We study Diffusion Schr\"odinger Bridge (DSB) models in the context of dynamical astrophysical systems, specifically tackling observational inverse prediction tasks within Giant Molecular Clouds (GMCs) for star formation. We introduce the Astro-DSB model, a variant of DSB with the pairwise domain assumption tailored for astrophysical dynamics. By investigating its learning process and prediction performance in both physically simulated data and in real observations (the Taurus B213 data), we present two main takeaways. First, from the astrophysical perspective, our proposed paired DSB method improves interpretability, learning efficiency, and prediction performance over conventional astrostatistical and other machine learning methods. Second, from the generative modeling perspective, probabilistic generative modeling reveals improvements over discriminative pixel-to-pixel modeling in Out-Of-Distribution (OOD) testing cases of physical simulations with unseen initial conditions and different dominant physical processes. Our study expands research into diffusion models beyond the traditional visual synthesis application and provides evidence of the models' learning abilities beyond pure data statistics, paving a path for future physics-aware generative models which can align dynamics between machine learning and real (astro)physical systems.
Accurately and efficiently simulating complex fluid dynamics is a challenging task that has traditionally relied on computationally intensive methods. Neural network-based approaches, such as convolutional and graph neural networks, have partially alleviated this burden by enabling efficient local feature extraction. However, they struggle to capture long-range dependencies due to limited receptive fields, and Transformer-based models, while providing global context, incur prohibitive computational costs. To tackle these challenges, we propose AMR-Transformer, an efficient and accurate neural CFD-solving pipeline that integrates a novel adaptive mesh refinement scheme with a Navier-Stokes constraint-aware fast pruning module. This design encourages long-range interactions between simulation cells and facilitates the modeling of global fluid wave patterns, such as turbulence and shockwaves. Experiments show that our approach achieves significant gains in efficiency while preserving critical details, making it suitable for high-resolution physical simulations with long-range dependencies. On CFDBench, PDEBench and a new shockwave dataset, our pipeline demonstrates up to an order-of-magnitude improvement in accuracy over baseline models. Additionally, compared to ViT, our approach achieves a reduction in FLOPs of up to 60 times.
We present DecoupledGaussian, a novel system that decouples static objects from their contacted surfaces captured in-the-wild videos, a key prerequisite for realistic Newtonian-based physical simulations. Unlike prior methods focused on synthetic data or elastic jittering along the contact surface, which prevent objects from fully detaching or moving independently, DecoupledGaussian allows for significant positional changes without being constrained by the initial contacted surface. Recognizing the limitations of current 2D inpainting tools for restoring 3D locations, our approach proposes joint Poisson fields to repair and expand the Gaussians of both objects and contacted scenes after separation. This is complemented by a multi-carve strategy to refine the object's geometry. Our system enables realistic simulations of decoupling motions, collisions, and fractures driven by user-specified impulses, supporting complex interactions within and across multiple scenes. We validate DecoupledGaussian through a comprehensive user study and quantitative benchmarks. This system enhances digital interaction with objects and scenes in real-world environments, benefiting industries such as VR, robotics, and autonomous driving. Our project page is at: https://wangmiaowei.github.io/DecoupledGaussian.github.io/.
Large-scale physical systems defined on irregular grids pose significant scalability challenges for deep learning methods, especially in the presence of long-range interactions and multi-scale coupling. Traditional approaches that compute all pairwise interactions, such as attention, become computationally prohibitive as they scale quadratically with the number of nodes. We present Erwin, a hierarchical transformer inspired by methods from computational many-body physics, which combines the efficiency of tree-based algorithms with the expressivity of attention mechanisms. Erwin employs ball tree partitioning to organize computation, which enables linear-time attention by processing nodes in parallel within local neighborhoods of fixed size. Through progressive coarsening and refinement of the ball tree structure, complemented by a novel cross-ball interaction mechanism, it captures both fine-grained local details and global features. We demonstrate Erwin's effectiveness across multiple domains, including cosmology, molecular dynamics, and particle fluid dynamics, where it consistently outperforms baseline methods both in accuracy and computational efficiency.
In recent years, Graph Neural Network (GNN) based models have shown promising results in simulating physics of complex systems. However, training dedicated graph network based physics simulators can be costly, as most models are confined to fully supervised training, which requires extensive data generated from traditional physics simulators. To date, how transfer learning could improve the model performance and training efficiency has remained unexplored. In this work, we introduce a pre-training and transfer learning paradigm for graph network simulators. We propose the scalable graph U-net (SGUNET). Incorporating an innovative depth-first search (DFS) pooling, the SGUNET is adaptable to different mesh sizes and resolutions for various simulation tasks. To enable the transfer learning between differently configured SGUNETs, we propose a set of mapping functions to align the parameters between the pre-trained model and the target model. An extra normalization term is also added into the loss to constrain the difference between the pre-trained weights and target model weights for better generalization performance. To pre-train our physics simulator we created a dataset which includes 20,000 physical simulations of randomly selected 3D shapes from the open source A Big CAD (ABC) dataset. We show that our proposed transfer learning methods allow the model to perform even better when fine-tuned with small amounts of training data than when it is trained from scratch with full extensive dataset. On the 2D Deformable Plate benchmark dataset, our pre-trained model fine-tuned on 1/16 of the training data achieved an 11.05\% improvement in position RMSE compared to the model trained from scratch.
Recent advancements in AI-generated content have significantly improved the realism of 3D and 4D generation. However, most existing methods prioritize appearance consistency while neglecting underlying physical principles, leading to artifacts such as unrealistic deformations, unstable dynamics, and implausible objects interactions. Incorporating physics priors into generative models has become a crucial research direction to enhance structural integrity and motion realism. This survey provides a review of physics-aware generative methods, systematically analyzing how physical constraints are integrated into 3D and 4D generation. First, we examine recent works in incorporating physical priors into static and dynamic 3D generation, categorizing methods based on representation types, including vision-based, NeRF-based, and Gaussian Splatting-based approaches. Second, we explore emerging techniques in 4D generation, focusing on methods that model temporal dynamics with physical simulations. Finally, we conduct a comparative analysis of major methods, highlighting their strengths, limitations, and suitability for different materials and motion dynamics. By presenting an in-depth analysis of physics-grounded AIGC, this survey aims to bridge the gap between generative models and physical realism, providing insights that inspire future research in physically consistent content generation.
Physical simulations are essential tools across critical fields such as mechanical and aerospace engineering, chemistry, meteorology, etc. While neural operators, particularly the Fourier Neural Operator (FNO), have shown promise in predicting simulation results with impressive performance and efficiency, they face limitations when handling real-world scenarios involving coupled multi-physics outputs. Current neural operator methods either overlook the correlations between multiple physical processes or employ simplistic architectures that inadequately capture these relationships. To overcome these challenges, we introduce a novel coupled multi-physics neural operator learning (COMPOL) framework that extends the capabilities of Fourier operator layers to model interactions among multiple physical processes. Our approach implements feature aggregation through recurrent and attention mechanisms, enabling comprehensive modeling of coupled interactions. Our method's core is an innovative system for aggregating latent features from multi-physics processes. These aggregated features serve as enriched information sources for neural operator layers, allowing our framework to capture complex physical relationships accurately. We evaluated our coupled multi-physics neural operator across diverse physical simulation tasks, including biological systems, fluid mechanics, and multiphase flow in porous media. Our proposed model demonstrates a two to three-fold improvement in predictive performance compared to existing approaches.
Trained neural networks (NN) are attractive as surrogate models to replace costly calculations in physical simulations, but are often unknowingly applied to states not adequately represented in the training dataset. We present the novel technique of soft checksums for scientific machine learning, a general-purpose method to differentiate between trustworthy predictions with small errors on in-distribution (ID) data points, and untrustworthy predictions with large errors on out-of-distribution (OOD) data points. By adding a check node to the existing output layer, we train the model to learn the chosen checksum function encoded within the NN predictions and show that violations of this function correlate with high prediction errors. As the checksum function depends only on the NN predictions, we can calculate the checksum error for any prediction with a single forward pass, incurring negligible time and memory costs. Additionally, we find that incorporating the checksum function into the loss function and exposing the NN to OOD data points during the training process improves separation between ID and OOD predictions. By applying soft checksums to a physically complex and high-dimensional non-local thermodynamic equilibrium atomic physics dataset, we show that a well-chosen threshold checksum error can effectively separate ID and OOD predictions.
This paper tackles the challenge of automatically performing realistic surgical simulations from readily available surgical videos. Recent efforts have successfully integrated physically grounded dynamics within 3D Gaussians to perform high-fidelity simulations in well-reconstructed simulation environments from static scenes. However, they struggle with the geometric inconsistency in reconstructing simulation environments and unrealistic physical deformations in simulations of soft tissues when it comes to dynamic and complex surgical processes. In this paper, we propose SurgiSim, a novel automatic simulation system to overcome these limitations. To build a surgical simulation environment, we maintain a canonical 3D scene composed of 3D Gaussians coupled with a deformation field to represent a dynamic surgical scene. This process involves a multi-stage optimization with trajectory and anisotropic regularization, enhancing the geometry consistency of the canonical scene, which serves as the simulation environment. To achieve realistic physical simulations in this environment, we implement a Visco-Elastic deformation model based on the Maxwell model, effectively restoring the complex deformations of tissues. Additionally, we infer the physical parameters of tissues by minimizing the discrepancies between the input video and simulation results guided by estimated tissue motion, ensuring realistic simulation outcomes. Experiments on various surgical scenarios and interactions demonstrate SurgiSim's ability to perform realistic simulation of soft tissues among surgical procedures, showing its enormous potential for enhancing surgical training, planning, and robotic surgery systems. The project page is at https://namaenashibot.github.io/SurgiSim/.
The task of 4D content generation involves creating dynamic 3D models that evolve over time in response to specific input conditions, such as images. Existing methods rely heavily on pre-trained video diffusion models to guide 4D content dynamics, but these approaches often fail to capture essential physical principles, as video diffusion models lack a robust understanding of real-world physics. Moreover, these models face challenges in providing fine-grained control over dynamics and exhibit high computational costs. In this work, we propose Phys4DGen, a novel, high-efficiency framework that generates physics-compliant 4D content from a single image with enhanced control capabilities. Our approach uniquely integrates physical simulations into the 4D generation pipeline, ensuring adherence to fundamental physical laws. Inspired by the human ability to infer physical properties visually, we introduce a Physical Perception Module (PPM) that discerns the material properties and structural components of the 3D object from the input image, facilitating accurate downstream simulations. Phys4DGen significantly accelerates the 4D generation process by eliminating iterative optimization steps in the dynamics modeling phase. It allows users to intuitively control the movement speed and direction of generated 4D content by adjusting external forces, achieving finely tunable, physically plausible animations. Extensive evaluations show that Phys4DGen outperforms existing methods in both inference speed and physical realism, producing high-quality, controllable 4D content. Our project page is available at the link: \url{https://jiajinglin.github.io/Phys4DGen/}.
Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more concise subspaces can be detected. However, the complexity and landscape of simulation objectives within the subspace have not been optimized, which leaves room for enhancement of the convergence speed. This work focuses on this point by proposing a general method for finding optimized subspace mappings, enabling further acceleration of neural reduced-order simulations while capturing comprehensive representations of the configuration manifolds. We achieve this by optimizing the Lipschitz energy of the elasticity term in the simulation objective, and incorporating the cubature approximation into the training process to manage the high memory and time demands associated with optimizing the newly introduced energy. Our method is versatile and applicable to both supervised and unsupervised settings for optimizing the parameterizations of the configuration manifolds. We demonstrate the effectiveness of our approach through general cases in both quasi-static and dynamics simulations. Our method achieves acceleration factors of up to 6.83 while consistently preserving comparable simulation accuracy in various cases, including large twisting, bending, and rotational deformations with collision handling. This novel approach offers significant potential for accelerating physical simulations, and can be a good add-on to existing neural-network-based solutions in modeling complex deformable objects.
Monocular depth estimation (MDE) and semantic segmentation (SS) are crucial for the navigation and environmental interpretation of many autonomous driving systems. However, their vulnerability to practical adversarial attacks is a significant concern. This paper presents a novel adversarial attack using practical patches that mimic manhole covers to deceive MDE and SS models. The goal is to cause these systems to misinterpret scenes, leading to false detections of near obstacles or non-passable objects. We use Depth Planar Mapping to precisely position these patches on road surfaces, enhancing the attack's effectiveness. Our experiments show that these adversarial patches cause a 43% relative error in MDE and achieve a 96% attack success rate in SS. These patches create affected error regions over twice their size in MDE and approximately equal to their size in SS. Our studies also confirm the patch's effectiveness in physical simulations, the adaptability of the patches across different target models, and the effectiveness of our proposed modules, highlighting their practical implications.
Climate change poses complex challenges, with extreme weather events becoming increasingly frequent and difficult to model. Examples include the dynamics of Combined Sewer Systems (CSS). Overburdened CSS during heavy rainfall will overflow untreated wastewater into surface water bodies. Classical approaches to modeling the impact of extreme rainfall events rely on physical simulations, which are particularly challenging to create for large urban infrastructures. Deep Learning (DL) models offer a cost-effective alternative for modeling the complex dynamics of sewer systems. In this study, we present a comprehensive empirical evaluation of several state-of-the-art DL time series models for predicting sewer system dynamics in a large urban infrastructure, utilizing three years of measurement data. We especially investigate the potential of DL models to maintain predictive precision during network outages by comparing global models, which have access to all variables within the sewer system, and local models, which are limited to data from a restricted set of local sensors. Our findings demonstrate that DL models can accurately predict the dynamics of sewer system load, even under network outage conditions. These results suggest that DL models can effectively aid in balancing the load redistribution in CSS, thereby enhancing the sustainability and resilience of urban infrastructures.
The integration of machine learning (ML) techniques for addressing intricate physics problems is increasingly recognized as a promising avenue for expediting simulations. However, assessing ML-derived physical models poses a significant challenge for their adoption within industrial contexts. This competition is designed to promote the development of innovative ML approaches for tackling physical challenges, leveraging our recently introduced unified evaluation framework known as Learning Industrial Physical Simulations (LIPS). Building upon the preliminary edition held from November 2023 to March 2024, this iteration centers on a task fundamental to a well-established physical application: airfoil design simulation, utilizing our proposed AirfRANS dataset. The competition evaluates solutions based on various criteria encompassing ML accuracy, computational efficiency, Out-Of-Distribution performance, and adherence to physical principles. Notably, this competition represents a pioneering effort in exploring ML-driven surrogate methods aimed at optimizing the trade-off between computational efficiency and accuracy in physical simulations. Hosted on the Codabench platform, the competition offers online training and evaluation for all participating solutions.
In this article, we propose an approach to leak localisation in a complex water delivery grid with the use of data from physical simulation (e.g. EPANET software). This task is usually achieved by a network of multiple water pressure sensors and analysis of the so-called sensitivity matrix of pressure differences between the network's simulated data and actual data of the network affected by the leak. However, most algorithms using this approach require a significant number of pressure sensors -- a condition that is not easy to fulfil in the case of many less equipped networks. Therefore, we answer the question of whether leak localisation is possible by utilising very few sensors but having the ability to relocate one of them. Our algorithm is based on physical simulations (EPANET software) and an iterative scheme for mobile sensor relocation. The experiments show that the proposed system can equalise the low number of sensors with adjustments made for their positioning, giving a very good approximation of leak's position both in simulated cases and real-life example taken from BattLeDIM competition L-Town data.
During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning architectures, as well as hybrid models, i.e., the combination of physical simulation models and machine learning. In this work, we briefly discuss which types of model are usually combined in dynamical systems modeling and propose a class of models that is capable of expressing mixed algebraic, discrete, and differential equation-based models. Further, we examine different established, as well as new ways of combining these models from the point of view of system theory and highlight two challenges - algebraic loops and local event functions in discontinuous models - that require a special approach. Finally, we propose a new wildcard architecture that is capable of describing arbitrary combinations of models in an easy-to-interpret fashion that can be learned as part of a gradient-based optimization procedure. In a final experiment, different combination architectures between two models are learned, interpreted, and compared using the methodology and software implementation provided.
Crystallization processes at the mesoscopic scale, where faceted, dendritic growth, and multigrain formation can be observed, are of particular interest within materials science and metallurgy. These processes are highly nonlinear, stochastic, and sensitive to small perturbations of system parameters and initial conditions. Methods for the simulation of these processes have been developed using discrete numerical models, but these are computationally expensive. This work aims to scale crystal growth simulation with a machine learning emulator. Specifically, autoregressive latent variable models are well suited for modeling the joint distribution over system parameters and the crystallization trajectories. However, successfully training such models is challenging due to the stochasticity and sensitivity of the system. Existing approaches consequently fail to produce diverse and faithful crystallization trajectories. In this paper, we introduce the Crystal Growth Neural Emulator (CGNE), a probabilistic model for efficient crystal growth emulation at the mesoscopic scale that overcomes these challenges. We validate CGNE results using the morphological properties of the crystals produced by numerical simulation. CGNE delivers a factor of 11 improvement in inference time and performance gains compared with recent state-of-the-art probabilistic models for dynamical systems.
Time-dependent partial differential equations (PDEs) for classic physical systems are established based on the conservation of mass, momentum, and energy, which are ubiquitous in scientific and engineering applications. These PDEs are strictly local-dependent according to the principle of locality in physics, which means that the evolution at a point is only influenced by the neighborhood around it whose size is determined by the length of timestep multiplied with the speed of characteristic information traveling in the system. However, deep learning architecture cannot strictly enforce the local-dependency as it inevitably increases the scope of information to make local predictions as the number of layers increases. Under limited training data, the extra irrelevant information results in sluggish convergence and compromised generalizability. This paper aims to solve this problem by proposing a data decomposition method to strictly limit the scope of information for neural operators making local predictions, which is called data decomposition enforcing local-dependency (DDELD). The numerical experiments over multiple physical phenomena show that DDELD significantly accelerates training convergence and reduces test errors of benchmark models on large-scale engineering simulations.
Artificial intelligence (AI) has revolutionized software development, shifting from task-specific codes (Software 1.0) to neural network-based approaches (Software 2.0). However, applying this transition in engineering software presents challenges, including low surrogate model accuracy, the curse of dimensionality in inverse design, and rising complexity in physical simulations. We introduce an interpolating neural network (INN), grounded in interpolation theory and tensor decomposition, to realize Engineering Software 2.0 by advancing data training, partial differential equation solving, and parameter calibration. INN offers orders of magnitude fewer trainable/solvable parameters for comparable model accuracy than traditional multi-layer perceptron (MLP) or physics-informed neural networks (PINN). Demonstrated in metal additive manufacturing, INN rapidly constructs an accurate surrogate model of Laser Powder Bed Fusion (L-PBF) heat transfer simulation, achieving sub-10-micrometer resolution for a 10 mm path in under 15 minutes on a single GPU. This makes a transformative step forward across all domains essential to engineering software.
Humanoid-Gym is an easy-to-use reinforcement learning (RL) framework based on Nvidia Isaac Gym, designed to train locomotion skills for humanoid robots, emphasizing zero-shot transfer from simulation to the real-world environment. Humanoid-Gym also integrates a sim-to-sim framework from Isaac Gym to Mujoco that allows users to verify the trained policies in different physical simulations to ensure the robustness and generalization of the policies. This framework is verified by RobotEra's XBot-S (1.2-meter tall humanoid robot) and XBot-L (1.65-meter tall humanoid robot) in a real-world environment with zero-shot sim-to-real transfer. The project website and source code can be found at: https://sites.google.com/view/humanoid-gym/.