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Mar 14

Learning to Fly -- a Gym Environment with PyBullet Physics for Reinforcement Learning of Multi-agent Quadcopter Control

Robotic simulators are crucial for academic research and education as well as the development of safety-critical applications. Reinforcement learning environments -- simple simulations coupled with a problem specification in the form of a reward function -- are also important to standardize the development (and benchmarking) of learning algorithms. Yet, full-scale simulators typically lack portability and parallelizability. Vice versa, many reinforcement learning environments trade-off realism for high sample throughputs in toy-like problems. While public data sets have greatly benefited deep learning and computer vision, we still lack the software tools to simultaneously develop -- and fairly compare -- control theory and reinforcement learning approaches. In this paper, we propose an open-source OpenAI Gym-like environment for multiple quadcopters based on the Bullet physics engine. Its multi-agent and vision based reinforcement learning interfaces, as well as the support of realistic collisions and aerodynamic effects, make it, to the best of our knowledge, a first of its kind. We demonstrate its use through several examples, either for control (trajectory tracking with PID control, multi-robot flight with downwash, etc.) or reinforcement learning (single and multi-agent stabilization tasks), hoping to inspire future research that combines control theory and machine learning.

Lucy-SKG: Learning to Play Rocket League Efficiently Using Deep Reinforcement Learning

A successful tactic that is followed by the scientific community for advancing AI is to treat games as problems, which has been proven to lead to various breakthroughs. We adapt this strategy in order to study Rocket League, a widely popular but rather under-explored 3D multiplayer video game with a distinct physics engine and complex dynamics that pose a significant challenge in developing efficient and high-performance game-playing agents. In this paper, we present Lucy-SKG, a Reinforcement Learning-based model that learned how to play Rocket League in a sample-efficient manner, outperforming by a notable margin the two highest-ranking bots in this game, namely Necto (2022 bot champion) and its successor Nexto, thus becoming a state-of-the-art agent. Our contributions include: a) the development of a reward analysis and visualization library, b) novel parameterizable reward shape functions that capture the utility of complex reward types via our proposed Kinesthetic Reward Combination (KRC) technique, and c) design of auxiliary neural architectures for training on reward prediction and state representation tasks in an on-policy fashion for enhanced efficiency in learning speed and performance. By performing thorough ablation studies for each component of Lucy-SKG, we showed their independent effectiveness in overall performance. In doing so, we demonstrate the prospects and challenges of using sample-efficient Reinforcement Learning techniques for controlling complex dynamical systems under competitive team-based multiplayer conditions.

The Slepian model based independent interval approximation of persistency and zero-level exceedance distributions

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

DGNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and require large amounts of {\em labeled} training data. We propose the Deep Generative Neural Operator (DGNO), a physics-aware framework that addresses these challenges by leveraging a deep, generative, probabilistic model in combination with a set of lower-dimensional, latent variables that simultaneously encode PDE-inputs and PDE-outputs. This formulation can make use of unlabeled data and significantly improves inverse problem-solving, particularly for discontinuous or discrete-valued input functions. DGNO enforces physics constraints without labeled data by incorporating as virtual observables, weak-form residuals based on compactly supported radial basis functions (CSRBFs). These relax regularity constraints and eliminate higher-order derivatives from the objective function. We also introduce MultiONet, a novel neural operator architecture, which is a more expressive generalization of the popular DeepONet that significantly enhances the approximating power of the proposed model. These innovations make DGNO particularly effective for challenging forward and inverse, PDE-based problems, such as those involving multi-phase media. Numerical experiments demonstrate that DGNO achieves higher accuracy across multiple benchmarks while exhibiting robustness to noise and strong generalization to out-of-distribution cases. Its adaptability, and the ability to handle sparse, noisy data while providing probabilistic estimates, make DGNO a powerful tool for scientific and engineering applications.

Physics-informed cluster analysis and a priori efficiency criterion for the construction of local reduced-order bases

Nonlinear model order reduction has opened the door to parameter optimization and uncertainty quantification in complex physics problems governed by nonlinear equations. In particular, the computational cost of solving these equations can be reduced by means of local reduced-order bases. This article examines the benefits of a physics-informed cluster analysis for the construction of cluster-specific reduced-order bases. We illustrate that the choice of the dissimilarity measure for clustering is fundamental and highly affects the performances of the local reduced-order bases. It is shown that clustering with an angle-based dissimilarity on simulation data efficiently decreases the intra-cluster Kolmogorov N-width. Additionally, an a priori efficiency criterion is introduced to assess the relevance of a ROM-net, a methodology for the reduction of nonlinear physics problems introduced in our previous work in [T. Daniel, F. Casenave, N. Akkari, D. Ryckelynck, Model order reduction assisted by deep neural networks (ROM-net), Advanced Modeling and Simulation in Engineering Sciences 7 (16), 2020]. This criterion also provides engineers with a very practical method for ROM-nets' hyperparameters calibration under constrained computational costs for the training phase. On five different physics problems, our physics-informed clustering strategy significantly outperforms classic strategies for the construction of local reduced-order bases in terms of projection errors.

MaskedMimic: Unified Physics-Based Character Control Through Masked Motion Inpainting

Crafting a single, versatile physics-based controller that can breathe life into interactive characters across a wide spectrum of scenarios represents an exciting frontier in character animation. An ideal controller should support diverse control modalities, such as sparse target keyframes, text instructions, and scene information. While previous works have proposed physically simulated, scene-aware control models, these systems have predominantly focused on developing controllers that each specializes in a narrow set of tasks and control modalities. This work presents MaskedMimic, a novel approach that formulates physics-based character control as a general motion inpainting problem. Our key insight is to train a single unified model to synthesize motions from partial (masked) motion descriptions, such as masked keyframes, objects, text descriptions, or any combination thereof. This is achieved by leveraging motion tracking data and designing a scalable training method that can effectively utilize diverse motion descriptions to produce coherent animations. Through this process, our approach learns a physics-based controller that provides an intuitive control interface without requiring tedious reward engineering for all behaviors of interest. The resulting controller supports a wide range of control modalities and enables seamless transitions between disparate tasks. By unifying character control through motion inpainting, MaskedMimic creates versatile virtual characters. These characters can dynamically adapt to complex scenes and compose diverse motions on demand, enabling more interactive and immersive experiences.

LESnets (Large-Eddy Simulation nets): Physics-informed neural operator for large-eddy simulation of turbulence

Acquisition of large datasets for three-dimensional (3D) partial differential equations are usually very expensive. Physics-informed neural operator (PINO) eliminates the high costs associated with generation of training datasets, and shows great potential in a variety of partial differential equations. In this work, we employ physics-informed neural operator, encoding the large-eddy simulation (LES) equations directly into the neural operator for simulating three-dimensional incompressible turbulent flows. We develop the LESnets (Large-Eddy Simulation nets) by adding large-eddy simulation equations to two different data-driven models, including Fourier neural operator (FNO) and implicit Fourier neural operator (IFNO) without using label data. Notably, by leveraging only PDE constraints to learn the spatio-temporal dynamics problem, LESnets retains the computational efficiency of data-driven approaches while obviating the necessity for data. Meanwhile, using large-eddy simulation equations as PDE constraints makes it possible to efficiently predict complex turbulence at coarse grids. We investigate the performance of the LESnets with two standard three-dimensional turbulent flows: decaying homogeneous isotropic turbulence and temporally evolving turbulent mixing layer. In the numerical experiments, the LESnets model shows a similar or even better accuracy as compared to traditional large-eddy simulation and data-driven models of FNO and IFNO. Moreover, the well-trained LESnets is significantly faster than traditional LES, and has a similar efficiency as the data-driven FNO and IFNO models. Thus, physics-informed neural operators have a strong potential for 3D nonlinear engineering applications.

ProtAgents: Protein discovery via large language model multi-agent collaborations combining physics and machine learning

Designing de novo proteins beyond those found in nature holds significant promise for advancements in both scientific and engineering applications. Current methodologies for protein design often rely on AI-based models, such as surrogate models that address end-to-end problems by linking protein structure to material properties or vice versa. However, these models frequently focus on specific material objectives or structural properties, limiting their flexibility when incorporating out-of-domain knowledge into the design process or comprehensive data analysis is required. In this study, we introduce ProtAgents, a platform for de novo protein design based on Large Language Models (LLMs), where multiple AI agents with distinct capabilities collaboratively address complex tasks within a dynamic environment. The versatility in agent development allows for expertise in diverse domains, including knowledge retrieval, protein structure analysis, physics-based simulations, and results analysis. The dynamic collaboration between agents, empowered by LLMs, provides a versatile approach to tackling protein design and analysis problems, as demonstrated through diverse examples in this study. The problems of interest encompass designing new proteins, analyzing protein structures and obtaining new first-principles data -- natural vibrational frequencies -- via physics simulations. The concerted effort of the system allows for powerful automated and synergistic design of de novo proteins with targeted mechanical properties. The flexibility in designing the agents, on one hand, and their capacity in autonomous collaboration through the dynamic LLM-based multi-agent environment on the other hand, unleashes great potentials of LLMs in addressing multi-objective materials problems and opens up new avenues for autonomous materials discovery and design.

VisualWebInstruct: Scaling up Multimodal Instruction Data through Web Search

Vision-Language Models have made significant progress on many perception-focused tasks, however, their progress on reasoning-focused tasks seem to be limited due to the lack of high-quality and diverse training data. In this work, we aim to address the scarcity issue of reasoning-focused multimodal datasets. We propose VisualWebInstruct - a novel approach that leverages search engine to create a diverse, and high-quality dataset spanning multiple disciplines like math, physics, finance, chemistry, etc. Starting with meticulously selected 30,000 seed images, we employ Google Image search to identify websites containing similar images. We collect and process the HTMLs from over 700K unique URL sources. Through a pipeline of content extraction, filtering and synthesis, we build a dataset of approximately 900K question-answer pairs, with 40% being visual QA pairs and the rest as text QA pairs. Models fine-tuned on VisualWebInstruct demonstrate significant performance gains: (1) training from Llava-OV-mid shows 10-20% absolute point gains across benchmarks, (2) training from MAmmoTH-VL shows 5% absoluate gain. Our best model MAmmoTH-VL2 shows state-of-the-art performance within the 10B parameter class on MMMU-Pro-std (40.7%), MathVerse (42.6%), and DynaMath (55.7%). These remarkable results highlight the effectiveness of our dataset in enhancing VLMs' reasoning capabilities for complex multimodal tasks.

MechAgents: Large language model multi-agent collaborations can solve mechanics problems, generate new data, and integrate knowledge

Solving mechanics problems using numerical methods requires comprehensive intelligent capability of retrieving relevant knowledge and theory, constructing and executing codes, analyzing the results, a task that has thus far mainly been reserved for humans. While emerging AI methods can provide effective approaches to solve end-to-end problems, for instance via the use of deep surrogate models or various data analytics strategies, they often lack physical intuition since knowledge is baked into the parametric complement through training, offering less flexibility when it comes to incorporating mathematical or physical insights. By leveraging diverse capabilities of multiple dynamically interacting large language models (LLMs), we can overcome the limitations of conventional approaches and develop a new class of physics-inspired generative machine learning platform, here referred to as MechAgents. A set of AI agents can solve mechanics tasks, here demonstrated for elasticity problems, via autonomous collaborations. A two-agent team can effectively write, execute and self-correct code, in order to apply finite element methods to solve classical elasticity problems in various flavors (different boundary conditions, domain geometries, meshes, small/finite deformation and linear/hyper-elastic constitutive laws, and others). For more complex tasks, we construct a larger group of agents with enhanced division of labor among planning, formulating, coding, executing and criticizing the process and results. The agents mutually correct each other to improve the overall team-work performance in understanding, formulating and validating the solution. Our framework shows the potential of synergizing the intelligence of language models, the reliability of physics-based modeling, and the dynamic collaborations among diverse agents, opening novel avenues for automation of solving engineering problems.

S2SNet: A Pretrained Neural Network for Superconductivity Discovery

Superconductivity allows electrical current to flow without any energy loss, and thus making solids superconducting is a grand goal of physics, material science, and electrical engineering. More than 16 Nobel Laureates have been awarded for their contribution to superconductivity research. Superconductors are valuable for sustainable development goals (SDGs), such as climate change mitigation, affordable and clean energy, industry, innovation and infrastructure, and so on. However, a unified physics theory explaining all superconductivity mechanism is still unknown. It is believed that superconductivity is microscopically due to not only molecular compositions but also the geometric crystal structure. Hence a new dataset, S2S, containing both crystal structures and superconducting critical temperature, is built upon SuperCon and Material Project. Based on this new dataset, we propose a novel model, S2SNet, which utilizes the attention mechanism for superconductivity prediction. To overcome the shortage of data, S2SNet is pre-trained on the whole Material Project dataset with Masked-Language Modeling (MLM). S2SNet makes a new state-of-the-art, with out-of-sample accuracy of 92% and Area Under Curve (AUC) of 0.92. To the best of our knowledge, S2SNet is the first work to predict superconductivity with only information of crystal structures. This work is beneficial to superconductivity discovery and further SDGs. Code and datasets are available in https://github.com/zjuKeLiu/S2SNet

Text2PDE: Latent Diffusion Models for Accessible Physics Simulation

Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each presents its unique limitations and generally balances training cost, numerical accuracy, and ease of applicability to different problem setups. To address these limitations, we introduce several methods to apply latent diffusion models to physics simulation. Firstly, we introduce a mesh autoencoder to compress arbitrarily discretized PDE data, allowing for efficient diffusion training across various physics. Furthermore, we investigate full spatio-temporal solution generation to mitigate autoregressive error accumulation. Lastly, we investigate conditioning on initial physical quantities, as well as conditioning solely on a text prompt to introduce text2PDE generation. We show that language can be a compact, interpretable, and accurate modality for generating physics simulations, paving the way for more usable and accessible PDE solvers. Through experiments on both uniform and structured grids, we show that the proposed approach is competitive with current neural PDE solvers in both accuracy and efficiency, with promising scaling behavior up to sim3 billion parameters. By introducing a scalable, accurate, and usable physics simulator, we hope to bring neural PDE solvers closer to practical use.

NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition

Neural networks have shown great potential in accelerating the solution of partial differential equations (PDEs). Recently, there has been a growing interest in introducing physics constraints into training neural PDE solvers to reduce the use of costly data and improve the generalization ability. However, these physics constraints, based on certain finite dimensional approximations over the function space, must resolve the smallest scaled physics to ensure the accuracy and stability of the simulation, resulting in high computational costs from large input, output, and neural networks. This paper proposes a general acceleration methodology called NeuralStagger by spatially and temporally decomposing the original learning tasks into several coarser-resolution subtasks. We define a coarse-resolution neural solver for each subtask, which requires fewer computational resources, and jointly train them with the vanilla physics-constrained loss by simply arranging their outputs to reconstruct the original solution. Due to the perfect parallelism between them, the solution is achieved as fast as a coarse-resolution neural solver. In addition, the trained solvers bring the flexibility of simulating with multiple levels of resolution. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations, which leads to an additional 10sim100times speed-up. Moreover, the experiment also shows that the learned model could be well used for optimal control.

CLIP meets GamePhysics: Towards bug identification in gameplay videos using zero-shot transfer learning

Gameplay videos contain rich information about how players interact with the game and how the game responds. Sharing gameplay videos on social media platforms, such as Reddit, has become a common practice for many players. Often, players will share gameplay videos that showcase video game bugs. Such gameplay videos are software artifacts that can be utilized for game testing, as they provide insight for bug analysis. Although large repositories of gameplay videos exist, parsing and mining them in an effective and structured fashion has still remained a big challenge. In this paper, we propose a search method that accepts any English text query as input to retrieve relevant videos from large repositories of gameplay videos. Our approach does not rely on any external information (such as video metadata); it works solely based on the content of the video. By leveraging the zero-shot transfer capabilities of the Contrastive Language-Image Pre-Training (CLIP) model, our approach does not require any data labeling or training. To evaluate our approach, we present the GamePhysics dataset consisting of 26,954 videos from 1,873 games, that were collected from the GamePhysics section on the Reddit website. Our approach shows promising results in our extensive analysis of simple queries, compound queries, and bug queries, indicating that our approach is useful for object and event detection in gameplay videos. An example application of our approach is as a gameplay video search engine to aid in reproducing video game bugs. Please visit the following link for the code and the data: https://asgaardlab.github.io/CLIPxGamePhysics/

VideoPhy: Evaluating Physical Commonsense for Video Generation

Recent advances in internet-scale video data pretraining have led to the development of text-to-video generative models that can create high-quality videos across a broad range of visual concepts, synthesize realistic motions and render complex objects. Hence, these generative models have the potential to become general-purpose simulators of the physical world. However, it is unclear how far we are from this goal with the existing text-to-video generative models. To this end, we present VideoPhy, a benchmark designed to assess whether the generated videos follow physical commonsense for real-world activities (e.g. marbles will roll down when placed on a slanted surface). Specifically, we curate diverse prompts that involve interactions between various material types in the physical world (e.g., solid-solid, solid-fluid, fluid-fluid). We then generate videos conditioned on these captions from diverse state-of-the-art text-to-video generative models, including open models (e.g., CogVideoX) and closed models (e.g., Lumiere, Dream Machine). Our human evaluation reveals that the existing models severely lack the ability to generate videos adhering to the given text prompts, while also lack physical commonsense. Specifically, the best performing model, CogVideoX-5B, generates videos that adhere to the caption and physical laws for 39.6% of the instances. VideoPhy thus highlights that the video generative models are far from accurately simulating the physical world. Finally, we propose an auto-evaluator, VideoCon-Physics, to assess the performance reliably for the newly released models.

FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulation

Humans manipulate various kinds of fluids in their everyday life: creating latte art, scooping floating objects from water, rolling an ice cream cone, etc. Using robots to augment or replace human labors in these daily settings remain as a challenging task due to the multifaceted complexities of fluids. Previous research in robotic fluid manipulation mostly consider fluids governed by an ideal, Newtonian model in simple task settings (e.g., pouring). However, the vast majority of real-world fluid systems manifest their complexities in terms of the fluid's complex material behaviors and multi-component interactions, both of which were well beyond the scope of the current literature. To evaluate robot learning algorithms on understanding and interacting with such complex fluid systems, a comprehensive virtual platform with versatile simulation capabilities and well-established tasks is needed. In this work, we introduce FluidLab, a simulation environment with a diverse set of manipulation tasks involving complex fluid dynamics. These tasks address interactions between solid and fluid as well as among multiple fluids. At the heart of our platform is a fully differentiable physics simulator, FluidEngine, providing GPU-accelerated simulations and gradient calculations for various material types and their couplings. We identify several challenges for fluid manipulation learning by evaluating a set of reinforcement learning and trajectory optimization methods on our platform. To address these challenges, we propose several domain-specific optimization schemes coupled with differentiable physics, which are empirically shown to be effective in tackling optimization problems featured by fluid system's non-convex and non-smooth properties. Furthermore, we demonstrate reasonable sim-to-real transfer by deploying optimized trajectories in real-world settings.

Towards World Simulator: Crafting Physical Commonsense-Based Benchmark for Video Generation

Text-to-video (T2V) models like Sora have made significant strides in visualizing complex prompts, which is increasingly viewed as a promising path towards constructing the universal world simulator. Cognitive psychologists believe that the foundation for achieving this goal is the ability to understand intuitive physics. However, the capacity of these models to accurately represent intuitive physics remains largely unexplored. To bridge this gap, we introduce PhyGenBench, a comprehensive Physics Generation Benchmark designed to evaluate physical commonsense correctness in T2V generation. PhyGenBench comprises 160 carefully crafted prompts across 27 distinct physical laws, spanning four fundamental domains, which could comprehensively assesses models' understanding of physical commonsense. Alongside PhyGenBench, we propose a novel evaluation framework called PhyGenEval. This framework employs a hierarchical evaluation structure utilizing appropriate advanced vision-language models and large language models to assess physical commonsense. Through PhyGenBench and PhyGenEval, we can conduct large-scale automated assessments of T2V models' understanding of physical commonsense, which align closely with human feedback. Our evaluation results and in-depth analysis demonstrate that current models struggle to generate videos that comply with physical commonsense. Moreover, simply scaling up models or employing prompt engineering techniques is insufficient to fully address the challenges presented by PhyGenBench (e.g., dynamic scenarios). We hope this study will inspire the community to prioritize the learning of physical commonsense in these models beyond entertainment applications. We will release the data and codes at https://github.com/OpenGVLab/PhyGenBench

PhysGame: Uncovering Physical Commonsense Violations in Gameplay Videos

Recent advancements in video-based large language models (Video LLMs) have witnessed the emergence of diverse capabilities to reason and interpret dynamic visual content. Among them, gameplay videos stand out as a distinctive data source, often containing glitches that defy physics commonsense. This characteristic renders them an effective benchmark for assessing the under-explored capability of physical commonsense understanding in video LLMs. In this paper, we propose PhysGame as a pioneering benchmark to evaluate physical commonsense violations in gameplay videos. PhysGame comprises 880 videos associated with glitches spanning four fundamental domains (i.e., mechanics, kinematics, optics, and material properties) and across 12 distinct physical commonsense. Through extensively evaluating various state-ofthe-art video LLMs, our findings reveal that the performance of current open-source video LLMs significantly lags behind that of proprietary counterparts. To bridge this gap, we curate an instruction tuning dataset PhysInstruct with 140,057 question-answering pairs to facilitate physical commonsense learning. In addition, we also propose a preference optimization dataset PhysDPO with 34,358 training pairs, where the dis-preferred responses are generated conditioned on misleading titles (i.e., meta information hacking), fewer frames (i.e., temporal hacking) and lower spatial resolutions (i.e., spatial hacking). Based on the suite of datasets, we propose PhysVLM as a physical knowledge-enhanced video LLM. Extensive experiments on both physical-oriented benchmark PhysGame and general video understanding benchmarks demonstrate the state-ofthe-art performance of PhysVLM.

Reduced-Order Neural Operators: Learning Lagrangian Dynamics on Highly Sparse Graphs

We present a neural operator architecture to simulate Lagrangian dynamics, such as fluid flow, granular flows, and elastoplasticity. Traditional numerical methods, such as the finite element method (FEM), suffer from long run times and large memory consumption. On the other hand, approaches based on graph neural networks are faster but still suffer from long computation times on dense graphs, which are often required for high-fidelity simulations. Our model, GIOROM or Graph Interaction Operator for Reduced-Order Modeling, learns temporal dynamics within a reduced-order setting, capturing spatial features from a highly sparse graph representation of the input and generalizing to arbitrary spatial locations during inference. The model is geometry-aware and discretization-agnostic and can generalize to different initial conditions, velocities, and geometries after training. We show that point clouds of the order of 100,000 points can be inferred from sparse graphs with sim1000 points, with negligible change in computation time. We empirically evaluate our model on elastic solids, Newtonian fluids, Non-Newtonian fluids, Drucker-Prager granular flows, and von Mises elastoplasticity. On these benchmarks, our approach results in a 25times speedup compared to other neural network-based physics simulators while delivering high-fidelity predictions of complex physical systems and showing better performance on most benchmarks. The code and the demos are provided at https://github.com/HrishikeshVish/GIOROM.

Physics3D: Learning Physical Properties of 3D Gaussians via Video Diffusion

In recent years, there has been rapid development in 3D generation models, opening up new possibilities for applications such as simulating the dynamic movements of 3D objects and customizing their behaviors. However, current 3D generative models tend to focus only on surface features such as color and shape, neglecting the inherent physical properties that govern the behavior of objects in the real world. To accurately simulate physics-aligned dynamics, it is essential to predict the physical properties of materials and incorporate them into the behavior prediction process. Nonetheless, predicting the diverse materials of real-world objects is still challenging due to the complex nature of their physical attributes. In this paper, we propose Physics3D, a novel method for learning various physical properties of 3D objects through a video diffusion model. Our approach involves designing a highly generalizable physical simulation system based on a viscoelastic material model, which enables us to simulate a wide range of materials with high-fidelity capabilities. Moreover, we distill the physical priors from a video diffusion model that contains more understanding of realistic object materials. Extensive experiments demonstrate the effectiveness of our method with both elastic and plastic materials. Physics3D shows great potential for bridging the gap between the physical world and virtual neural space, providing a better integration and application of realistic physical principles in virtual environments. Project page: https://liuff19.github.io/Physics3D.

Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

How Far is Video Generation from World Model: A Physical Law Perspective

OpenAI's Sora highlights the potential of video generation for developing world models that adhere to fundamental physical laws. However, the ability of video generation models to discover such laws purely from visual data without human priors can be questioned. A world model learning the true law should give predictions robust to nuances and correctly extrapolate on unseen scenarios. In this work, we evaluate across three key scenarios: in-distribution, out-of-distribution, and combinatorial generalization. We developed a 2D simulation testbed for object movement and collisions to generate videos deterministically governed by one or more classical mechanics laws. This provides an unlimited supply of data for large-scale experimentation and enables quantitative evaluation of whether the generated videos adhere to physical laws. We trained diffusion-based video generation models to predict object movements based on initial frames. Our scaling experiments show perfect generalization within the distribution, measurable scaling behavior for combinatorial generalization, but failure in out-of-distribution scenarios. Further experiments reveal two key insights about the generalization mechanisms of these models: (1) the models fail to abstract general physical rules and instead exhibit "case-based" generalization behavior, i.e., mimicking the closest training example; (2) when generalizing to new cases, models are observed to prioritize different factors when referencing training data: color > size > velocity > shape. Our study suggests that scaling alone is insufficient for video generation models to uncover fundamental physical laws, despite its role in Sora's broader success. See our project page at https://phyworld.github.io

CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics

In recent years, applying deep learning to solve physics problems has attracted much attention. Data-driven deep learning methods produce fast numerical operators that can learn approximate solutions to the whole system of partial differential equations (i.e., surrogate modeling). Although these neural networks may have lower accuracy than traditional numerical methods, they, once trained, are orders of magnitude faster at inference. Hence, one crucial feature is that these operators can generalize to unseen PDE parameters without expensive re-training.In this paper, we construct CFDBench, a benchmark tailored for evaluating the generalization ability of neural operators after training in computational fluid dynamics (CFD) problems. It features four classic CFD problems: lid-driven cavity flow, laminar boundary layer flow in circular tubes, dam flows through the steps, and periodic Karman vortex street. The data contains a total of 302K frames of velocity and pressure fields, involving 739 cases with different operating condition parameters, generated with numerical methods. We evaluate the effectiveness of popular neural operators including feed-forward networks, DeepONet, FNO, U-Net, etc. on CFDBnech by predicting flows with non-periodic boundary conditions, fluid properties, and flow domain shapes that are not seen during training. Appropriate modifications were made to apply popular deep neural networks to CFDBench and enable the accommodation of more changing inputs. Empirical results on CFDBench show many baseline models have errors as high as 300% in some problems, and severe error accumulation when performing autoregressive inference. CFDBench facilitates a more comprehensive comparison between different neural operators for CFD compared to existing benchmarks.

GEO: Generative Engine Optimization

The advent of large language models (LLMs) has ushered in a new paradigm of search engines that use generative models to gather and summarize information to answer user queries. This emerging technology, which we formalize under the unified framework of generative engines (GEs), can generate accurate and personalized responses, rapidly replacing traditional search engines like Google and Bing. Generative Engines typically satisfy queries by synthesizing information from multiple sources and summarizing them using LLMs. While this shift significantly improves user utility and generative search engine traffic, it poses a huge challenge for the third stakeholder - website and content creators. Given the black-box and fast-moving nature of generative engines, content creators have little to no control over when and how their content is displayed. With generative engines here to stay, we must ensure the creator economy is not disadvantaged. To address this, we introduce Generative Engine Optimization (GEO), the first novel paradigm to aid content creators in improving their content visibility in GE responses through a flexible black-box optimization framework for optimizing and defining visibility metrics. We facilitate systematic evaluation by introducing GEO-bench, a large-scale benchmark of diverse user queries across multiple domains, along with relevant web sources to answer these queries. Through rigorous evaluation, we demonstrate that GEO can boost visibility by up to 40\% in GE responses. Moreover, we show the efficacy of these strategies varies across domains, underscoring the need for domain-specific optimization methods. Our work opens a new frontier in information discovery systems, with profound implications for both developers of GEs and content creators.

Towards Universal Mesh Movement Networks

Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Amp\`ere PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page is at https://erizmr.github.io/UM2N/.

AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Prediction

Air quality prediction and modelling plays a pivotal role in public health and environment management, for individuals and authorities to make informed decisions. Although traditional data-driven models have shown promise in this domain, their long-term prediction accuracy can be limited, especially in scenarios with sparse or incomplete data and they often rely on black-box deep learning structures that lack solid physical foundation leading to reduced transparency and interpretability in predictions. To address these limitations, this paper presents a novel approach named Physics guided Neural Network for Air Quality Prediction (AirPhyNet). Specifically, we leverage two well-established physics principles of air particle movement (diffusion and advection) by representing them as differential equation networks. Then, we utilize a graph structure to integrate physics knowledge into a neural network architecture and exploit latent representations to capture spatio-temporal relationships within the air quality data. Experiments on two real-world benchmark datasets demonstrate that AirPhyNet outperforms state-of-the-art models for different testing scenarios including different lead time (24h, 48h, 72h), sparse data and sudden change prediction, achieving reduction in prediction errors up to 10%. Moreover, a case study further validates that our model captures underlying physical processes of particle movement and generates accurate predictions with real physical meaning.

Better Neural PDE Solvers Through Data-Free Mesh Movers

Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some methods utilize reinforcement learning or supervised learning techniques to create adaptive and dynamic meshes, due to the dynamic nature of these systems. However, these approaches face two primary challenges: (1) the need for expensive optimal mesh data, and (2) the change of the solution space's degree of freedom and topology during mesh refinement. To address these challenges, this paper proposes a neural PDE solver with a neural mesh adapter. To begin with, we introduce a novel data-free neural mesh adaptor, called Data-free Mesh Mover (DMM), with two main innovations. Firstly, it is an operator that maps the solution to adaptive meshes and is trained using the Monge-Amp\`ere equation without optimal mesh data. Secondly, it dynamically changes the mesh by moving existing nodes rather than adding or deleting nodes and edges. Theoretical analysis shows that meshes generated by DMM have the lowest interpolation error bound. Based on DMM, to efficiently and accurately model dynamic systems, we develop a moving mesh based neural PDE solver (MM-PDE) that embeds the moving mesh with a two-branch architecture and a learnable interpolation framework to preserve information within the data. Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems. The code can be found at: https://github.com/Peiyannn/MM-PDE.git.