,,$
(12)

Integrating with respect to time, we find

$\displaystyle\xi^{i}_{1}(t)$
$\displaystyle=2\alpha\,\delta^{ij}\int^{t}_{0}dt^{\prime}\int^{t^{\prime}}_{0}dt^{\prime\prime}\,\mathcal{N}_{jk}(t^{\prime\prime})\,\xi^{k}_{0}$
(13) $\displaystyle\xi^{i}_{2}(t)$
$\displaystyle=\left(2\alpha\right)^{2}\delta^{ij}\delta^{kl}\int^{t}_{0}dt^{\prime}\int^{t^{\prime}}_{0}dt^{\prime\prime}\int^{t^{\prime\prime}}_{0}dt^{\prime\prime\prime}\int^{t^{\prime\prime\prime}}_{0}dt^{\prime\prime\prime\prime}\,\mathcal{N}_{jk}(t^{\prime\prime})\mathcal{N}_{lm}(t^{\prime\prime\prime\prime})\,\xi^{m}_{0},$
(14)

where we assumed that the unperturbed arm length $\xi^{i}_{0}$ is a constant.
The equations for $\eta^{i}_{1}(t)$ and $\eta^{i}_{2}(t)$, and
$\zeta^{i}_{1}(t)$ and $\zeta^{i}_{2}(t)$ are the same as (13) and (14), but
with $\eta^{i}_{0}$ and $\zeta^{i}_{0}$ replacing $\xi^{i}_{0}$.

We can now calculate the 2-point functions. It turns out that all we need to
obtain the noise correlation are the 2-point functions of $\xi_{1}^{i}(t)$,
$\eta_{1}^{i}(t)$, and $\zeta_{1}^{i}(t)$. In the next section, we will show
why this is the case. For now, we will just calculate the various 2-point
functions that we will use later.

Since we will not use terms like $\xi^{i}_{2}(t)$ and other higher order
expansion terms, we will relabel $\xi^{i}_{1}(t)$, $\eta^{i}_{1}(t)$, and
$\zeta^{i}_{1}(t)$ as $\delta\xi^{i}(t)$, $\delta\eta^{i}(t)$, and
$\delta\zeta^{i}(t)$, respectively, so that

$\begin{split}\xi^{i}(t)&=\xi_{0}^{i}(t)+\delta\xi^{i}(t)+\mathcal{O}(\mathcal{N}^{2})+\dots\,,\\\
\eta^{i}(t)&=\eta_{0}^{i}(t)+\delta\eta^{i}(t)+\mathcal{O}(\mathcal{N}^{2})+\dots\,,\\\
\zeta(t)^{i}&=\zeta_{0}^{i}(t)+\delta\zeta^{i}(t)+\mathcal{O}(\mathcal{N}^{2})+\dots\,.\end{split}$
(15)

Let’s start by finding
$\expectationvalue{\delta\xi^{i}(t)\delta\eta^{j}(t)}_{s}$. Using equation
(13) and (8), we find

$\expectationvalue{\delta\xi^{i}(t)\delta\eta^{j}(t^{\prime})}_{s}=(2\alpha)^{2}\,\delta^{ik}\delta^{jl}\xi_{0}^{m}\eta_{0}^{n}\int^{t}_{0}dt^{\prime}\int^{t^{\prime}}_{0}dt^{\prime\prime}\int^{t^{(3)}}_{0}dt^{(4)}\int^{t^{(4)}}_{0}dt^{(5)}K_{kmln}^{\Psi}(t,t^{\prime}),$
(16)

where the noise kernel in the Minkowski vacuum is given by

$K_{ijkl}^{0}(t,t^{\prime})=-\frac{32\pi^{4}}{15}[2\delta_{ij}\delta_{kl}-3(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk})]\int_{0}^{\Lambda}d\omega\,\omega^{5}\cos{[\omega(t-t^{\prime})]},$
(17)

with $\Lambda$ being the cut-off frequency. We impose a cut-off frequency
because if not regularized, this integral would be divergent. Additionally,
since we are only interested in the correlated modes, the cut-off is naturally
$\Lambda\sim L^{-1}$, where $L$ is the largest separation between any two
masses in our apparatus. For example, in Figure 1, $L=|\vec{\zeta}|$. We also
point out that the noise kernel for different quantum states that are
rotationally invariant have the same factors of Kronecker delta’s present in
equation (17). This means that although the variance of the quantum noise is
different, its angular dependency is the same. For instance, this is true for
thermal states and squeezed states Cho:2021gvg ; Kanno:2020usf . Additionally,
the noise kernel for a squeezed state with squeeze parameter $r$ would also be
enhanced by a factor of $e^{r}$. Evaluating the integrals and taking the limit
$t^{\prime}\rightarrow t$, we find

$\expectationvalue{\delta\xi^{i}(t)\delta\eta^{j}(t)}_{s}=A(\Lambda,t)\delta^{ik}\delta^{jl}\xi_{0}^{m}\eta_{0}^{n}[-2\delta_{km}\delta_{ln}+3(\delta_{kl}\delta_{mn}+\delta_{kn}\delta_{ml})],$
(18)

where we defined the unitless time-dependent amplitude

$A(\Lambda,t)\simeq\frac{\kappa^{2}}{240\pi^{2}}\Lambda^{4}t^{2}$ (19)

More information about this calculation can be found in Cho:2021gvg  and
Bak:2022oyn . Since there are different ways of regularizing the integral in
equation (17), we only keep the first term in $A(\Lambda,t)$. More information
about this can be found in our very recent paper newPaper .

Using equation $(\ref{2-point function})$ we can now find the 2-point
functions for all components. Since $\xi^{i}(t)$ is along the z-axis, we know
that its only nonzero component is $\xi^{3}(t)$, which is also equal to its
magnitude. In addition, we only need to consider $\delta\xi^{3}(t)$, since we
cannot measure $\delta\xi^{1}(t)$ and $\delta\xi^{2}(t)$ due to the fact that
these fluctuations are perpendicular to the path of the laser in the detector.
Then, the only 2-point functions of interest involving $\delta\xi^{i}(t)$ and
$\delta\eta^{i}(t)$ are

$\begin{split}\expectationvalue{\delta\xi^{3}(t)\delta\eta^{1}(t)}_{s}&=-2\,\xi_{0}^{3}\eta_{0}^{1}\,A(\Lambda,t)\\\
\expectationvalue{\delta\xi^{3}(t)\delta\eta^{2}(t)}_{s}&=-2\,\xi_{0}^{3}\eta_{0}^{2}\,A(\Lambda,t)\\\
\expectationvalue{\delta\xi^{3}(t)\delta\eta^{3}(t)}_{s}&=+4\,\xi_{0}^{3}\eta_{0}^{3}\,A(\Lambda,t).\end{split}$
(20)

Notice that the 2-point functions for perpendicular components are
proportional to $-2$, while the 2-point functions for parallel components are
proportional to $+4$. In addition, all 2-point functions of $\delta\xi^{i}(t)$
and $\delta\eta^{j}(t)$ are directly proportional to corresponding factors of
$\xi^{i}_{0}$ and $\eta_{0}^{j}$. Finally, all 2-point functions are
proportional to the amplitude $A(\Lambda,t)$. The same is true for all other
2-point functions involving $\delta\xi^{3}(t)$ and $\delta\zeta^{i}(t)$.
Specifically,

$\begin{split}\expectationvalue{\delta\xi^{3}(t)\delta\zeta^{1}(t)}_{s}&=-2\,\xi_{0}^{3}\zeta_{0}^{1}\,A(\Lambda,t)\\\
\expectationvalue{\delta\xi^{3}(t)\delta\zeta^{2}(t)}_{s}&=-2\,\xi_{0}^{3}\zeta_{0}^{2}\,A(\Lambda,t)\\\
\expectationvalue{\delta\xi^{3}(t)\delta\zeta^{3}(t)}_{s}&=+4\,\xi_{0}^{3}\zeta_{0}^{3}\,A(\Lambda,t).\end{split}$
(21)

###  2.3 Obtaining the Noise Correlation

Our goal in this section is to obtain the graviton noise correlation in the
two detectors, which is

$\text{corr}(\delta\xi,\delta\rho)=\frac{\text{cov}(\delta\xi,\delta\rho)}{\sqrt{\text{Var}(\delta\xi)}\,\sqrt{\text{Var}(\delta\rho)}}$
(22)

Notice that in this equation $\delta\xi$ and $\delta\rho$ are not vectors,
they are magnitudes. This is because we are interested in the fluctuations in
the detectors’ arms, not in the fluctuations in their Cartesian components.

Let’s start by determining $\text{cov}(\delta\xi,\delta\rho)$. To do this,
let’s momentarily go back to our original notation where
$\xi(t)=\xi_{0}(t)+\xi_{1}(t)+\xi_{2}(t)+\dots$ and
$\rho(t)=\rho_{0}(t)+\rho_{1}(t)+\rho_{2}(t)+\dots$. By definition, we have

$\displaystyle\begin{split}\text{cov}(\xi(t),\rho(t))=&\langle[\xi(t)-\langle\xi(t)\rangle_{s}][\rho(t)-\langle\rho(t)\rangle_{s}]\rangle_{s}\\\
=&\langle[\xi_{0}(t)+\xi_{1}(t)+\xi_{2}(t)+\dots-\langle\xi_{0}(t)+\xi_{1}(t)+\xi_{2}(t)+\dots\rangle_{s}]\\\
&\,[\rho_{0}(t)+\rho_{1}(t)+\rho_{2}(t)+\dots-\langle\rho_{0}(t)+\rho_{1}(t)+\rho_{2}(t)+\dots\rangle_{s}]\rangle_{s}\\\
=&\langle\xi_{1}(t)\rho_{1}(t)\rangle_{s}+\mathcal{O}(\mathcal{N}^{3})+\mathcal{O}(\mathcal{N}^{4})+\dots\\\
=&\langle\xi_{1}(t)\rho_{1}(t)\rangle_{s}=\text{cov}(\delta\xi(t),\delta\rho(t)),\end{split}$
(23)

where we used the fact that
$\expectationvalue{\delta\xi(t)}_{s}=\expectationvalue{\delta\rho(t)}_{s}=0$.
This means that, to leading order in the stochastic tensor $\mathcal{N}$, the
covariance of the detectors arm length is equal to the covariance of the
noise. The same is also true for the correlation. In addition, the above
equation also demonstrated why we can neglect $\xi_{2}(t)$, $\rho_{2}(t)$, and
all higher order terms.

Next, using the fact that $\vec{\xi}(t)$ is along the z-axis, we find

$\displaystyle\begin{split}\text{cov}(\delta\xi(t),\delta\rho(t))=&\langle\delta\xi(t)\delta\rho(t)\rangle_{s}=\langle\bigl{[}\delta\vec{\xi}(t)\cdot\vec{\xi}_{0}/\xi_{0}\bigr{]}\bigl{[}\delta\vec{\rho}(t)\cdot\vec{\rho}_{0}/\rho_{0}\bigr{]}\rangle_{s}\\\
=&\bigl{(}\langle\delta\xi^{3}(t)\delta\rho^{1}(t)\rangle_{s}\,\rho_{0}^{1}+\langle\delta\xi^{3}(t)\delta\rho^{2}(t)\rangle_{s}\,\rho_{0}^{2}+\langle\delta\xi^{3}(t)\delta\rho^{3}(t)\rangle_{s}\,\rho_{0}^{3}\bigr{)}/\rho_{0}\end{split}$
(24)

The 2-point functions in the above equation are evaluated exactly like the
ones in the previous section. For example,

$\displaystyle\begin{split}\expectationvalue{\delta\xi^{3}(t)\delta\rho^{1}(t)}_{s}=&\expectationvalue{\delta\xi^{3}(t)[\delta\zeta^{1}(t)-\delta\eta^{1}(t)]}_{s}\\\
=&\expectationvalue{\delta\xi^{3}(t)\delta\zeta^{1}(t)}_{s}-\expectationvalue{\delta\xi^{3}(t)\delta\eta^{1}(t)}_{s}\\\
=&-2\,\xi^{3}_{0}(\zeta^{1}_{0}-\eta^{1}_{0})\,A(\Lambda,t)\\\
=&-2\,\xi^{3}_{0}\rho^{1}_{0}\,A(\Lambda,t)\end{split}$ (25)

With similar calculations, we determine

$\begin{split}\expectationvalue{\delta\xi^{3}(t)\delta\rho^{2}(t)}_{s}&=-2\,\xi_{0}^{3}\rho_{0}^{2}\,A(\Lambda,t)\\\
\expectationvalue{\delta\xi^{3}(t)\delta\rho^{3}(t)}_{s}&=+4\,\xi_{0}^{3}\rho_{0}^{3}\,A(\Lambda,t)\end{split}$
(26)

Substituting these into equation (24), we determine

$\text{cov}(\delta\xi(t),\delta\rho(t))=\left[-2\left(\rho^{1}_{0}\right)^{2}-2\left(\rho^{2}_{0}\right)^{2}+4\left(\rho^{3}_{0}\right)^{2}\right]A(\Lambda,t)\,\xi_{0}/\rho_{0}$
(27)

Next, we need to find $\text{Var}(\delta\xi(t))$ and
$\text{Var}(\delta\rho(t))$. With a calculation extremely similar to the one
of equation (23), we determine

$\begin{split}\text{Var}(\xi(t))&\approx\text{Var}(\delta\xi(t))=\expectationvalue{\delta\xi(t)\delta\xi(t)}_{s}\\\
\text{Var}(\rho(t))&\approx\text{Var}(\delta\rho(t))=\expectationvalue{\delta\rho(t)\delta\rho(t)}_{s}\end{split}$
(28)

Since $\vec{\xi}(t)$ is along the z-axis,

$\text{Var}(\delta\xi(t))=\expectationvalue{\delta\xi^{3}(t)\delta\xi^{3}(t)}_{s}=+4\left(\xi_{0}\right)^{2}A(\Lambda_{\xi},t),$
(29)

where $\Lambda_{\xi}\sim\xi^{-1}$ is cut-off frequency of the first detector.
Similarly, it is straightforward to show that

$\text{Var}(\delta\rho(t))=\expectationvalue{\delta\rho^{3}(t)\delta\rho^{3}(t)}_{s}=+4\left(\rho_{0}\right)^{2}A(\Lambda_{\rho},t),$
(30)

where $\Lambda_{\rho}\sim\rho_{0}^{-1}$ is cut-off frequency of the second
detector. The details of this calculation are shown in the appendix.

Substituting equations (27), (29), and (30) into equation (22), we determine

$\text{corr}(\delta\xi(t),\delta\rho(t))=\frac{A(\Lambda,t)}{\sqrt{A(\Lambda_{\xi},t)A(\Lambda_{\rho},t)}}\frac{\left[-\left(\rho^{1}_{0}\right)^{2}-\left(\rho^{2}_{0}\right)^{2}+2\left(\rho^{3}_{0}\right)^{2}\right]}{2\left(\rho_{0}\right)^{2}}$
(31)

Finally, after converting the above equation from Cartesian coordinates to
spherical coordinates and writing the amplitudes $A$ in terms of the arm
lengths of the detectors and the size of the system, we obtain

$\text{corr}(\delta\xi(t),\delta\rho(t))\simeq\frac{\xi_{0}^{2}\rho_{0}^{2}}{L^{4}}\left[\frac{1}{2}\,(3\cos^{2}\theta-1)\right],$
(32)

where the polar angle $\theta$ is the angle between the two detectors, since
$\vec{\xi}(t)$ is along the z-axis. Also, as previously mentioned,
$\text{corr}(\xi(t),\rho(t))=\text{corr}(\delta\xi(t),\delta\rho(t))$.

Figure 2: Plot of the correlation $\text{corr}(\delta\xi(t),\delta\rho(t))$ vs
the polar angle $\theta$ for $L=\xi_{0}=\rho_{0}$ as described by equation
(32). When the detectors are aligned the noise correlation is $1$, while when
they are orthogonal the noise correlation is $-1/2$. The correlation is zero
at $\theta=\cos^{-1}\left(\pm 1/\sqrt{3}\right)$, which correspond to roughly
$54.7^{\circ}$ and $125.3^{\circ}$.

###  2.4 Phenomenology

Equation (32) indicates that the correlation of the graviton noise in the two
detectors is constant in time and it depends on the arm length of the
detectors, the size of the system, and the angle between the orientation of
detectors. Since the size of the system is always smaller than or equal to the
arm length of the individual detectors, the factor that involves the $\xi$,
$\rho$, and $L$ is never larger than one, and it is equal to one only if
$L=\xi_{0}=\rho_{0}$. The closer the detectors are, the larger this factor is.
On the contrary, this ratio becomes zero in the limit that the detectors are
infinitely far away from each other.

Figure 2 contains the plot of the correlation
$\text{corr}(\delta\xi(t),\delta\rho(t))$ vs the polar angle $\theta$ for the
special case $L=\xi_{0}=\rho_{0}$. As we can see, a maximum correlation of $1$
occurs when theta is $0$ or $\pi$, meaning that the correlation is maximized
when the detectors are aligned. On the contrary, a correlation of $-1/2$
occurs when the detectors are orthogonal so that $\theta$ is $\pi/2$. The
correlation is never below this value. Finally, the correlation is zero for
values of $\theta$ of roughly $54.7^{\circ}$ and $125.3^{\circ}$.

##  3 Discussion

We have calculated the correlation in the fundamental quantum-gravitational
noise between a pair of gravitational wave detector arms. While the amplitude
of the noise depends on the quantum state of the gravitational field, the
correlation has a characteristic form, at least for states with rotational
symmetry such as the vacuum state. We found, unsurprisingly, that the
correlation falls off as the arms are separated in space. The correlation
otherwise depends only on the angle between the orientations of the detector
arms: it is maximal when they are aligned and zero for $\cos^{2}\theta=1/3$
i.e. for an angle of $54.7^{\circ}$ or $125.3^{\circ}$. This suggests that, in
order to maximally distinguish the gravitational noise from other sources of
noise, an ideal configuration of gravitational wave detectors could consist of
three arms, two of which are aligned with the third at an angle of
$54.7^{\circ}$ or $125.3^{\circ}$. The detectors should be close enough to
maximize the correlation while still being far enough apart to eliminate
correlated noise from other environmental sources. Under these conditions,
noise that was correlated between the two aligned detectors but uncorrelated
with the third one would likely be graviton noise. Conversely, our result can
be used to identify the correlated environmental noise by assessing whether
there is any correlation in the noise of the detectors placed at an angle of
$54.7^{\circ}$ or $125.3^{\circ}$: if such correlations are observed, then the
observed noise cannot be due to gravitons.

Acknowledgments
We thank Sang-Eon Bak for helpful discussions. MP is supported in part by
Heising-Simons Foundation grant 2021-2818, Department of Energy grant DE-
SC0019470 and Government of India DST VAJRA Faculty Scheme VJR/2017/000117.

##  Appendix A Appendix

Here are the calculations to derive the variance of $\delta\rho(t)$ given in
equation (30).

Since $\expectationvalue{\delta\rho(t)}_{s}=0$, we have

$\displaystyle\begin{split}\text{Var}(\delta\rho(t))=&\expectationvalue{\delta\rho(t)\delta\rho(t)}_{s}\\\
=&\expectationvalue{\left[\delta\vec{\rho}(t)\cdot\vec{\rho_{0}}/\rho_{0}\right]\left[\delta\vec{\rho}(t)\cdot\vec{\rho_{0}}/\rho_{0}\right]}_{s}\\\
=&\Bigl{[}\expectationvalue{\delta\rho^{1}(t)\delta\rho^{1}(t)}_{s}\left(\rho^{1}_{0}\right)^{2}+\expectationvalue{\delta\rho^{2}(t)\delta\rho^{2}(t)}_{s}\left(\rho^{2}_{0}\right)^{2}\\\
&+\expectationvalue{\delta\rho^{3}(t)\delta\rho^{3}(t)}_{s}\left(\rho^{3}_{0}\right)^{2}+2\expectationvalue{\delta\rho^{1}(t)\delta\rho^{2}(t)}_{s}\rho^{1}_{0}\rho^{2}_{0}\\\
&+2\expectationvalue{\delta\rho^{1}(t)\delta\rho^{3}(t)}_{s}\rho^{1}_{0}\rho^{3}_{0}+2\expectationvalue{\delta\rho^{2}(t)\delta\rho^{3}(t)}_{s}\rho^{2}_{0}\rho^{3}_{0}\Bigr{]}/\left(\rho_{0}\right)^{2}\end{split}$
(33)

Thus, we need to evaluate the 2-point functions involving all possible
combinations of the components of $\delta\rho^{i}(t)$. For example,

$\displaystyle\begin{split}\expectationvalue{\delta\rho^{1}(t)\delta\rho^{1}(t)}_{s}=&\expectationvalue{\left[\delta\zeta^{1}(t)-\delta\eta^{1}(t)\right]\left[\delta\zeta^{1}(t)-\delta\eta^{1}(t)\right]}_{s}\\\
=&\expectationvalue{\delta\zeta^{1}(t)\delta\zeta^{1}(t)}_{s}+\expectationvalue{\delta\eta^{1}(t)\delta\eta^{1}(t)}_{s}-2\expectationvalue{\delta\zeta^{1}(t)\delta\eta^{1}(t)}_{s}\end{split}$
(34)

or

$\displaystyle\begin{split}\expectationvalue{\delta\rho^{1}(t)\delta\rho^{2}(t)}_{s}=&\expectationvalue{\left[\delta\zeta^{1}(t)-\delta\eta^{1}(t)\right]\left[\delta\zeta^{2}(t)-\delta\eta^{2}(t)\right]}_{s}\\\
=&\expectationvalue{\delta\zeta^{1}(t)\delta\zeta^{2}(t)}_{s}+\expectationvalue{\delta\eta^{1}(t)\delta\eta^{2}(t)}_{s}\\\
&-\expectationvalue{\delta\zeta^{1}(t)\delta\eta^{2}(t)}_{s}-\expectationvalue{\delta\zeta^{2}(t)\delta\eta^{1}(t)}_{s}\end{split}$
(35)

From these two examples, we infer that in order to evaluate
$\expectationvalue{\delta\rho^{i}(t)\delta\rho^{j}(t)}_{s}$, we need to
evaluate $\expectationvalue{\delta\zeta^{i}(t)\delta\eta^{j}(t)}_{s}$ for all
possible values of $i$ and $j$.

Following the same procedure shown in the previous sections, it is easy to
obtain equations for $\delta\eta^{i}(t)$ and $\delta\zeta^{i}(t)$ analogous to
(13). We can then combine these and obtain

$\expectationvalue{\delta\zeta^{i}(t)\delta\eta^{j}(t^{\prime})}_{s}=(2\alpha)^{2}\,\delta^{ik}\delta^{jl}\zeta_{0}^{m}\eta_{0}^{n}\int^{t}_{0}dt^{\prime}\int^{t^{\prime}}_{0}dt^{\prime\prime}\int^{t^{(3)}}_{0}dt^{(4)}\int^{t^{(4)}}_{0}dt^{(5)}K^{\Psi}_{kmln}(t,t^{\prime}),$
(36)

where the noise kernel is the same as the one from equation (17). Then, it
follows that

$\expectationvalue{\delta\zeta^{i}(t)\delta\eta^{j}(t)}_{s}=A(\Lambda,t)\delta^{ik}\delta^{jl}\zeta_{0}^{m}\eta_{0}^{n}[-2\delta_{km}\delta_{ln}+3(\delta_{kl}\delta_{mn}+\delta_{kn}\delta_{ml})],$
(37)

where $A(\Lambda,t)$ is given in equation (19). We can now evaluate the
2-point functions for all values of $i$ and $j$.

Suppose that $i=1$. Then,

$\expectationvalue{\delta\zeta^{1}(t)\delta\eta^{j}(t)}_{s}=A(\Lambda,t)\delta^{11}\delta^{jl}\zeta_{0}^{m}\eta_{0}^{n}[-2\delta_{1m}\delta_{ln}+3(\delta_{1l}\delta_{mn}+\delta_{1n}\delta_{ml})]$
(38)

Using this, we obtain

$\displaystyle\begin{split}j=1:\expectationvalue{\delta\zeta^{1}(t)\delta\eta^{1}(t)}_{s}/A(\Lambda,t)=&\,\delta^{11}\delta^{11}\zeta_{0}^{m}\eta_{0}^{n}[-2\delta_{1m}\delta_{1n}+3(\delta_{11}\delta_{mn}+\delta_{1n}\delta_{m1})]\\\
=&-2\zeta^{1}_{0}\eta^{1}_{0}+3\left(\vec{\zeta}_{0}\cdot\vec{\eta}_{0}+\zeta^{1}_{0}\eta^{1}_{0}\right)\\\
=&\,3\vec{\zeta}_{0}\cdot\vec{\eta}_{0}+\zeta^{1}_{0}\eta^{1}_{0}\\\
j=2:\expectationvalue{\delta\zeta^{1}(t)\delta\eta^{2}(t)}_{s}/A(\Lambda,t)=&\,\delta^{11}\delta^{22}\zeta_{0}^{m}\eta_{0}^{n}[-2\delta_{1m}\delta_{2n}+3(\delta_{12}\delta_{mn}+\delta_{1n}\delta_{m2})]\\\
=&-2\zeta_{0}^{1}\eta_{0}^{2}+3\zeta_{0}^{2}\eta_{0}^{1}\\\
j=3:\expectationvalue{\delta\zeta^{1}(t)\delta\eta^{3}(t)}_{s}/A(\Lambda,t)=&\,\delta^{11}\delta^{33}\zeta_{0}^{m}\eta_{0}^{n}[-2\delta_{1m}\delta_{3n}+3(\delta_{13}\delta_{mn}+\delta_{1n}\delta_{m3})]\\\
=&-2\zeta_{0}^{1}\eta_{0}^{3}+3\zeta_{0}^{3}\eta_{0}^{1}\end{split}$ (39)

From this example, we infer that

$\expectationvalue{\delta\zeta^{i}(t)\delta\eta^{j}(t)}_{s}/A(\Lambda,t)=\begin{cases}\,3\vec{\zeta}_{0}\cdot\vec{\eta}_{0}+\zeta^{i}_{0}\eta^{j}_{0}&\text{if}\>\;i=j\\\
-2\zeta_{0}^{i}\eta_{0}^{j}+3\zeta_{0}^{j}\eta_{0}^{i}&\text{if}\>\;i\neq
j\end{cases}$ (40)

Also, completely analogous rules apply to
$\expectationvalue{\delta\zeta^{i}(t)\delta\zeta^{j}(t)}_{s}$ and
$\expectationvalue{\delta\eta^{i}(t)\delta\eta^{j}(t)}_{s}$.

Using these we can now evaluate
$\expectationvalue{\delta\rho^{i}(t)\delta\rho^{j}(t)}_{s}$ for all values of
$i$ and $j$. For example,

$\displaystyle\begin{split}\expectationvalue{\delta\rho^{1}(t)\delta\rho^{1}(t)}_{s}/A(\Lambda,t)=&\left[\expectationvalue{\delta\zeta^{1}(t)\delta\zeta^{1}(t)}_{s}+\expectationvalue{\delta\eta^{1}(t)\delta\eta^{1}(t)}_{s}-2\expectationvalue{\delta\zeta^{1}(t)\delta\eta^{1}(t)}_{s}\right]/A(\Lambda,t)\\\
=&\,3\left(\zeta_{0}\right)^{2}+\left(\zeta_{0}^{1}\right)^{2}+3\left(\eta_{0}\right)^{2}+\left(\eta_{0}^{1}\right)^{2}-6\vec{\zeta}_{0}\cdot\vec{\eta}_{0}-2\zeta_{0}^{1}\eta_{0}^{1}\\\
=&\,3\left(\vec{\zeta}_{0}-\vec{\eta}_{0}\right)^{2}+\left(\zeta_{0}^{1}-\eta_{0}^{1}\right)^{2}\\\
=&\,3\left(\rho_{0}\right)^{2}+\left(\rho_{0}^{1}\right)^{2}\end{split}$ (41)

and

$\displaystyle\begin{split}\expectationvalue{\delta\rho^{1}(t)\delta\rho^{2}(t)}_{s}/A(\Lambda,t)=&\bigl{[}\expectationvalue{\delta\zeta^{1}(t)\delta\zeta^{2}(t)}_{s}+\expectationvalue{\delta\eta^{1}(t)\delta\eta^{2}(t)}_{s}\\\
&-\expectationvalue{\delta\zeta^{1}(t)\delta\eta^{2}(t)}_{s}-\expectationvalue{\delta\zeta^{2}(t)\delta\eta^{1}(t)}_{s}\bigr{]}/A(\Lambda,t)\\\
=&\,\left(-2\zeta_{0}^{1}\zeta_{0}^{2}+3\zeta_{0}^{2}\zeta_{0}^{1}\right)+\left(-2\eta_{0}^{1}\eta_{0}^{2}+3\eta_{0}^{2}\eta_{0}^{1}\right)\\\
&-\left(-2\zeta_{0}^{1}\eta_{0}^{2}+3\zeta_{0}^{2}\eta_{0}^{1}\right)-\left(-2\zeta_{0}^{2}\eta_{0}^{1}+3\zeta_{0}^{1}\eta_{0}^{2}\right)\\\
=&\,\zeta_{0}^{1}\zeta_{0}^{2}+\eta_{0}^{1}\eta_{0}^{2}-\zeta_{0}^{1}\eta_{0}^{2}-\zeta_{0}^{2}\eta_{0}^{1}\\\
=&\left(\zeta_{0}^{1}-\eta_{0}^{1}\right)\left(\zeta_{0}^{2}-\eta_{0}^{2}\right)\\\
=&\,\rho_{0}^{1}\rho_{0}^{2}\end{split}$ (42)

From these calculations, we infer the following rules

$\expectationvalue{\delta\rho^{i}(t)\delta\rho^{j}(t)}_{s}/A(\Lambda,t)=\begin{cases}\,3\left(\rho_{0}\right)^{2}+\left(\rho_{0}^{i}\right)^{2}&\text{if}\>\;i=j\\\
\,\rho_{0}^{i}\rho_{0}^{j}&\text{if}\>\;i\neq j\end{cases}$ (43)

Finally, we can use these rules to finish evaluating
$\text{Var}(\delta\rho(t))$. We obtain

$\displaystyle\begin{split}\text{Var}(\delta\rho(t))=&\Bigl{[}\expectationvalue{\delta\rho^{1}(t)\delta\rho^{1}(t)}_{s}\left(\rho^{1}_{0}\right)^{2}+\expectationvalue{\delta\rho^{2}(t)\delta\rho^{2}(t)}_{s}\left(\rho^{2}_{0}\right)^{2}\\\
&+\expectationvalue{\delta\rho^{3}(t)\delta\rho^{3}(t)}_{s}\left(\rho^{3}_{0}\right)^{2}+2\expectationvalue{\delta\rho^{1}(t)\delta\rho^{2}(t)}_{s}\rho^{1}_{0}\rho^{2}_{0}\\\
&+2\expectationvalue{\delta\rho^{1}(t)\delta\rho^{3}(t)}_{s}\rho^{1}_{0}\rho^{3}_{0}+2\expectationvalue{\delta\rho^{2}(t)\delta\rho^{3}(t)}_{s}\rho^{2}_{0}\rho^{3}_{0}\Bigr{]}/\left(\rho_{0}\right)^{2}\\\
=&\Bigl{[}\left(3\left(\rho_{0}\right)^{2}+\left(\rho_{0}^{1}\right)^{2}\right)\left(\rho^{1}_{0}\right)^{2}+\left(3\left(\rho_{0}\right)^{2}+\left(\rho_{0}^{2}\right)^{2}\right)\left(\rho^{2}_{0}\right)^{2}\\\
&+\left(3\left(\rho_{0}\right)^{2}+\left(\rho_{0}^{3}\right)^{2}\right)\left(\rho^{3}_{0}\right)^{2}+2\,\rho_{0}^{1}\rho_{0}^{2}\,\rho^{1}_{0}\rho^{2}_{0}\\\
&+2\,\rho_{0}^{1}\rho_{0}^{3}\,\rho^{1}_{0}\rho^{3}_{0}+2\,\rho_{0}^{2}\rho_{0}^{3}\,\rho^{2}_{0}\rho^{3}_{0}\Bigr{]}A(\Lambda,t)/\left(\rho_{0}\right)^{2}\\\
=&\left[3\left(\rho_{0}\right)^{2}\left[\left(\rho_{0}^{1}\right)^{2}+\left(\rho_{0}^{2}\right)^{2}+\left(\rho_{0}^{3}\right)^{2}\right]+\left[\left(\rho_{0}^{1}\right)^{2}+\left(\rho_{0}^{2}\right)^{2}+\left(\rho_{0}^{3}\right)^{2}\right]^{2}\right]A(\Lambda,t)/\left(\rho_{0}\right)^{2}\\\
=&\,4\left(\rho_{0}\right)^{2}A(\Lambda,t).\end{split}$ (44)

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# Perspectives on AI Architectures and Co-design for Earth System
Predictability

###### Abstract

Recently, the U.S. Department of Energy (DOE), Office of Science, Biological
and Environmental Research (BER), and Advanced Scientific Computing Research
(ASCR) programs organized and held the Artificial Intelligence for Earth
System Predictability (AI4ESP) workshop series. From this workshop, a critical
conclusion that the DOE BER and ASCR community came to is the requirement to
develop a new paradigm for Earth system predictability focused on enabling
artificial intelligence (AI) across the field, lab, modeling, and analysis
activities, called ModEx. The BER’s ‘Model-Experimentation’, ModEx, is an
iterative approach that enables process models to generate hypotheses. The
developed hypotheses inform field and laboratory efforts to collect
measurement and observation data, which are subsequently used to parameterize,
drive, and test model (e.g., process-based) predictions. A total of 17
technical sessions were held in this AI4ESP workshop series. This paper
discusses the topic of the ‘AI Architectures and Co-design’ session and
associated outcomes. The AI Architectures and Co-design session included two
invited talks, two plenary discussion panels, and three breakout rooms that
covered specific topics, including: (1) DOE HPC Systems, (2) Cloud HPC
Systems, and (3) Edge computing and Internet of Things (IoT). We also provide
forward-looking ideas and perspectives on potential research in this co-design
area that can be achieved by synergies with the other 16 session topics. These
ideas include topics such as: (1) reimagining co-design, (2) data acquisition
to distribution, (3) heterogeneous HPC solutions for integration of AI/ML and
other data analytics like uncertainty quantification with earth system
modeling and simulation, and (4) AI-enabled sensor integration into earth
system measurements and observations. Such perspectives are a distinguishing
aspect of this paper.

This study aims to provide perspectives on AI architectures and co-design
approaches for Earth-system predictability. Such visionary perspectives are
essential because AI-enabled model-data integration has shown promise in
improving predictions associated with climate change, perturbations, and
extreme events. Our forward-looking ideas guide what is next in co-design to
enhance Earth-system models, observations, and theory using state-of-the-art
and futuristic computational infrastructure.

##  1 Introduction

The U.S. Department of Energy (DOE) recently concluded a workshop on
Artificial Intelligence for Earth-System Predictability (AI4ESP) (Hickmon et
al., 2022). This workshop was hosted by the DOE’s Office of Science,
Biological and Environmental Research (BER) and Advanced Scientific Computing
Research (ASCR) Programs. A total of 17 sessions with researchers worldwide
participated and discussed how artificial intelligence (AI) could enhance
Earth-system predictability across the field, lab, modeling, and analysis
activities (Hoffman et al., 2017, Fig-1.3). The primary focus of the
discussion was on using AI for transforming BER’s “Model-Experimentation”
(ModEx) integration (Chambers et al., 2012, page-93).

Traditionally, the ModEx paradigm (Hoffman et al., 2017, Section-1) integrates
observations, experiments, and measurements performed in the field or
laboratory with conceptual/process models in an iterative fashion. Recent
advances in AI have shown promise to accelerate the traditional ModEx
efficiently (Tsai et al., 2021; Cromwell et al., 2021; Mudunuru et al., 2022).
Such a transformation in the ModEx loop is needed to efficiently and
accurately integrate the DOE’s observational capabilities and
platforms111Popular BER observational capabilities include Atmospheric
Radiation Measurement Climate Research Facility (ARM) (ARM, 2022) and
Environmental Molecular Sciences Laboratory (EMSL) (EMSL, 2022), process
models and software infrastructure222State-of-the-art DOE-funded, open-source,
and massively-parallel multi-physics codes include PFLOTRAN (Lichtner et al.,
2020), Advanced Terrestrial Simulator (ATS) (ATS, 2022), and Energy Exascale
Earth System Model (E3SM) (E3SM, 2022), and computational hardware333ASCR-
funded computational infrastructure and scientific user facilities include
Argonne Leadership Computing Facility (ALCF) (ALCF, 2022), National Energy
Research Scientific Computing Center (NERSC) (NERSC, 2022), and Oak Ridge
Leadership Computing Facility (OLCF) (OLCF, 2022). However, achieving this AI-
enabled ModEx vision requires significant advancements in co-design and
associated AI architectures (Germann et al., 2013; Zhang et al., 2019; Beckman
et al., 2020; Descour et al., 2021; Bringmann et al., 2021). This paper
provides perspectives on AI architectures and co-design approaches needed to
develop AI-enabled ModEx for Earth-system predictability. These perspectives
include co-designing computational and storage infrastructure for automated ML
feature engineering and model selection, integration of sensors, process
models, and ML methods for efficient data assimilation. We also provide
futuristic system ideas on co-designing frameworks and platforms to enable the
BER community to accelerate the application of AI architectures in the ModEx
lifecycle.

The outline of our paper is as follows: Sec. 2 presents the state-of-the-
science on AI architectures and co-design that AI4ESP workshop participants
discussed. Section 3 provides four different futuristic concepts, and Sec. 4
discusses the grand challenges of developing such ideas. We also discuss
near-, middle-, and long-term goals to overcome these grand challenges.
Section 5 provides perspectives for potential research that will provide
synergy with other AI4ESP workshop sessions. Conclusions are drawn in Sec. 6.

##  2 State-of-the-Science

In this section, we describe the state-of-the-science on AI architectures and
co-design. The focus is the computing resources and DOE user facilities used
in capturing and curating data, the development of advanced AI/ML models, and
inferences for quantifying and improving earth system modeling and simulation
predictability.

###  2.1 DOE’s High-Performance Computing User Facilities

Over the past few decades, DOE has invested hundreds of millions of dollars in
developing high-performance computing (HPC) user facilities (Stevens et al.,
2020; Vetter et al., 2022; Heroux et al., 2022). DOE’s investments towards
exascale computing include Leadership Computing Facilities (LCFs) at Argonne
national laboratory (ALCF) (e.g., Aurora), Oak Ridge National Laboratory
(OLCF) (e.g., Frontier), and National Energy Research Scientific Computing
Center (NERSC), (e.g., Perlmutter). Frontier is ranked the fastest
supercomputing system on the November 2022 Top 500 list. The latest
generations of DOE’s leadership-class computing facilities are based on
integrating central processing unit (CPU) and graphics processing unit (GPU)
processors into heterogeneous systems. Concurrently, DOE’s Biological and
Environmental Research Program has invested substantial resources in state-of-
the-art scientific models (E3SM, 2022; Lichtner et al., 2020; ATS, 2022)
including the flagship Energy Exascale Earth System Model (E3SM) (E3SM, 2022)
that is specifically designed to target efficient utilization of the exascale
supercomputers. These HPC resources have significantly improved model
predictability in various areas, including earth system modeling, subsurface
flow and transport models, etc. (e.g., E3SM, PFLOTRAN). As part of the DOE’s
Exascale Computing Project, a selected subset of earth science applications
E3SM-MMF (2022); Subsurface-ECP (2022) firmly focused on model development for
the exascale era. Furthermore, efforts like the E3SM-MMF sub-project (E3SM-
MMF, 2022) under ECP had targeted co-design activities, including strong
engagements with vendors on early architecture evaluation and algorithm
design. Experience from such efforts indicates the need for expansion to AI
architecture co-design and increased coverage of earth science applications.
Such advancements allowed us to achieve energy-efficient performance on GPUs
while leveraging the commercial drivers for GPU-based AI/ML performance.

With the slowing of Moore’s Law, the computing community recognized the
increased need for architectural specialization. Hence, the next generation of
HPC systems are likely to incorporate increased heterogeneity beyond the
current hybrid CPU and GPU designs. The DOE’s efforts in AI for Science (Baker
et al., 2019; Stevens et al., 2020) are exploring capabilities that provide a
foundation for the integration of HPC applications (e.g., ALCF’s AI testbeds
(Testbed, 2022)) with data science and AI/ML frameworks.

###  2.2 Cloud computing

Cloud providers444Popular providers include Amazon Web Services (AWS) (AWS,
2022), Google Cloud Platform (GCP) (GCP, 2022), and Azure (Azure, 2022) have
user-friendly tools to run AI/ML workloads. But there needs to be more
compatibility among AI/ML tool capabilities and user interfaces among
different providers that make it difficult to achieve interoperability in a
federation of clouds (Chouhan et al., 2020; Rosa et al., 2021; Saxena et al.,
2021). While specific Earth system model (ESM) data are presently stored on
cloud storage systems (Xu et al., 2019), the data stores are associated with a
patchwork of individual groups and projects, lacking a federated view. Cloud
providers can presently accommodate petabytes to exabytes of data for data
storage. The commercial cloud cost is based on accessing and computing or
analyzing the data. It can become prohibitively expensive if data transmission
in to/out of the Cloud becomes frequent. Commercial AI/ML cloud infrastructure
and services are predominately motivated by text and image data. Cloud
providers have demonstrated AI-at-Scale for these applications. For example,
the most significant AI-based Natural Language Processing (NLP) models
approaching 1 trillion parameters have been demonstrated on Selene (Chen et
al., 2019) (the 9th fastest supercomputing system on the November 2022 Top 500
list). Workflow services exist on the Cloud for specific applications,
including many AI/ML methods, and raw materials are available on cloud
platforms to create more complex workflows. However, ESM workflows that
combine external data sources or coordinate with HPC simulations efficiently
and accurately currently do not exist. Computer science expertise is required
to create such workflows in a form suitable for domain scientists (Chen et
al., 2017; Bauer et al., 2021).

###  2.3 Edge Computing

Recently, AI methods for classifying patterns, anomaly detection, unsupervised
learning for data compression, inference at the edge, and continuous learning
with streaming sensor data have gained considerable traction in the ESM
community (Beckman et al., 2020; Talsma et al., 2022). This advancement was
possible because of the rapid forward deployment of AI models on intelligent
computing devices such as Raspberry Pi/Shake, Nvidia Jetson Nano, Google Coral
Dev Board, and Intel Neural Compute Stick connected to sensors. (Catlett et
al., 2017, 2020; Mudunuru et al., 2021). The integration of edge computing
with smart sensors (e.g., AI@SensorEdge) has many distinct deployment
scenarios, including National Oceanic and Atmospheric Administration (NOAA)
and National Aeronautics and Space Administration (NASA) earth-observing
satellite imagery with edge processing in space or at dedicated ground
stations to control DOE’s Atmospheric Radiation Measurement (ARM) or
Environmental Molecular Science Laboratory (EMSL) user facility instruments
(Beckman et al., 2020). We can also integrate edge computing with the diverse
collection of distributed sensors that collect observations and measurements
for the DOE’s ARM user facility. Adaptive sensors with embedded hardware
accelerators are now emerging (e.g., Waggle, PurpleAir) (Beckman et al., 2016;
Stavroulas et al., 2020; Barkjohn et al., 2021). New concepts for distributed
applications are also under development, such as geomorphic computing, where
weather research and forecasting models are distributed, federated, and able
to adapt dynamically to the environment (Daepp et al., 2022).

##  3 Future System Concepts

In this section, we describe several plausible future systems concepts that
participants in the breakout room focus groups discussed in the AI4ESP
workshop. The focus was on the evolution of DOE’s Leadership Computing
Facility (LCF) systems for HPC and AI. These large-scale heterogeneous
computing systems provide a foundation for advancing AI architectures and co-
design using HPC. Moreover, these future concepts have the potential to
provide a radically different approach to future earth system modeling and AI-
enabled ModEx.

###  3.1 Centralized Large-scale HPC Concept

The baseline system concept is the future evolution of large-scale HPC and
cloud computing systems. This next step will extend post-exascale
architectures beyond the first generation of DOE’s heterogeneous systems
integrating CPUs and GPUs. As the HPC and Cloud computing communities
increasingly rely on hardware specialization to improve performance, co-design
approaches will support the development of accelerators (Lie, 2021; Reuther et
al., 2021; Cortés et al., 2021) for frequently used kernels in scientific
modeling and AI/ML methods. New specialized accelerators may arise to support
additional data science capabilities such as uncertainty quantification,
streaming analytics, or graph analysis (Halappanavar et al., 2021; Acer et
al., 2021). These future large-scale computing systems with extreme
heterogeneity must be co-designed to support the increased computational and
dataset sizes associated with earth science predictability and scientific
machine reasoning (Yang et al., 2016; Zhang et al., 2020; Yu et al., 2022).

###  3.2 Edge sensors with Centralized HPC/Cloud Resources Concept

In the second system concept, environmental data are recorded from a broad
collection of point (Christensen and Blanco Chia, 2017; Winter et al., 2021)
and distributed sensors (e.g., fiber optics) (Lindsey et al., 2019) spread
across the globe. These advanced sensors are designed to monitor specific
items of interest (e.g., river flow, nutrients, temperature, chemical
concentration, light) and to communicate these data back to a centralized
location (Beckman et al., 2020). At this centralized facility, large HPC or
cloud computing environments will process the incoming data streams for
integration into online simulations of extreme weather events, climate,
hydrology, and their impacts on earth systems.

We could utilize AI/ML capabilities within this system concept at multiple
points. First, the velocity of sensor data coming into the system will
potentially overrun even the most significant data processing centers’
capabilities. Hence, such a volume of data is unlikely to be able to be stored
in memory or even temporary storage resources (such as file systems or object
stores). Advanced AI/ML models could be trained and tailored to summarize or
select relevant features from the incoming data streams. Such an encoding or
feature selection process will significantly reduce the amount of data that
needs to be kept and integrated into ongoing simulations. Another potential is
for AI/ML models to identify anomalies or precursors Yuan et al. (2019) from
the incoming data streams that might suggest areas of interest for simulations
to be focused on – for instance, the start of a hurricane or the high
likelihood of significant rain-on-snow events or wildfires.

Due to the distributed nature and inhospitable environments (e.g., remote
locations, extreme temperatures, or pressures) where sensors may need to be
placed or roam, it is unlikely that a reliable data stream will reach the
centralized location for all possible inputs. One common use case is the
intelligent city scenario to study urban science. Figure 1 is a notional
depiction of various deployed sensors, computing, and data storage
capabilities (Zhu et al., 2021). AI/ML models could be used in such an
environment to fill measurement gaps and present a more consistent view of
observational data to a future simulation run on a large-compute resource.

Figure 1: A smart city scenario with a large number of sites for fixed sensor
deployments that measure temperature, wind profile, $\mathrm{CO}_{2}$
concentration, precipitation, etc., plus a variety of mobile devices that can
also be used to augment the collection of measurement and observation data
intermittently. An urban setting will support advanced wireless communications
like 5G and eventually 6G to understand the interactions between cities and
climate. [Figure developed by Advanced Wireless Communications lab at PNNL]

###  3.3 Federated Processing from the Edge to the Data Center Concept

The third potential system design extends the second concept by leveraging
much more processing in or near the distributed sensor network. We can process
the sensor data directly on the sensor itself or in a nearby edge server
(e.g., fog computing) with processing elements that may stream a small
collection of sensor data into it (Stevens et al., 2020, Chapter-15). Local
processing stations can then send their raw or locally processed data to a
centralized HPC and/or cloud resource for inclusion in simulation models and
centralized AI/ML models as in the first system concept.

The advantage of this approach is that data down-selection and feature
extraction can be performed locally, significantly reducing the volume of data
that must be transmitted to a centralized resource. Assuming that a
sufficiently performant local network among sensors can be established,
process model parameters and partial results, perhaps even AI/ML model
updates, can be exchanged within a locale, allowing for a genuinely federated
design aspect. Initially, this concept takes advantage of existing gateways
and local area networks serving sensors in the field. Through co-design
collaborations, it is possible to expand that service to include
application/sensor-specific processing to filter, analyze, compress, encrypt,
and unify multiple sensor streams transmitting measurements through the
wireless network.

###  3.4 Dynamic and Adaptive Federated Processing Concept

The last system concept builds on the previous three by augmenting feedback
and control paths within distributed networks of sensor-local resources (Di
Lorenzo et al., 2021; Charles et al., 2021). Local control offers lower
latency decision-making to dynamically control what information is observed,
measured, recorded, and relayed by the sensor network (Morell and Alba, 2022).
Such a design has powerful implications – By dynamically controlling sensors
online, simulations of the earth’s weather and climate can essentially focus
sensor inputs on specific quantities or geographic locations of interest.
Examples might include where severe weather events are expected or whether
climate scientists identify where specific information is needed to help
improve the quality of their models. This concept expands to multiple HPC
and/or Cloud data centers for federated AI/ML modeling. AI/ML models can play
a crucial part in this system by performing continuous, autonomous online
inspection of evolving simulations or recorded data to identify areas of data
insufficiency or statistical weakness. Furthermore, a dynamic and adaptive
system may be able to carefully obtain and select data to improve the quality
of its training, reducing the need for vast, potentially intractable datasets
to be collected over long periods (Catlett et al., 2017).

##  4 Grand Challenges

The system concepts that integrate federated processing are beyond the
capabilities of affordable technologies today. It will require significant
investment both in foundational technology systems and co-design programs.
Such synergy between climate scientists, mathematicians, AI/ML experts,
computer scientists, and hardware engineers is needed to balance the competing
performance, energy, cost, and security challenges associated with AI-enabled
ModEx. The following subsections describe technical challenges that will arise
in the areas: (1) programmability and usability, (2) data movement, (3) energy
efficiency, and (4) privacy and security of data.

###  4.1 Programmability and Usability

The current and near-term challenge is integrating scientific modeling and
simulation applications with AI/ML methods. This drives the need to integrate
earth system HPC applications written in C/C++ and/or Fortran with AI/ML
methods that use Python-based ML frameworks (Ott et al., 2020). Programming
models are under development to support the convergence of applications and
workflows onto heterogeneous computing systems. Many AI/ML architectures
provide hardware support for reduced or mixed precision, and tools will be
required to analyze which specific model components can use these
capabilities. We must create protocols and tools for ESP data-sharing and data
federation on the cloud. The usability challenge is managing the complexity of
mapping converged application workloads to future heterogeneous computing
architectures that integrate specialized hardware accelerators with commodity
CPU/GPU/TPU processors.

Domain scientists are interested in exploring the capabilities of new
heterogeneous advanced architecture computing systems. Interfacing with
sensors and AI analytics at the Edge will allow domain scientists to extract
actionable information needed for improved modeling of disturbances and
extreme events. This type of co-design is needed for most ESP applications.
For example, watershed science, hydrology, ecohydrology, climate variability
and extremes, aerosols and clouds, and atmospheric modeling are cross-cutting
themes where AISensorEdge has the highest impact. Co-design approaches that
interface with distributed sensor networks will allow us to (1) collect
reliable and relevant watershed data under disturbances, (2) monitor land-
atmosphere-coastal interactions by embedding intelligence on the Atmospheric
Radiation Measurement (ARM) instruments, (3) understand wildfire events and
their impact on ecosystems in near-real-time, and (4) assess critical
infrastructure impacted by extreme events (e.g., see Human Systems and
Dynamics, chapter 9 in AI4ESP report).

Still, there are challenges in understanding how to map AI4ESP workflows to
the diverse collection of computing system options. Understanding how AI/ML
capabilities originally developed for generic commercial workloads may or may
not be applicable for Earth System Predictability (ESP) hybrid modeling
applications or observation and measurement capabilities is essential. From
centralized large-scale modeling and training to edge computing inferencing
and federated learning, new challenges arise for the composition and
distribution of applications, algorithms, and methods. This is an important
opportunity for the AI4ESP community to develop a new generation of proxy
applications and benchmarks for modeling and observation capabilities. For
example, AI-enabled co-design will enable us to emulate and deploy DOE codes
such as PFLOTRAN, ATS, and E3SM at the sensor edge for empowering ARM
instruments and EMSL user facilities. The focus should be facilitating
communication and co-design collaborations with hardware designers, system
software developers, algorithm developers, and domain scientists.

###  4.2 Data Movement

The expected volume of data associated with a complete, coordinated earth
sensor capability will be unprecedented. Not only will such a network generate
a previously unimaginable quantity and diversity of data, but the computing
and network load for processing, transmitting, and subsequent storage of this
volume will be orders of magnitude higher than any system available today.
Data movement costs in terms of energy and latency motivate the interest in
the federation and distribution of computing across the AI4ESP scientific
ecosystem. AI/ML technologies could help reduce such volumes by identifying
patterns and anomalies and summarizing sub-volume. We will require significant
investment in AI/ML approaches to ensure that the modeling capabilities will
be compatible and efficient for the types of data being recorded, especially
where this may deviate from commercial photo or video capabilities.
Technologies that may assist in energy-efficient data transfers include
investment in silicon photonic network capabilities and wide-area 5G- or
6G-like communication networks that enable sensors to communicate over
short/medium distances without needing physical wiring (Beckman et al., 2020).
On the storage side, cloud technologies such as high-performance, large-volume
data object stores could likely provide a capability to address increased
sparse data storage volumes. However, this would pose a significant cost
barrier using current commercial cloud pricing. We may also use AI/ML to
enable innovative compression techniques on earth system data to increase
information density without increasing storage costs. Additionally, DOE HPC
centers could incorporate concepts and methods from cloud storage systems into
future parallel file and storage systems to slowly move toward such
capability.

###  4.3 Energy Efficiency

Large-scale networks with integrated sensors, federated processing, and wide-
area communication networks to handle data transmissions will likely be very
expensive in energy consumption. While this was a lower-priority focus for
exascale computing, data processing and communication remain power-expensive.
Co-design has the potential to help improve this situation through the use of
novel materials, devices, and processing techniques (e.g., neuromorphic-based
accelerators to analyze images/video). However, significant investment will
still be required in foundational technologies if large-scale, power-efficient
sensing networks are to be realized. Co-design to balance performance and
energy efficiency will also address how the modeling, machine learning,
uncertainty quantification, and other streaming analytics capabilities are
partitioned across the ESM scientific ecosystem. Such a co-design that
integrates DOE’s heterogeneous HPC systems with cloud computing, edge servers,
and sensors with IoT devices will transform the ModEx loop.

###  4.4 Privacy and Security of Data

As earth systems modeling becomes increasingly integrated with a distributed
network of observations and perhaps federated processing capabilities. The
information’s quality, accuracy, and robustness through such a sensor network
will become more critical. It must also be secured if the information
generated from modeling and measurement capabilities is used to support high-
consequence national or international scientific policy decisions. The
implications of potential data tampering or nefarious modification are clear,
as a national or international resource for accurate scientific prediction
could be severely affected. Data privacy concerns are particularly valid in a
data acquisition system where individual human subject images or videos may be
captured, or their behavior discerned from the data. An example includes
sensor capabilities that could identify patterns in human systems data (e.g.,
in citizen science or urban environments). Co-design has a potential role in
this space – by including security experts in cyber-physical designs from the
outset, secure data transmission and processing can be integrated as a first-
level citizen rather than as a last, software-derived additional layer. In
addition, data privacy may be afforded if local artifacts associated with
specific individuals can be aggregated into a larger, federated model with
individual patterns obfuscated or redacted into the complete model of the
system.

##  5 Synergy with other AI4ESP Workshop Sessions

In this section, we provide visionary perspectives for future ideas and
potential research in synergy with other workshop sessions. Table 1 summarizes
this synergy with short- ($<5$ years), medium- (5-year), and long-term
(10-year) goals. The focus is on how AI architectures and co-design approaches
are related to the integrative water cycle and associated water cycle
extremes.

Table 1: This table provides short-, medium-, and long-term goals needed to overcome the grand challenges discussed in Section 4. Gradual progress on these specific goals will allow us to advance on the future system concepts needed for improving earth system predictability. Short-term goals | Medium-term goals | Long-term goals | Co-design opportunities
---|---|---|---
Benchmark datasets | Data formats for federated learning | Improve efficiency across ESP domains | Anomaly analysis for extreme events
Distributed AI/ML workflows | AI/ML for UQ | AI-at-scale demonstration | AI for down- and up-scaling
AI/ML surrogates | AI/ML + physics simulators | AI for streaming analytics | AI/ML + IoT + Exascale ecosystem
AI/ML abstractions for edge | AI@SensorEdge | AI-enabled automation | Digital Twin for ESP

Atmospheric modeling – Need for advancing the modeling of subgrid physics
across scales and guiding or automating process model calibration. This
includes (1) co-design approaches for parameterization and knowledge transfer
across scales and (2) AI infrastructure for datasets, software, testing,
validation, and training workflows for efficient model calibration.

Land modeling – AI architectures for efficient transfer of information between
land and atmospheric models. This includes (1) subgrid parameterizations to
capture the full complexity within a grid, (2) capturing heterogeneity
utilizing LCFs, and (3) addressing observational gaps using advanced AI
architectures (e.g., transformers).

Hydrology – Advanced AI architectures are needed for parameter estimation,
down-scaling, and imputation to improve data products. Model-data co-design
approaches are needed to identify how many and what types of observations are
required to reach a desired process model performance without actual
measurements being available. This includes 5G or other high-speed networking
or software pipelines that can accelerate the transfer of information between
field instrumentation and process models for near real-time sampling
decisions.

Watershed science – Co-design approaches are needed to understand better (1)
the quality of collected data, (2) the predictability of a watershed’s
response (e.g., the evolution of microbial activity) under disturbances and
long-term perturbations using process-based models (e.g., PFLOTRAN), (3) when,
how, and where to collect data (e.g., wildfires, flooding, drought events),
and (4) how to deal with large data volumes.

Ecohydrology – Advanced AI architectures are needed for developing new data
products and benchmark datasets across spatial scales from microbial and leaf
scales to watershed and continental scales. Novel co-design approaches that
build and collect labeled earth science data needed for process models and
open-sourcing them to the BER community would facilitate rapid testing of
existing AI/ML methods.

Aerosols and clouds – Co-design approaches that can extract valuable
information or identify indicator patterns of forced changes and emergent
properties of the actual and simulated climate system are essential. Future
system concepts that can develop databases for indicator patterns (e.g.,
nucleation of ice or particles, snow formation) and emergent properties
provide a path toward knowledge discovery and reveal missing mechanisms that
must be incorporated in process models.

Coastal dynamics, oceans, and ice – Advanced AI architectures that can improve
(1) the standardization and merging of disparate datasets, (2) scale-awareness
and dependency in process models (e.g., capturing coastal, ocean, and
cryosphere processes across scales and from sparse datasets).

Climate variability and extremes – Co-design approaches for climate
variability, signal identification, and sources of predictability are
essential. These include AI architectures to detect signatures and features
corresponding to tropical cyclones, fronts, atmospheric rivers, hailstones,
tornadoes, and ice storms.

Human systems and dynamics – Co-design approaches that can provide a better
understanding of human and earth systems. For example, advancements in AI
architectures are needed to gain better insights into urban prediction and
long-term urban policy due to extreme events.

##  6 Conclusions

In this perspective paper, we have described the need for co-design approaches
for efficient and accurate integration of process models and observations for
improved earth system predictability. Current state-of-science and HPC
facilities provide a starting point to address the grand challenges of the
‘Model-Experimentation’ loop. Future system concepts that connect the edge
sensors to intelligent computing devices and, subsequently, the process models
that reside in fog/cloud/exascale infrastructure are needed to transform the
ModEx lifecycle. Our near-term to long-term goals allows us to develop AI
architectures and co-design approaches using future system concepts. Community
integration and effort between domain and computational experts allow us to
transform how we model the integrative and associated water cycle extremes.

## Nomenclature

  * •

AI4ESP: The Artificial Intelligence for Earth System Predictability

  * •

AI: Artificial Intelligence

  * •

ALCF: Argonne Leadership Computing Facility

  * •

ARM: Atmospheric Radiation Measurement Climate Research Facility

  * •

ASCR: Advanced Scientific Computing Research

  * •

ATS: Advanced Terrestrial Simulator

  * •

AWS: Amazon Web Services

  * •

E3SM: Energy Exascale Earth System Model

  * •

ESM: Earth System Model

  * •

ESP: Earth System Predictability

  * •

EMSL: Environmental Molecular Sciences Laboratory

  * •

BER: Biological and Environmental Research

  * •

CPU: Central Processing Unit

  * •

DOE: Department of Energy

  * •

GCP: Google Cloud Platform

  * •

GPU: Graphics Processing Unit

  * •

HPC: High-Performance Computing

  * •

IoT: Internet of Things

  * •

LCF: Leadership Computing Facility

  * •

ModEx: Model-Experimentation

  * •

ML: Machine Learning

  * •

NASA: National Aeronautics and Space Administration

  * •

NERSC: National Energy Research Scientific Computing Center

  * •

NLP: Natural Language Processing

  * •

NOAA: National Oceanic and Atmospheric Administration

  * •

OLCF: Oak Ridge Leadership Computing Facility

  * •

TPU: Tensor Processing Unit

  * •

UQ: Uncertainty Quantification

###### Acknowledgements.

The authors acknowledge all the efforts made as part of the Artificial
Intelligence for Earth System Predictability (AI4ESP) workshop. MKM
acknowledges the support from the Environmental Molecular Sciences Laboratory,
a DOE Office of Science User Facility sponsored by the Biological and
Environmental Research program under Contract No. DE-AC05-76RL01830. PJ’s
research was supported as part of the Energy Exascale Earth System Model
(E3SM) project, funded by the U.S. Department of Energy, Office of Science,
and Office of Biological and Environmental Research. SS and MN research was
supported by the Exascale Computing Project (17-SC-20-SC), a collaborative
effort of the U.S. Department of Energy Office of Science and the National
Nuclear Security Administration. MBG’s research was performed under the
auspices of the U.S. Department of Energy by Lawrence Livermore National
Laboratory under Contract DE-AC52-07NA27344. MKM, JAA, and MH acknowledge the
contributions of Johnathan Cree and Elena Peterson at PNNL’s Advanced Wireless
Communications Lab, who developed the figure in this paper. This manuscript
has been authored by Pacific Northwest National Laboratory (PNNL), operated by
Battelle Memorial Institute for the U.S. Department of Energy under Contract
No. DE-AC05-76RL01830. This manuscript has been authored by Oak Ridge National
Laboratory, operated by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725
with the U.S. Department of Energy. The US government retains and the
publisher, by accepting the article for publication, acknowledges that the US
government retains a nonexclusive, paid-up, irrevocable, worldwide license to
publish or reproduce the published form of this manuscript or allow others to
do so, for US government purposes. DOE will provide public access to these
results of federally sponsored research in accordance with the DOE Public
Access Plan. There is no data developed in this paper

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