# Automatic detection of large-scale flux ropes and their geoeffectiveness
with a machine learning approach

Sanchita Pal  NASA Postdoctoral Program Fellow, NASA Goddard Space Flight
Center, Greenbelt, MD 20771, USA  Luiz F. G. dos Santos  SETI Institute,
Mountain View, CA 94043, USA  Andreas J. Weiss  NASA Postdoctoral Program
Fellow, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Thomas
Narock  Center for Natural, Computer, and Data Sciences, Goucher College,
Baltimore, MD, United States  Ayris Narock  ADNET Systems Inc., 7515 Mission
Drive, Lanham, MD 20706, USA  Heliophysics Science Division, NASA Goddard
Space Flight Center, Greenbelt, MD 20771, USA  Teresa Nieves-Chinchilla
Heliophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA  Lan K. Jian  Heliophysics Science Division, NASA Goddard Space
Flight Center, Greenbelt, MD 20771, USA  Simon W. Good  Department of Physics,
University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland

###### Abstract

Detecting large-scale flux ropes (FRs) embedded in interplanetary coronal mass
ejections (ICMEs) and assessing their geoeffectiveness are essential since
they can drive severe space weather. At 1 au, these FRs have an average
duration of 1 day. Their most common magnetic features are large, smoothly
rotating magnetic fields. Their manual detection has become a relatively
common practice over decades, although visual detection can be time-consuming
and subject to observer bias. Our study proposes a pipeline that utilizes two
supervised binary-classification machine learning (ML) models trained with
solar wind magnetic properties to automatically detect large-scale FRs and
additionally determine their geoeffectiveness. The first model is used to
generate a list of auto-detected FRs. Using the properties of southward
magnetic field the second model determines the geoeffectiveness of FRs. Our
method identifies 88.6% and 80% large-scale ICMEs (duration $\geq 1$ day)
observed at 1 au by Wind and Sun Earth Connection Coronal and Heliospheric
Investigation (STEREO) mission, respectively. While testing with a continuous
solar wind data obtained from Wind, our pipeline detected 56 of the 64 large-
scale ICMEs during 2008 - 2014 period (recall= 0.875) but many false positives
(precision= 0.56) as we do not take into account any additional solar wind
properties than the magnetic properties. We found an accuracy of 0.88 when
estimating the geoeffectiveness of the auto-detected FRs using our method.
Thus, in space weather now-casting and forecasting at L1 or any planetary
missions, our pipeline can be utilized to offer a first-order detection of
large-scale FRs and geoeffectiveness.

Sun: coronal mass ejection, flux rope, space weather, geomagnetic storm,
magnetic field

##  1 Introduction

Magnetic flux ropes (FRs) are fundamental solar and heliospheric structures
that are formed by twisted bundles of magnetic field lines. They can originate
at the Sun or in the heliosphere. They are commonly associated with coronal
mass ejections (CMEs; Crooker et al., 1997; Webb & Howard, 2012), streamer
blow-outs (SBOs; Vourlidas & Webb, 2018; Nitta et al., 2021), small transients
(STs; Kilpua et al., 2009; Yu et al., 2014, 2016) in solar wind, local small-
scale magnetic flux rope structures near the heliospheric current sheet (HCS)
(Moldwin et al., 1995, 2000) and magnetospheric flux transfer events (FTEs;
Sun et al., 2020).

The large-scale FRs of interplanetary counterparts of CMEs (ICMEs) may have a
significant contribution of flux from coronal reconnection (Qiu et al., 2007;
Gopalswamy et al., 2017; Pal et al., 2017, 2018; Pal, 2022) and thus may
transport large quantities of solar mass, magnetic flux and helicity away from
the Sun. Frequently these FRs are called magnetic clouds (MCs; Burlaga et al.,
1981) which have an enhanced magnetic field strength, a smooth and coherent
rotation in magnetic field lines (e.g. Burlaga et al., 1981; Klein & Burlaga,
1982), declining velocity (e.g. Klein & Burlaga, 1982; Russell & Shinde,
2003), low proton temperature and low proton $\beta$ (the ratio between proton
thermal pressure and magnetic pressure) characteristics (e.g. Richardson &
Cane, 1995). At 1 au, ICME FRs have an average radial dimension of $\sim$0.25
au (Klein & Burlaga, 1982). A duration of approximately 1 day, corresponds to
a characteristics dimension $\sim$0.25 au (Klein & Burlaga, 1982; Kahler &
Webb, 2007; Lugaz et al., 2009). However, studies like Richardson & Cane
(2004) show that there may be a lack of MCs in ICMEs observed at different
heliocentric distances and different phases of the solar cycle. It may be
possible that all ICMEs contain a well-defined flux rope close to their
origin, but as ICMEs evolve on their way out from the Sun, their flux rope
signatures may weaken (Crooker et al., 1997). Alternatively, ICMEs may always
contain identifiable FRs but, when they are traversed far from their central
FR axis, their FRs cannot be detected (e.g. Jian et al., 2006). Jian et al.
(2006) and Nieves-Chinchilla et al. (2018) adopted a less restrictive term
called magnetic obstacles (MOs) to address the magnetic structure inside
ICMEs. The MOs are described as periods inside ICMEs having low proton $\beta$
where in some cases, the magnetic field lines display smooth and monotonic
rotations.

Apart from ICME FRs, small transients (STs) that may last from a few tens of
minutes to a few hours are one of the important sources of FRs in the
heliosphere. They are components of slow solar wind and may originate from the
cusps of coronal streamers (Sheeley et al., 1997, 2008; Wang et al., 2000). Yu
et al. (2014, 2016) have explained the ST characteristics in details. They
differ from ICME FRs in a number of ways, including their duration (0.5–12
hours), the absence of a speed differential with respect to the slow
background solar wind, and the lack of a discernible amplification of the
heavy ion charge state within them. Some of the STs may have the geometry of
small-scale flux ropes (SFRs) that are local structures mostly observed near
HCS and are generated due to magnetic reconnection and a turbulence cascade
(Cartwright & Moldwin, 2008, 2010). Although SFRs show the typical magnetic
configuration of FRs (i.e., smooth rotation) they may have proton $\beta$ less
than or greater than 1.

Decades of studies have been conducted to explore how solar magnetic fields
affect the geospace environment through the solar wind and solar storms (Nandy
et al., 2023). The major solar storms including ICMEs may shape the near-Earth
heliospheric environment in a way that may trigger the most extreme forms of
space weather at Earth. Even a moderate type geomagnetic storm is capable to
adversely affect assets in geospace environment (Baruah et al., 2024). It is
challenging to predict their impact on the Earth as they may continuously
evolve in the heliosphere while propagating (Manchester et al., 2017; Luhmann
et al., 2020; Pal et al., 2022, 2023). Their geo-effectiveness and capability
to trigger magnetic storms have societal impacts, which cannot be disregarded
in modern society. With high proton number density, increased proton speed and
magnetic field component $B_{z}$ anti-parallel to the geomagnetic field, ICMEs
impact the magnetosphere and also allow solar energetic particles to drift in
the magnetosphere. A simplified explanation of ICME - magnetosphere
interaction (Dungey, 1961) states that if an ICME $B_{z}$ is directed opposite
to the Earth’s field, magnetic reconnection takes place at the day-side
magnetosphere, and reconnected magnetic flux accumulates in the night side
magnetotail region. Thus, the magnetic reconnection at the magnetotail leads
to solar plasma injection toward the Earth on the night side. This results in
the formation of aurora and a ring current around the Earth, which causes a
reduction in the geomagnetic field measured by the disturbance storm time
(Dst) index.

The ICME speed $V$ and its southward magnetic field component $-B_{z}$ are of
the most importance in creating geomagnetic storms (Fairfield & Cahill, 1966;
Cane et al., 2000; Wu & Lepping, 2002). Certainly, a sufficiently long
duration ($\delta t$) of $-B_{z}$ is also necessary (Wang et al., 2003). The
product of the average value of $\overline{-VB_{z}}$ and $\delta t$ defines
the magnetic flux transferred from the interplanetary medium into the
magnetosphere. Wang et al. (2003) performed a statistical study of the
relationship between $\overline{-VB_{z}}$, $\delta t$ and $Dst_{min}$ that
revealed the importance of $\overline{-VB_{z}}$ and its duration $\delta t$
for generating geomagnetic storms. The study found an empirical formula
$Dst_{min}=-19.01-8.43(\overline{-VB_{z}})^{1.09}(\delta t)^{0.3}$ that
indicates a more prominent contribution of large $\overline{-VB_{z}}$ over
$\delta t$ to create a strong geomagnetic storm. They found a high anti-
correlation with correlation coefficient (CC) of $-0.95$ between
($\overline{-VB_{z}})^{1.09}(\delta t)^{0.3}$ and $Dst_{min}$, whereas, a
comparatively weak linear correlation with CC of $-0.7$ was found between
($\overline{-VB_{z}})(\delta t$) and $Dst_{min}$. This suggests a non-linear
relation between $Dst_{min}$ and $\delta t$, whereas $Dst_{min}$ and
$\overline{-VB_{z}}$ have an almost linear relationship.

Visual inspection of the solar wind magnetic field and plasma environment via
spacecraft data to identify ICMEs is widely practiced though it is quite time-
consuming, ambiguous, subjective, and biased by the observer’s interpretations
(Shinde & Russell, 2003). Some studies have begun to introduce the use of
supervised machine learning (ML) algorithms that have the potential to learn
the properties of labeled events by themselves. Their use in space physics is
progressing since they can tackle a large and ever-growing database
accumulated over decades. In solar physics, ML-based techniques have recently
bloomed as a very attractive way of using our computing resources to extract
conclusions from solar data (Asensio Ramos et al., 2023).

Nguyen et al. (2019) proposed a pipeline that used a Convolutional Neural
Network (CNN) trained with 33 solar wind magnetic and plasma parameters
obtained and derived from in situ spacecraft to automatically detect the start
and end times of ICMEs in in-situ data. Their method found 84% of the listed
ICMEs collected from different existing catalogs where ICMEs are manually
detected using Wind spacecraft data during 2010–2015. Out of 158 ICMEs found
during the period using their pipeline, 25 ($\sim$16%) events were false
positives. dos Santos et al. (2020) implemented a tool based on handwriting
recognition models that uses a deep CNN to classify subsets of the ICMEs
introduced in Nieves-Chinchilla et al. (2019). The weights of their model were
trained with synthetic data obtained from a well-established physical flux
rope model. They simulated the noise of synthetic training data using data
points belonging to a normal distribution with standard deviations including
0.05 and 0.1. Their methodology classified 76% of 321 real cases (identified
manually by Nieves-Chinchilla et al. (2019) using Wind spacecraft data)
correctly during 1995–2015. Narock et al. (2022) attempted to predict the
orientation of heliospheric magnetic flux ropes once they are identified in
in-situ solar wind data using a model based on CNN architecture. Rüdisser et
al. (2022) converted the ICME detection problem to a time series segmentation
problem and proposed a pipeline for automatic detection of ICMEs using a
variation of an advanced U-Net (Ronneberger et al., 2015) method that has
recently proven successful in medical image segmentation. Using their method,
73% of the cataloged events observed by the Wind spacecraft during 1997-2015
were detected correctly. They found a total number of 254 ($\sim$40%) events
as false positives during that period. A comparable method was proposed by
Chen et al. (2022) that uses the residual U-net architecture and automatically
detected 77% of ICMEs during the period 1997 October 1 to 2016 January 1
collected by the Wind spacecraft. Based on Grad-Shafranov reconstruction
technique, several studies have developed automated SFR detection algorithms
(Hu et al., 2018), and applied them to the spacecraft data at different
heliocentric distances (Chen et al., 2019; Chen & Hu, 2020, 2022). Using ML-
based classification algorithm Farooki et al. (2024) compared SFRs, MCs, and
ambient solar wind plasma properties.

A recent study by Nair et al. (2023) summarises the results obtained from an
open data-science challenge called “MagNet: Model the Geomagnetic Field” to
Predict Dst from solar wind Data. The challenge attracted 1,197 model
submissions that used various ML approaches and predicted Dst in a real-time
modeling environment. Hu et al. (2023) developed a 6-hour ahead Dst prediction
model from solar wind observations using Gated Recurrent Unit networks. They
used several solar wind parameters like proton density, velocity, magnetic
field intensity, magnetic field vector in the z-direction, clock, and dipole
tilt angle of the magnetic field, and Dst index and boosted the performance of
the model by developing a multi-fidelity method. Xu et al. (2020) used an
ensemble-learning algorithm that combines the artificial neural network,
support vector regression, and long short-term memory network to predict the
Dst index 1–6 hr in advance. They used solar wind’s total magnetic field,
$B_{z}$, total electric field, solar wind speed, plasma temperature, and
proton pressure as inputs. Chandorkar et al. (2017) provided a method to
generate a probabilistic prediction of Dst using a Gaussian method approach.
Gruet et al. (2018) constructed the Dst index prediction model by combining
the long short-term memory (LSTM) network with the Gaussian process approach.
To forecast the Dst index during 80 intense geomagnetic storms ($Dst_{min}\leq
100$ nT) during 1995 - 2014, Lu et al. (2016) applied a support vector machine
(SVM) and combined that with a distance correlation technique. They utilized
13 observed and derived plasma and magnetic parameters of the solar wind as
inputs. Pricopi et al. (2022) developed binary classification models to
predict the geoeffectiveness of CMEs, i.e. whether a CME is associated with a
geomagnetic storm having $Dst_{min}\leq 30$ nT or not. They used supervised ML
models like logistic regression, k-nearest neighbors, SVM, feed-forward
artificial neural networks, and ensemble models trained on white-light
coronagraph data sets of CMEs close to the Sun. They achieved an adequate hit
rate with these models. Choi et al. (2012) found a better performance of SVM
than the performance of simple classification based on constant classifiers,
when they used SVM for the prediction of geoeffective CMEs. The SVM algorithm
is proven to be efficient in a wide range of solar and space physics research,
such as flare classification (e.g. Qahwaji & Colak, 2007; Sinha et al., 2022),
ICME arrival time prediction (e.g. Liu et al., 2018), Dst index prediction
(e.g. Lu et al., 2016), and sunspot occurrence prediction (e.g. Rodríguez et
al., 2022).

Previous studies reveal an impressive performance of ML-based methods in the
field of automatic ICME detection and their geoeffectiveness prediction.
Integrating automatic detection of both space weather driving events and their
geoeffectiveness in a single pipeline is an efficient way for quickly
assessing the real-time space weather and issuing alert. In this study, we
present a pipeline that automatically detects large-scale ICME associated FRs
from continuous spacecraft measurements at 1 au and additionally indicates
their geoeffectiveness – whether they are minor to intensely geoeffective
($Dst_{min}\leq-50$ nT) or not. For the FR detection process, the pipeline
uses CNN architecture trained with more realistic synthetic FR and non-flux
rope (NFR) magnetic fields prepared using a physics-based FR model combined
with power spectral densities of magnetic field fluctuations in FRs and NFRs
derived from spacecraft data. For indicating the geoeffectiveness of the
automatically detected FRs, our pipeline uses another supervised binary
classifier trained with geoeffective magnetic parameters of real events.

In Section 2, we present our proposed pipeline and describe our methodology of
pre-processing the dataset, training the models, and post-processing
techniques. Section 3 discusses the results and Section 4 summarises and
concludes the article.

##  2  Description of pipeline

We combine a supervised ML model ‘M1’ with our current understanding of ICME
FR and non flux rope (NFR) solar wind segments and integrate this to another
supervised ML model ‘M2’ to first detect the ICME FR intervals from solar wind
data and then their geoeffectiveness. This work utilizes only the magnetic
properties rather than other solar wind properties like composition and
plasma. This is because in the future, we plan to make this pipeline usable in
classification of real-time solar wind being observed by various planetary
missions. Unlike magnetic field data, plasma and composition data are
generally not available in real-time with reliable quality from planetary
missions.

In the pipeline, the first model ‘M1’ is an image classification model that
uses CNN architecture. It is trained on synthetic large-scale FRs and NFRs
prepared by combining a well-established physical flux rope model and a
sophisticated additive background solar wind profile model based on the power
spectrum density (PSD) of solar wind magnetic field corresponding to real ICME
FRs and NFRs. We refer to the model as DeepFRi – Deep convolutional neural
network FR identification)”. The second model that detects the
geoeffectiveness of FRs is named as DicFR – Disturbance storm time (Dst) index
classification of identified FRs. Note that the DicFR model aims to classify
auto-identified FRs based on their geoeffectiveness, i.e. whether they are
moderate to intensely geoeffective or not. It doesn’t intend to predict the
Dst index value (e.g. Hu et al., 2022). In the upper panel of Figure 1, using
a flowchart we show the operations that we perform in this work to auto-
identify FRs and their geoeffectiveness from solar wind data. As a final
result, the pipeline generates a list that contains auto-identified FR start
and end times, and their geoeffectiveness categories. Below we describe the
pre-processing of data, the models, and the post-processing steps including
boundary determination of auto-identified FRs and listing them with their
predicted geoeffectiveness categories.

Figure 1: Upper panel- (a) A flowchart of our pipeline that shows the
processes followed to convert raw data from the Wind spacecraft to a list of
auto-detected FRs and their geoeffectiveness categories. The input and the
final output of the flowchart are shown in yellow boxes. The models used are
shown in grey boxes. The dashed boxes enclose the pre-processing and post-
processing steps. As an example, (b) a 3-day interval Wind magnetic field
vector data is shown on the right side where the intervals between black and
green vertical lines indicate two consecutive windows ($W_{42}$ and $W_{43}$)
of 24 hours duration, respectively. The corresponding merged hodogram is shown
at (c). Lower panel- schematic of M1 model architecture. The gray squares
represent output of each layers. (d) Schematic of the CNN architecture used
for M1 model. The squares represent the output of each layer. The architecture
consists of three sets of convolutional and max-pooling layers using ReLU
activation, followed by two fully connected layers with ReLU and sigmoid as
the activation functions, respectively.

###  2.1 Data Pre-processing

As our first model DeepFRi is intended to classify solar wind into FRs and
NFRs based on their magnetic characteristics, we use only processed and
calibrated Magnetic Field Investigation (MFI Lepping et al., 1995) instrument
data at 1 min resolution during 1995 - 2021 from the Wind spacecraft. The
Wind/MFI instrument-measured solar wind magnetic field data in Geocentric
Solar Ecliptic (GSE) coordinate system ($x_{gse},y_{gse},z_{gse}$). We first
window the MFI data in 24-hour intervals having $24\times 60$ data points and
check for the data gaps. If there are data gaps within the window and the gaps
cover no more than 10% of the window size the window is still considered as an
acceptable input. The size of the window is chosen to be 24 hours because we
focus here only to detect ICME-associated large-scale FRs and in general, at 1
au, the average ICME FRs are of $\sim$24-hour duration (Klein & Burlaga, 1982;
Bothmer & Schwenn, 1998). To verify this, we consider 695 manually identified
ICME FRs obtained from Wind ICME catalog (Nieves-Chinchilla et al., 2018) and
STEREO ICME catalog (Jian et al., 2018) which are observed by both Wind and
the Solar TErrestrial RElations Observatory (STEREO; Kaiser et al., 2008)
spacecraft, respectively at 1 au and find their mean duration as 24.3 hours.
Next, we sample each window into $npoint$, where each point corresponds to
$\sim 5$-min average of solar wind magnetic field data. After down-sampling
the window, we normalize each magnetic field component with the solar wind
magnetic field intensity in that window. Next, the normalized magnetic field
components of the down-sampled window are plotted in three different planes
$x_{gse}-y_{gse}$, $y_{gse}-z_{gse}$ and $z_{gse}-x_{gse}$, where each of them
is in the -1 to 1 range and of pixel size (Width) 54 $\times$ (Height) 54.
These are called magnetic field hodograms. After generating three different
hodogram images, we merge them into a single image of pixel size (Width) 162
$\times$ (Height) 54. Thus, each window corresponds to a merged hodogram
acceptable for our M1 model input.

If we consider a time interval ($T_{dur}$) starting at $t_{s}$ hours and
ending at $t_{e}$ hours, we divide the interval in $n$ number of windows –
$W_{0},W_{1},...W_{n-1}$, where $n$ is an integer with a unit of hours. Thus,
$T_{dur}$ (in hours) can be expressed as,

$\begin{split}T_{dur}=\sum_{n=0}^{(t_{e}-t_{s})+24h}W_{n},\\\
W_{n}=\int_{t_{s}-24h+n}^{t_{s}+n}dt.\end{split}$ (1)

Here, dt is in hour.

As an example, in Figure 1, we show a magnetic vector time series ($T_{dur}$).
Inside $T_{dur}$, two windows – $W_{n}$ and $W_{n+1}$ (n = 42) of 24 hours
duration are the intervals between the pairs of black and green vertical
lines. A merged hodogram corresponding to $W_{42}$ is also shown which can be
directly used as input to M1.

For the second model M2 that is intended to classify the geoeffectiveness, we
extract the geoeffective magnetic properties from Wind/MFI time series of the
auto-detected FR intervals in Geocentric Solar Magnetospheric system (GSM).
The model is trained using FR geoeffective properties and the minimum value of
$Dst$ index during the FR intervals obtained from OMNIWeb database. The
geoeffective magnetic characteristics that we consider for this case are the
minimum value of the magnetic field component in the $-z_{\mathrm{gsm}}$
direction ($-B_{z_{\mathrm{gsm}},min}$) and the duration of
$-B_{z\mathrm{gsm}}$ with respect to the whole $B_{z\mathrm{gsm}}$ duration in
a window. The second feature is named $R_{Bz}$. To obtain this, we consider
only the hodogram in the $y_{\mathrm{gsm}}-z_{\mathrm{gsm}}$ plane and find
the ratio of the number of points in a plane formed by
$y_{\mathrm{gsm}}-(-z_{\mathrm{gsm}})$ and the total number of points in the
whole $y_{\mathrm{gsm}}-z_{\mathrm{gsm}}$ plane. Thus, once we obtain an
automated catalog of FRs from model M1, we process each identified FR to
obtain $-B_{z_{\mathrm{gsm}},min}$ and $R_{Bz}$ and provide them as input to
the M2 model that is trained to classify FRs as geoeffective or non-
geoeffective.

###  2.2 Models

In this Section, we describe model architectures, the method of training the
models and their evaluations.

####  2.2.1 Model architectures

The model M1 uses a binary classification CNN architecture that is based on
handwriting recognition models. A CNN is a deep learning architecture
consisting of interconnected nodes or neurons having learnable filters
constructing layers, whose objectives are to detect features and patterns
present in a data set. Thus, a certain number of layers process information in
a way similar to the human brain (LeCun et al., 2015; Goodfellow et al.,
2016). In each layer, filters are convolved along the input data, and using a
nonlinear activation function the layer indicates the presence (or absence) of
the requested pattern. A complete description of the principles of CNN can be
found in Géron (2017).

The architecture of M1 shown in the lower panel of Figure 1 is quite similar
to that of the model used by dos Santos et al. (2020) which implemented a
binary class handwritten digit-recognition model (Cireşan et al., 2011). The
input to our model are merged hodograms of size 162$\times$54 and the output
is a two-element vector that describes the probability of the hodogram being
an FR or NFR. We use three convolution layers with kernel size 3 $\times$ 3,
two of which are followed by max-pooling layers with kernel size 2 $\times$
2\. The convolution layer expands the dimension, whereas the max-pooling
layers contract them. Finally, the array is flattened to 256 nodes and the
network completes with two fully connected layers. These last layers take the
dimensions from 256 inputs to 64 outputs, then 64 inputs to 2 outputs. All the
convolution layers and the first fully connected layer use a Rectified Linear
Units (ReLU; Nair & Hinton, 2010)) activation whereas the final layer uses a
sigmoid activation function. The model and training are implemented with
Tensorflow (Abadi et al., 2016) version 2.10.0 in a Python 3.10.8 environment.
Once the model is constructed, it is trained using realistic simulated FR and
NFR hodograms. The preparation of the synthetic hodograms is described in the
next section.

The type of geoeffectiveness of a given FR is detected by M2. To classify the
FR geoeffectiveness we consider the Dst index, which is an index of magnetic
activity derived from a network of near-equatorial geomagnetic observatories
that measures the decrease in the horizontal component of the Earth’s field
due to the ring current (Daglis, 2001). We choose the Dst index threshold as
$-50$ nT to include moderate to intense storms (Gonzalez et al., 1994), in
which the contribution of ICME FRs is prominent. We classify the events having
$Dst_{min}<-50$ nT and $Dst_{min}>-50$ nT as ‘1’ and ‘0’, respectively. The M2
is a supervised binary-classifier machine learning model. We choose support
vector machine (SVM) classifier – a widely applied ML approach in solar and
heliospheric physics and was first proposed by Cortes & Vapnik (1995). A
general architecture of SVM model can be found in Álvarez-Alvarado et al.
(2021). SVMs can identify both linear and nonlinear relationships between
features by using linear and nonlinear kernels that can map these features
into a higher dimensional space and thus SVMs may potentially explore
previously unknown properties in the data. From previous studies (e.g., Wang
et al. (2003); Kane (2005)) it is well known that the duration of southward
solar wind magnetic field component has a nonlinear relationship with the
$Dst_{min}$, whereas the product of solar wind velocity and the minimum value
of southward magnetic field intensity has a linear relationship with the
$Dst_{min}$ (Gonzalez & Echer, 2005; Gopalswamy, 2008). Here, we use both
linear and nonlinear kernels in M2.

####  2.2.2 Preparation of training dataset

As the number of observed and cataloged events is not enough to train a neural
network, in this work we generate several synthetic ICME FRs
($\mathbf{B_{FR}}(t)$) and NFRs ($\mathbf{B_{NFR}}(t)$) to train the model M1.
The $\mathbf{B_{FR}}(t)$ is generated combining a physics-based FR model –
namely the circular-cylindrical (CC; Nieves-Chinchilla et al., 2016) model
output $\mathbf{B_{m}}(t)$, with additive background noise
$\delta\mathbf{B_{FR}}(t)$. Here, $\mathbf{B_{m}}(t)$ consists of the time
series of each magnetic field component – $B_{mx}(t),B_{my}(t),B_{mz}(t)$
obtained in the GSE coordinate system assuming several different spacecraft
trajectories through the modeled CC flux ropes. The CC model provides a
conventional smooth rotation in the FR magnetic field, while the additive
noise $\delta B_{FR}(t)$ provides the type of fluctuations that are observed
in real FRs. Our generation process for synthetic FR data is inspired by dos
Santos et al. (2020) who used a modeled FR with additive Gaussian noise set
called “5% noise” and “10% noise”, where the noise values were drawn from
normal distributions having standard deviations of 0.05 and 0.1, respectively.
The study did not implement physics-based fluctuations to their synthetic
data. In our study, the background noise is modeled using the PSD of solar
wind magnetic field fluctuations at inertial-range frequencies
($10^{-3}-10^{-2}$ Hz). This frequency range corresponds to the spatial scales
of magnetohydrodynamic turbulence. Typically, in this frequency range,
magnetic field fluctuation power is higher in the solar wind than within FRs.
This trend can be seen, for example, in the upstream wind and ICME FR of an
event observed by Parker Solar Probe (PSP; Fox et al., 2016) at 0.25 au (Good
et al., 2020). In Figure 2a, we show the magnetic field components along with
the magnitude of an ICME FR and its upstream and downstream solar wind
conditions observed by Wind at 1 au. In Figure 2b, we show the wavelet PSD of
the magnetic field fluctuations sampled at inertial range frequencies. The
vertical lines show the boundaries of the FR.

Figure 2: (a) Magnetic vector components ($B_{x}$, $B_{y}$, $B_{z}$) in GSE
and magnetic field intensity ($|B|$) of solar wind containing an identifiable
ICME FR bounded by vertical lines. (b) The wavelet PSD of $\mathbf{B}$ field
fluctuations sampled at inertial range frequencies. (c) $P_{x}$, $P_{y}$,
$P_{z}$ are the PSDs of $B_{x}$, $B_{y}$, $B_{z}$ field line fluctuations,
respectively, where the field lines are normalized by maximum magnetic field
intensity and belong to the ICME FR (blue), and non-FR segments (green and
orange) before and after the ICME in 24-hours interval, respectively.

We use 399 ICME events from the Wind ICME catalog during 1995–2021 to obtain
the PSD of real ICME FRs and NFRs required to generate synthetic events. This
catalog refers to the ICME FRs as magnetic obstacles (MOs) and notes their
start and end boundaries as ‘MO start time’ and ‘MO/ICME end time’,
respectively. The MOs having a sheath (a pile-up of solar wind commonly
observed ahead of ICME FRs) are listed such that the sheath start time is
listed as the ‘ICME start time’. The catalog also lists the minimum Dst value
$Dst_{min}$ during each event and mean magnetic field intensity. We decided
not to merge other catalog events to the Wind ICME catalog because the
criteria to select event boundaries are not exactly similar for all available
catalogs.

#### Generation of synthetic flux ropes

Synthetic ICME FRs are generated by considering the local configuration of FRs
as cylindrical structures with circular cross-sections. The model does not
impose any condition on the internal force distribution but makes assumptions
about the axial and poloidal current density components. In this work, we keep
the ratio between the poloidal and axial current density components as $C1$ =
1, which implies that the structure can behave as force-free structure (see
Nieves-Chinchilla et al. (2016) for more details). We generate several
different unique FR magnetic field time series by varying the model inputs –

  * •

$\theta$ (the angle between the FR axis and ecliptic plane,
-80${}^{\circ}\leq\theta\leq 80^{\circ}$) and $\phi$ (an angle formed by FR
axis and $+x_{gse}$, 5${}^{\circ}\leq\phi\leq 355^{\circ}$) are chosen from
equi-distributed points on surface of a sphere with polar angle $\theta$ and
azimuthal angle $\phi$ (Deserno, 2004).

  * •

$Y_{0}$ (the perpendicular distance between the spacecraft trajectory and FR
center normalized to the FR radius) from 0 to 0.75 from either side of the FR
center in steps of 0.05, and

  * •

$H$ (handedness of the FR) either -1 or 1.

This results in 161,000 simulated FR magnetic field vectors
($\mathbf{B_{m}}(t)$) normalized to the magnetic field intensity.

To obtain the additive background profile $\delta B_{FR}(t)$ for generating
realistic simulated FRs, we followed Weiss et al. (2021, 2022) that generated
random and unique noise-field time series with PSD $P_{fr}(k)$ similar to the
PSD of real FR magnetic fields. This method is inspired by an analogous
process used to generate primordial perturbations for dark matter N-body
simulations (Hahn & Abel, 2011). The $\delta\mathbf{B_{FR}}(t)$ is expressed
as

$\mathbf{\delta B_{FR}}(t)=\mathcal{F}^{-1}(\sqrt{P_{\mathrm{fr}}(k)}u(k)),$
(2)

where $u(t)$ is a random Gaussian sequence with mean 0 and standard deviation
1 and its Fourier transform $u(k)=\mathcal{F}(u(t))$. As Gaussian noise has a
flat power spectrum, multiplying it in Fourier space with $\sqrt{(}P_{fr}(k))$
and transforming back to real space (time domain) provides a noisy sequence
$\delta\mathbf{B_{FR}}(t)$ with PSD the same as $P_{fr}(k)$. We compute
$P_{fr}(k)$ for each magnetic field component (normalized to magnetic field
intensity) by applying Welch’s algorithm (Welch, 1967) on the real event
intervals. By averaging several periodograms of overlapping segments that are
shorter than the total length of the data, this approach averages out the
noise in the data. The real event intervals are gathered from the Wind ICME
catalog. We use the ‘Welch’ function available in the ‘signal’ library of the
‘SciPy’ package in Python, where $nperseg=2^{8}$ is considered for the length
of each overlapping segment at which the modified periodogram is computed.
Before applying Welch’s method, we detrended the normalized magnetic
components with three different detrending time intervals $\Delta T$ – [10,
30, 60] minutes. The detrending of signals helps remove any kind of pattern at
the detrending timescale in the data. In Figure 2c, we show $P_{fr}(k)$ as a
function of spacecraft-frame frequency for the ICME FR shown in 2a, with the
PSD for each of the three FR magnetic field components in blue. The $\Delta T$
used to create $P_{fr}(k)$ in this case is 30 min. Therefore, the y-axis
ranges from $\sim 5\times 10^{-4}-10^{-2}$. The inertial-range spectral slope
in the FR is found as $\sim-1.6$. The spectral index in the inertial range
found in this case is consistent with various theories of Alfvénic MHD
turbulence (Schekochihin, 2022).

Using the Wind ICME catalog, we generate 399 PSDs of real FR events, randomly
pick a PSD to generate a unique $\delta B_{FR}(t)$ and add it to each
component of $\mathbf{B_{m}}(t)$ to finally obtain a synthetic FR magnetic
field $\mathbf{B_{FR}}(t)$, where

$\mathbf{B_{FR}}(t)=\mathbf{B_{m}}(t)+\delta\mathbf{B_{FR}}(t)$ (3)

Note that here each of the $\mathbf{B_{FR}}(t)$ has $npoint$ number of points
in it. Thus, we simulate a total number of 161,000 unique synthetic large-
scale FR magnetic field time series with each having underlying PSDs equal to
one of the real events. As this work focuses on the geometry of magnetic
structures rather than the magnitude, we plotted each $\mathbf{B_{FR}}(t)$ in
three different planes $x_{gse}-y_{gse}$, $y_{gse}-z_{gse}$ and
$z_{gse}-x_{gse}$ in the -1 to 1 range and generated three different images of
resolution 54 $\times$ 54, where each of them are called hodograms. Finally,
the hodograms of three different planes are merged into a single image of size
(Width) 162 $\times$ (Height) 54. In Figure 3a and b we show a simulated FR
time series and hodogram, respectively, where the orange curves on Figure 3a
represents $\mathbf{B_{m}}(t)$. The CC model inputs $\theta$, $\phi$, $Y_{0}$
and $H$ and the detrending factor $\Delta T$ for generating this particular
synthetic FR is used as $60$ deg, $32$ deg, 0.65, $1$ and 30 min,
respectively.

Figure 3: (a) Example of a simulated FR time series $\mathbf{B_{FR}}$ and (b)
hodogram in $x_{gse}-y_{gse}$, $y_{gse}-z_{gse}$ and $z_{gse}-x_{gse}$ planes.
The light-orange line over-plotted on (a) represents the $\mathbf{B_{m}}$
signal. (c) Example of a simulated NFR time series $\mathbf{B_{NFR}}$ and its
(d) hodogram in three different planes. The magnetic field vectors are
normalized with intensity $|B|$.

#### Generation of synthetic non-flux ropes

Since we do not anticipate any typical rotation in NFRs, we only include the
process of generating the solar wind background profile
$\delta\mathbf{B_{NFR}}(t)$ to create synthetic NFRs. To create
$\delta\mathbf{B_{NFR}}(t)$ we compute PSDs of the normalized magnetic field
components of real NFRs, $P_{nfr}(k)$. From the Wind/MFI data, we randomly
selected 2200 real unique NFR intervals having durations of 24 hours. A
24-hour duration for the NFRs was selected because this is equal to the
average ICME duration at 1 au. Each of the NFRs starts at least 2 hours after
the ‘ICME/MO end time’ and ends at least 2 hours before ‘MO start time’
mentioned in Wind ICME catalog. Additionally, we obtain 303 sheath intervals
from theWind ICME catalog which are bounded by ‘ICME start time’ and ‘MO start
time’. Thus we generate a total number of 2503 $P_{nfr}(k)$s, each of them
corresponding to a real NFR that does not have any overlap with ICME MOs
cataloged in the Wind ICME catalog. In Figure 2c, we show with green and
orange lines $P_{nfr}(k)$ as a function of spacecraft-frame frequency for the
three different magnetic field components of two 24-hour NFR segments ahead of
and after the ICME FR shown in Figure 2a. The spectral slope is found to be
$\sim-1.8$ for both upstream and downstream NFR segments. The $\Delta T$ used
to create $P_{nfr}(k)$ in this case, is 30 min. As no rotation in the NFRs’
magnetic field components is expected, we generate the NFRs using Equation 2,
where $P_{fr}$ is replaced by $P_{nfr}$. Thus,

$\mathbf{B_{NFR}}(t)=\delta\mathbf{B_{NFR}}(t)=\mathcal{F}^{-1}(\sqrt{P_{\mathrm{nfr}}(k)}u(k)).$
(4)

Once we generate a similar number of synthetic NFR time series as FRs, we
obtain their hodograms in each plane and merge them into a single image of
similar size as the synthetic FR hodograms. In Figure 3c and d, we show an
example synthetic NFR time series and hodograms, respectively, where the
$\Delta T$ for generating this particular synthetic NFR is used as 30 min.
Finally, we generate nine sets of synthetic FR and NFR data, where each data
set is prepared using a unique combination of $\Delta T$ values for both FRs
and NFRs.

####  2.2.3 Model training and evaluation

Once we prepare the synthetic data set, we randomly select 30% of the training
data for validation. To train the network weights, we use the Adam optimizer
(Kingma & Ba, 2014) with an initial learning rate of 0.001. We find that the
accuracy and loss converge quickly for the validation set and infer that this
may happen due to the simplicity of the classification problem in the
simulation space. To avoid over-fitting we limit the training of the network
to 50 epochs. Thus, we train nine M1 models of similar architecture using nine
different sets of synthetic data. Using a system with a 10-core CPU processor
and 16 GB RAM, we finish training each model in 58 minutes. After training
each, we save their weights, evaluate each model with real cases, and derive
the evaluation metrics. Finally, out of nine trained M1 models, we choose a
model that provides the highest Area Under the Curve (AUC) value measuring the
area under the ‘Receiver Operating Characteristic’ (ROC) curve and designate
this M1 as the DeepFRi model.

For evaluating the performance of M1 models, we obtain 127 real ICME FRs
having duration between 20-30 hours from Wind ICME catalog and an equal number
of non-ICME windows of 24 hours randomly chosen from Wind/MFI data. We use
these events to evaluate the M1 models and derive evaluation metrics –
accuracy, precision, recall, F1 Score and AUC for each M1. These are the
standard metrics for evaluating machine learning models. They are described
using four terms, namely true positives (TP: cases where the predicted and
original classification agree on being positive (i.e. FR)), true negatives
(TN: cases where the predicted and original classification agree on being
negative (i.e. NFR)), false positive (FP: if the prediction is positive (i.e.
FR) but the ground truth is negative (i.e. NFR)), and false negative (FN: if
the classification is negative (i.e. NFR) and the ground truth is positive
(i.e. FR)). In Table 1, column 1, we describe the evaluation metrics.

Figure 4: (a) The Area Under the Curve (AUC) values of nine M1 models with
similar architecture trained with nine different combinations of simulated FR
and NFR data. The detrending factors used to generate the simulated training
data are 10, 30, and 60 mins. The maximum AUC value achieved as 0.87. (b) The
ROC (green) and precision-recall (blue) curves corresponding to the M1 having
maximum AUC accepted as the final model named DeepFRi. (c) Color map showing
cross-validation scores obtained for different values of the hyperparameters
$C$ [1-100.7] and $\gamma$ [10${}^{-1}-1$] of the RBF kernel of SVM model in
M2.

In Figure 4a, we display the AUC values of nine M1 models with circles of
varying shades of red colour. We notice that training the same model
architecture with different data sets prepared using different detrending
factors leads to varying AUC values. The maximum obtained AUC is 0.87. In
Figure 4b, we show the ROC (in green) and precision-recall (in blue) curves of
one of the highest performing models named as DeepFRi trained with a set of
synthetic FRs and NFRs, whose underlying PSDs are prepared using the linear
detrending scales of $\Delta T=10$ and $60$ minutes, respectively. The green
and blue circles over-plotted to the curves corresponds to the decision
threshold. The evaluation scores including accuracy, precision, recall and F1
Score of the DeepFRi, are indicated in Column 3 of Table 1.

Table 1: Evaluation metrics of the DeepFRi and DicFR models.  Performance Metrics |  Description |  DeepFRi performance | DicFR performance
---|---|---|---
Accuracy |  $\frac{TP+TN}{Total\ number\ instances}$ | 0.8 | 0.83
Precision |  $\frac{TP}{TP+FP}$ | 0.78 | 0.85
Recall |  $\frac{TP}{TP+FN}$ | 0.82 | 0.76
F1-Score |  $\frac{2*Precision*Recall}{Precision+Recall}$ | 0.8 | 0.805

To train M2, we randomly select 75% of ICMEs listed in the Wind ICME catalog.
We use the Python scikit-learn library to implement SVM in M2. SVM has been
integrated into the Python scikit-learn library (Pedregosa et al., 2011). It
has open-source access and a well-established documentation http://scikit-
learn.org/stable/. We use the stratified k-fold cross-validation method with
k=5. It is implemented in the cross-validation module of the scikit-learn
library. The non-linear radial basis function (RBF) kernel of SVM has two
hyper-parameters – ($`C^{\prime}$ and $\gamma$) that need to be tuned to
achieve the highest model performance. The $C$ is a regularization parameter
that trades off correct classification versus maximizing the margin of the
decision function. A low $C$ value corresponds to a large margin and simple
decision function and a high $C$ value leads to overfitting. The $\gamma$ is a
kernel width parameter that affects the shape of the class-dividing
hyperplane. While using the RBF kernel, we preliminary set the range of $C$
and $\gamma$ as [$10^{-2},10^{2}$] (Pricopi et al., 2022) and tune the
parameters in that range to obtain the highest cross-validation score. Based
on the performance, we further shrink the range of $C$ to [$10^{0},10^{0.7}$]
and $\gamma$ to [$10^{-1},10^{0}$] and find the best-performing model with the
highest cross-validation score of 0.77 at $C$ = 4.428, $\gamma$ = 0.543, and
random state = 42. In Figure 4c, we provide a color-map showing the variation
of cross-validation scores with different values of $C$ and $\gamma$. While
using the linear kernel of SVM in M2, we find the cross-validation score to be
0.75. We compare our model performance with that of the K-nearest neighbor
(KNN; Mucherino et al., 2009; Taunk et al., 2019) classifier. The KNN follows
a similarity-based algorithm where the label of an event is assigned based on
that of the majority of $K$ most similar examples. Here similarity is
expressed in terms of the generalized concept of distance. The maximum cross-
validation score achieved in the case of the KNN classifier is 0.75 with
$K=12$. Therefore, we choose M2 with the SVM architecture and with a tuned RBF
kernel to use as the DicFR model.

To evaluate the performance of DicFR, we use the remaining 25% cases from Wind
ICME catalog. In Column 4 of Table 1, we provide the evaluation scores of the
DicFR model.

###  2.3 Post-processing

The DeepFRi model classifies each input window as FRs or NFRs and assigns them
a binary value $V_{W}=1$ or 0, respectively. We first convert the hodograms to
time-series data. Through a few post-processing steps, we derive a list of
large-scale FR intervals containing the category of their geoeffectiveness.
Below we describe the post-processing steps.

Step 1: First we note the start time of each window that is predicted as
$V_{W}=1$, by the model. If two consecutive windows (e.g. $W_{1}$ and $W_{2}$)
with $V_{W}=1$ have start times are more than 24 hours apart, we record both
the windows’ end time and start time as corresponding to the previous FR’s end
and the next FR’s start boundaries, respectively. Thus we check whether the
same condition holds for the next two consecutive windows ($W_{3}$ and
$W_{4}$), and so on. If the condition is not satisfied, we continue examining
the rest of the window start times until the requirement is satisfied.
Following this process, we generate a list (List 1′) where each row contains a
start and end time of an interval and each data points inside the intervals
belong to windows with $V_{W}=1$.

Step 2: In the next step, we compute the cumulative sum $V_{cumsum}$ of
$V_{W}$ values of the windows within each interval in List 1′. Note that each
interval may contain a single or multiple number of windows. Intervals
containing multiple windows can have $V_{cumsum}$ values varying over time.
Once we derive the $V_{cumsum}$ for each interval, we obtain its full width at
half maximum (FWHM) duration and define it as an auto-detected FR interval.
These intervals are noted in List 1. In Figure 5a, we show an interval
containing solar wind magnetic field vectors which have been used as input to
our model. The red-shaded rectangles indicate the times when $V_{W}=1$. Using
a black dashed curve, we show $V_{cumsum}$. We note the start and end times of
the FR interval as $t^{s}_{DeepFRi}$ and $t^{e}_{DeepFRi}$ in black vertical
lines, respectively. The cyan vertical lines show the FR boundaries noted in
the Wind ICME catalog.

Step 3: Finally, we use a magnetic field magnitude threshold $B_{Th}$ and
check whether each interval’s mean magnetic field intensity $B_{mean}$ crosses
$B_{Th}$. To obtain $B_{Th}$, we derive the cumulative distribution function
($F(X)=P[X\leq x]$), where X is the $B_{mean}$ of real events from Wind ICME
catalog with duration 24 hours or more. We assign $B_{Th}$ such as $P(X\geq
B_{Th})=0.9$. Once the auto-detected FR intervals satisfy the threshold
criteria, they are put in the list List 2.

Step 4: We derive the geoeffective properties of the FR intervals required to
provide input to the DicFR model. The DicFR model classifies the intervals as
class 1 (geoeffective) or class 0 (non-geoeffective) and a Final List is
created that contains $t^{s}_{DeepFRi}$, $t^{e}_{DeepFRi}$ and FR
geoeffectiveness category (class 0 or 1).

Figure 5: (a) A solar wind magnetic field interval during 2013/01/16 12:00 -
2013/01/19 12:00 UT. Each red-shaded rectangle has duration of 24 hours and
$V_{W}=1$. The black dashed line indicates $V_{cumsum}$. The black vertical
lines mark the $t^{s}_{DeepFRi}$ and $t^{e}_{DeepFRi}$ interval. The cyan
vertical lines show boundaries of the event obtained from the Wind ICME
catalog. (b) Sensitivity of the DeepFRi model as a function of ICME FR
duration. The purple, black and green colored lines correspond to the ICMEs
observed by Wind, STEREO and PSP spacecraft, respectively. The recall values
belonging to the gray-shaded regions are $\geq 0.8$. (c) A 30-day interval of
solar wind magnetic field vectors where the blue shaded regions indicate auto-
detected geoeffective FR intervals. The solid vertical lines indicate FR start
and end times obtained from RL.

##  3 Results and Discussion

We now assess the performance of our pipeline by comparing its output to the
existing manually detected open-source ICME lists. For this purpose, we use
the list of ICME events observed by STEREO A and B during 2007–2020 available
at STEREO ICME catalog and the reference list (RL) used by Nguyen et al.
(2019). The RL is a union of different Wind ICME lists obtained from Jian et
al. (2006); Lepping et al. (2006); Richardson & Cane (2010); Chi et al. (2016)
and Nieves-Chinchilla et al. (2018) and compiled by Nguyen et al. (2019)
available at https://github.com/gautiernguyen/Automatic-detection-of-ICMEs-
at-1-AU-a-deep-learning-approach and a recently created list of ICMEs observed
by PSP during 2018 - 2022 (Salman et al., 2024). For this purpose, we use
magnetic field data derived from the In-Situ Measurements of Particles and CME
Transients (IMPACT; Luhmann et al., 2008) instrument onboard STEREO twin
spaceceraft and Fields (FIELDS; Bale et al., 2016) investigation of PSP. It is
important to note that any existing ICME FR catalogs are likely not exhaustive
and the event start and end times are based on the interpretation of data by
human expertise. We first checked how our model identifies the listed events
in the catalogs. We then chose a seven-year interval (2008–2014) of continuous
Wind/MFI data, prepared the Final List, compared that with the open-source
lists, and obtained the recall and precision values for both models in the
pipeline. In Figure 5b, we show the sensitivity of DeepFRi as a function of
duration of ICME FRs obtained from different spacecraft. In the left panel, we
show how the model’s recall value changes while testing it on real events with
duration ranging from $\sim$5-90 hours observed at 1 au. The gray-shaded
region corresponds to recall $\geq 0.8$. The high recall values in the shaded
region indicate the better performance of DeepFRi while testing it with large-
scale FRs. We notice that the recall becomes 0.886 while testing the model
with events having $\geq$ 24 hours interval obtained from RL list. However, we
observe that even if we used 24-hour window in training purpose, our model
identified 75% of the ICME FRs observed by Wind having duration $\geq$15
hours.

We provided 2008-2014 Wind/MFI data to our pipeline. The data is first pre-
processed and provided to the DeepFRi model following the steps described in
Section 2.1. The DeepFRi model classified 639 windows as class 1, where each
window lasts $\sim$24 hours and two consecutive window start times are minimum
1 hour apart. By following Step 1 – Step 3 described in Section 2.3 we
generated a List 1 with 296 FRs and List 2 with 110 FR intervals having mean
intensity greater than $B_{Th}$. In Figure 5c, we show a small 30-day subset
of the whole interval 2008 - 2014. The blue-shaded regions show the intervals
identified by our pipeline as geoeffective FRs presented in the Final List.
The vertical solid lines are FR boundaries noted in RL.

We compared our auto-generated FR lists to the RL events and obtained the
number of TPs, FPs, TNs, and FNs. We derived model precision and recall
following the process described in Table 1. Out of 64 events with duration
$\geq 24$ hours obtained from RL during 2008-2014, we found 56 events that are
detected by our pipeline and presented in List 1. We computed the recall as
0.875. while comparing List 2 to the RL events, we find the recall as 0.8 and
precision as 0.56. The high number of FPs suggests that the DeepFRi model
identifies a number of rotations in solar wind magnetic field that may not
correspond to ICME FRs. Including additional solar wind features e.g.
temperature, proton $\beta$, velocity etc in detection process may help
reducing the FPs.

In Figure 6a and b we summarise the result that we found while applying the
DeepFRi model to detect ICME FRs during the 2008 - 2014 time period. The blue
bars in Figure 6a indicate the number of FRs detected by DeepFRi each year.
The over-plotted gold bars show the number of events that belong to the RL and
are also detected by our DeepFRi model. The number of events listed in RL for
each year between 2008 and 2014 with duration more than or equal to 24 hours
is displayed in Figure 6b by the orange bars. Black bars are superimposed on
the orange ones to display the events listed in RL detected by DeepFRi.

Nguyen et al. (2019) used 33 different magnetic field and plasma parameters
directly measured and derived from in situ observations to automatically
detect ICME FRs using a CNN architecture. During 2010 – 2015, using Wind
spacecraft data, they obtained a maximum recall of 0.84 and average precision
of 0.697. When they considered only the magnetic field magnitude and component
data, they found an average precision of 0.593 that is similar to what we
obtain. Using Deep Residual U-Net model and training with the same 33 FR
parameters used by Nguyen et al. (2019), a study by Rüdisser et al. (2022)
found the recall and precision to be $0.67$ and $0.7$, respectively. Our
pipeline finds the start of an ICME present in the Wind ICME catalog with a
mean absolute error (MAE) of $\sim 7$ hours, and the end time with an MAE of
$\sim 6$ hours. In both Nguyen et al. (2019) and Rüdisser et al. (2022), the
MAE values for the ICME start and end are less than that of our result because
while training, they used a more sophisticated set of features and multiple
sliding window sizes. Moreover, they optimized the decision threshold such
that their model can determine the ICME intervals with high precision.

With careful manual observation of solar wind plasma and magnetic data, Salman
et al. (2024) identified ICMEs observed by PSP during 2018 - 2022 at
heliocentric distances in the range of 0.23 - 0.83 au. We notice that the
DeepFRi model can detect more than 80% of listed PSP ICMEs when their duration
is $\geq$ 18 hours. In the right panel of Figure 5b, we show the change of
recall values while the model performance is tested on PSP events whose
duration ranges from $\sim$6-48 hours. Note that the number of FNs increases
because we train our model using 24 hours magnetic field data window and the
PSD of fluctuations at 1 au. Good et al. (2023) studied the turbulence
properties of ICMEs in the inner heliosphere and found that with increasing
heliocentric distance the power of magnetic field fluctuation decreases. Using
PSP, Chen et al. (2020) showed the variation of solar wind magnetic field PSD
at different heliocentric distances. They found a significant radial evolution
of the power of magnetic field fluctuations and the inertial range spectral
slope of magnetic field PSDs. Therefore, for achieving better results at
distances less than 1 au using our model, the preparation of the training
dataset should include magnetic field PSDs at those distances.

Now, we compare the geoeffectiveness of auto-detected FRs obtained from the
pipeline and available in the Final List with the real minimum Dst index
during these intervals and RL events. During 2008 - 2014, we found 110 auto-
detected FRs with the boundaries identified by $t^{s}_{DeepFRi}$ and
$t^{e}_{DeepFRi}$ using our pipeline. We derive $R_{Bz}$ and
$-B_{z_{\mathrm{gsm}},min}$ for each interval and provide these as inputs to
the DicFR model. The model provides a binary output that indicates if the
interval contains a $Dst_{min}<-50$ nT or not. Once the geoeffectiveness is
predicted, the Final List is generated following Step 4 described in Section
2.3. In our local system, it took $\sim$30 minutes to generate the Final List
from the 2008 - 2014 interval of raw Wind/MFI data. After comparing with the
geoeffectiveness category obtained from real $Dst_{min}$ values of the auto-
detected FR intervals, we find the accuracy of the model to be 0.88, recall to
be 0.8, precision to be 0.77 and F1-Score to be 0.78. The Final List may
include non-ICME FRs, whereas the DicFR model is trained only on ICME FRs.
Furthermore, certain events might have $R_{Bz}$ and
$-B_{z_{\mathrm{gsm}},min}$ parameter values similar to those of geoeffective
FRs, but their pressure and velocity might not be similar to those of
geoeffective ones. This may lead to the generation of more false positive
events.

In Figure 6c and d we summarise the DicFR model output using histograms. The
green and red bars in the plots indicate the number of DeepFRi-detected FR
intervals classified as non-geoeffective (class 0) and geoeffective (class 1),
respectively. In Figure 6c, the solid and dashed-line bars superimposed on the
red and green bars indicate the number of DeepFRi detected events that are
geoeffective and non-geoeffective in reality, respectively. In Figure 6d, the
black solid and dashed-line bars indicate the number of geoeffective and non-
geoeffective events as identified in the RL. The red and green bars show the
number of events correctly classified by DicFR.

Figure 6: (a) Histogram with blue bars showing the number of events identified
by the DeepFRi model during 2008-2014. The listed number of ICMEs detected by
DeepFRi is shown using gold bars. The false positive events that have
$Dst_{min}<-50$nT are represented by the region between dotted and dashed
lines at the bars of 2011–2014. (b) The number of ICMEs listed in RL each year
between 2008 and 2014 with duration $\geq 24$ hours are shown with orange
bars. The solid line bars represent DeepFRi-identified ICMEs belonging to the
RL. (c) DicFR model-classified (class 1 (red): geoeffective and class 0
(green): non-geoeffective) FRs obtained from DeepFRi each year between
2008-2014. The solid and dashed-line bars represent the real geoeffective and
non-geoeffective classes found from the Dst index available at the OMNIWeb
database. (d) Solid and dashed line bars represent class 1 and class 0 events
listed in the RL. Green and red bars represent DicFR-identified classes of the
events.

##  4 Summary and Conclusion

This work provides a procedure to automatically detect heliospheric large-
scale flux ropes (FRs) in solar wind data obtained from spacecraft at 1 au and
classify their geoeffectiveness. We establish a pipeline that accepts solar
wind magnetic field data from spacecraft and produces a list that contains
auto-detected FR boundaries and information on whether the FR interval can
produce moderate to intense geomagnetic storms or not. To accomplish this
operation, the pipeline uses two models called DeepFRi and DicFR which are
based on two ML techniques – convolutional neural network (CNN) and support
vector machine (SVM), respectively. The DeepFRi model is trained with
simulated FR (positive class) and non-FR (negative class) events prepared by
combining a modeled magnetic topology of FRs and power spectral densities of
the magnetic field fluctuations in the solar wind. The DicFR model is trained
with two geoeffective characteristics – maximum southward magnetic field
intensity and duration of southward magnetic field with respect to the whole
FR intervals. Furthermore, these two models only use solar wind magnetic field
parameters.

The pipeline we propose here introduces a way of automatically now-casting FRs
including their geoeffective characteristics. The pipeline can be used for
space weather operations with further improvements. Currently, the pipeline
uses calibrated and processed magnetic field data. To utilise this in auto-
flagging space weather events in real-time and issuing alert, additional data
pre-processing steps are required. This includes the preparation and
calibration of raw data obtained straight from instruments. We use the
existing knowledge of FRs’ generic structure, its duration, and FR and NFR
magnetic field fluctuations properties at 1 au to train the models in our
pipeline. In this work, we mainly focus on detection of 1-au ICME FRs and
their geoeffectiveness. While applying this pipeline at distances less than 1
au, it under-performs, which reflects the changing FR duration and solar wind
fluctuations with radial distance from the Sun. Therefore, before using this
pipeline at other radial distances, re-training of the models based on the
local FR and NFR properties is required.

The reason for considering only magnetic field information in this work is
mainly the lower availability of continuous solar wind plasma and composition
information from probes at different locations. For example, during the cruise
phase, a planetary mission Juno spent 5 years in the solar wind between 1 -
5.4 au and allowed us to study only the magnetic properties of ICMEs (Davies
et al., 2021) using its Magnetic Field Investigation instrument (MAG;
Connerney et al., 2017). Another planetary mission, BepiColombo (Benkhoff et
al., 2021), which aims to understand Mercury, provides magnetic data but no
solar wind plasma information. Therefore, our framework is capable of
detecting FRs from spacecraft that provide only magnetic data, and also from
Solar Orbiter (Müller et al., 2020) and PSP, even when one or several plasma
measuring instruments malfunction and are unable to provide data coverage. It
can also be applicable to other spacecraft like Cluster, Helios, Ulysses,
Venus Express, etc. that have measured the solar wind magnetic field over the
past two decades throughout the heliosphere. However, training with only the
magnetic field features leaves us with a number of false positive cases. While
our pipeline may be helpful for space weather event identification purposes,
we recommend manually verifying each auto-detected event utilizing its plasma
and composition properties for event-based scientific study. After examining
the false negative events, we have determined that our pipeline is unable to
identify events that are too close to each other to be distinguished
separately, have a short duration, or lack any rotation. However, an ensemble
of training dataset with different windows may lead to success in the
identification of short-duration ICME FRs and thus may decrease the number of
false negative events. In future, we intend to modify the models in our
pipeline to facilitate the identification of short-duration ICMEs.

Due to the lack of a very large FR database, we use synthetic data to train
our model based on the architecture of a handwriting recognition model. For
preparing the training dataset, we utilize a simplistic physics-based FR model
that is unable to provide complicated magnetic configurations of distorted
FRs. That may lead to the misclassification of solar wind data. This means
that creating intricate FR models with more observable features is necessary,
as is incorporating the models to produce better training data. Recently a
study by Nieves-Chinchilla et al. (2023) has established a technique that may
enable the modeling of realistic distortion of FR cross-sections. This work
only aims to classify solar wind in flux rope and non-flux rope segments. To
make our framework more comprehensive, we intend in the future to
automatically classify the detected FRs in different categories based on their
rotation, distortion and more complex structures. This may call for more
advanced and complicated FR models to prepare training dataset.

The performance of the second model, DicFR, which detects the geoeffectiveness
of the DeepFRi-identified FRs in the pipeline, could be improved by including
parameters like solar wind velocity and proton density during the FR interval.
As we focused only on magnetic field information, we decided not to involve
any plasma parameters in this particular study. We employed ICME-related FRs
to train both the DeepFRi and DicFR models since they are more likely to cause
geomagnetic storms than non-ICME ones. Integrating the second model into our
pipeline makes it more favorable to space weather applications. Our tool could
substantially contribute to space weather now-casting and forecasting
processes.

The trained ML model weights, codes that are used to apply the pipeline to the
solar wind data and List 1, List 2 and Final List derived during the test
period 2008 - 2014 are made available in https://github.com/spal4532/DeepFRi-
and-DicFR. Users may download our pipeline in their local system and run on
real 1-au solar wind data to prepare auto-detected FR lists and their
geoeffectiveness.

We acknowledge the data source Goddard Space Flight Center’s Space Physics
Data Facility (SPDF) from where we downloaded the solar wind data and the
open-source catalogs of Wind ICME, STEREO observed ICMEs and reference ICME
list from https://github.com/gautiernguyen/Automatic-detection-of-ICMEs-
at-1-AU-a-deep-learning-approach. S.P and A.J.W are thankful for the support
of NASA Postdoctoral Program fellowship, L.K.J. thanks for the support of the
STEREO mission and Heliophysics Guest Investigator Grant 80NSSC23K0447. T.N-C.
thanks for the support of the Solar Orbiter and Parker Solar Probe missions,
Heliophysics Guest Investigator Grant 80NSSC23K0447 and the GSFC-Heliophysics
Innovation Funds. S.W.G. is supported by the Research Council of Finland
(grants 338486 and 346612).

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