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.
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.
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.
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.
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/.
Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been computationally expensive and challenging to use in inverse problems, whereas Neural solvers aim to address both concerns through machine learning. We propose a general formulation for continuous convolutions using separable basis functions as a superset of existing methods and evaluate a large set of basis functions in the context of (a) a compressible 1D SPH simulation, (b) a weakly compressible 2D SPH simulation, and (c) an incompressible 2D SPH Simulation. We demonstrate that even and odd symmetries included in the basis functions are key aspects of stability and accuracy. Our broad evaluation shows that Fourier-based continuous convolutions outperform all other architectures regarding accuracy and generalization. Finally, using these Fourier-based networks, we show that prior inductive biases, such as window functions, are no longer necessary. An implementation of our approach, as well as complete datasets and solver implementations, is available at https://github.com/tum-pbs/SFBC.
Data-driven modeling of complex physical systems is receiving a growing amount of attention in the simulation and machine learning communities. Since most physical simulations are based on compute-intensive, iterative implementations of differential equation systems, a (partial) replacement with learned, 1-step inference models has the potential for significant speedups in a wide range of application areas. In this context, we present a novel benchmark for the evaluation of 1-step generative learning models in terms of speed and physical correctness. Our Urban Sound Propagation benchmark is based on the physically complex and practically relevant, yet intuitively easy to grasp task of modeling the 2d propagation of waves from a sound source in an urban environment. We provide a dataset with 100k samples, where each sample consists of pairs of real 2d building maps drawn from OpenStreetmap, a parameterized sound source, and a simulated ground truth sound propagation for the given scene. The dataset provides four different simulation tasks with increasing complexity regarding reflection, diffraction and source variance. A first baseline evaluation of common generative U-Net, GAN and Diffusion models shows, that while these models are very well capable of modeling sound propagations in simple cases, the approximation of sub-systems represented by higher order equations systematically fails. Information about the dataset, download instructions and source codes are provided on our website: https://www.urban-sound-data.org.
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.
Traditional partial differential equation (PDE) solvers can be computationally expensive, which motivates the development of faster methods, such as reduced-order-models (ROMs). We present GPLaSDI, a hybrid deep-learning and Bayesian ROM. GPLaSDI trains an autoencoder on full-order-model (FOM) data and simultaneously learns simpler equations governing the latent space. These equations are interpolated with Gaussian Processes, allowing for uncertainty quantification and active learning, even with limited access to the FOM solver. Our framework is able to achieve up to 100,000 times speed-up and less than 7% relative error on fluid mechanics problems.
General circulation models (GCMs) are the foundation of weather and climate prediction. GCMs are physics-based simulators which combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine learning (ML) models trained on reanalysis data achieved comparable or better skill than GCMs for deterministic weather forecasting. However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present the first GCM that combines a differentiable solver for atmospheric dynamics with ML components, and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best ML and physics-based methods. NeuralGCM is competitive with ML models for 1-10 day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for 1-15 day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics such as global mean temperature for multiple decades, and climate forecasts with 140 km resolution exhibit emergent phenomena such as realistic frequency and trajectories of tropical cyclones. For both weather and climate, our approach offers orders of magnitude computational savings over conventional GCMs. Our results show that end-to-end deep learning is compatible with tasks performed by conventional GCMs, and can enhance the large-scale physical simulations that are essential for understanding and predicting the Earth system.
We explore the possibility of fully replacing a plasma physics kinetic simulator with a graph neural network-based simulator. We focus on this class of surrogate models given the similarity between their message-passing update mechanism and the traditional physics solver update, and the possibility of enforcing known physical priors into the graph construction and update. We show that our model learns the kinetic plasma dynamics of the one-dimensional plasma model, a predecessor of contemporary kinetic plasma simulation codes, and recovers a wide range of well-known kinetic plasma processes, including plasma thermalization, electrostatic fluctuations about thermal equilibrium, and the drag on a fast sheet and Landau damping. We compare the performance against the original plasma model in terms of run-time, conservation laws, and temporal evolution of key physical quantities. The limitations of the model are presented and possible directions for higher-dimensional surrogate models for kinetic plasmas are discussed.
Climate change is increasing the intensity and frequency of many extreme weather events, including heatwaves, which results in increased thermal discomfort and mortality rates. While global mitigation action is undoubtedly necessary, so is climate adaptation, e.g., through climate-sensitive urban planning. Among the most promising strategies is harnessing the benefits of urban trees in shading and cooling pedestrian-level environments. Our work investigates the challenge of optimal placement of such trees. Physical simulations can estimate the radiative and thermal impact of trees on human thermal comfort but induce high computational costs. This rules out optimization of tree placements over large areas and considering effects over longer time scales. Hence, we employ neural networks to simulate the point-wise mean radiant temperatures--a driving factor of outdoor human thermal comfort--across various time scales, spanning from daily variations to extended time scales of heatwave events and even decades. To optimize tree placements, we harness the innate local effect of trees within the iterated local search framework with tailored adaptations. We show the efficacy of our approach across a wide spectrum of study areas and time scales. We believe that our approach is a step towards empowering decision-makers, urban designers and planners to proactively and effectively assess the potential of urban trees to mitigate heat stress.
Zeroth-order (ZO) optimization has become a popular technique for solving machine learning (ML) problems when first-order (FO) information is difficult or impossible to obtain. However, the scalability of ZO optimization remains an open problem: Its use has primarily been limited to relatively small-scale ML problems, such as sample-wise adversarial attack generation. To our best knowledge, no prior work has demonstrated the effectiveness of ZO optimization in training deep neural networks (DNNs) without a significant decrease in performance. To overcome this roadblock, we develop DeepZero, a principled ZO deep learning (DL) framework that can scale ZO optimization to DNN training from scratch through three primary innovations. First, we demonstrate the advantages of coordinatewise gradient estimation (CGE) over randomized vector-wise gradient estimation in training accuracy and computational efficiency. Second, we propose a sparsityinduced ZO training protocol that extends the model pruning methodology using only finite differences to explore and exploit the sparse DL prior in CGE. Third, we develop the methods of feature reuse and forward parallelization to advance the practical implementations of ZO training. Our extensive experiments show that DeepZero achieves state-of-the-art (SOTA) accuracy on ResNet-20 trained on CIFAR-10, approaching FO training performance for the first time. Furthermore, we show the practical utility of DeepZero in applications of certified adversarial defense and DL-based partial differential equation error correction, achieving 10-20% improvement over SOTA. We believe our results will inspire future research on scalable ZO optimization and contribute to advancing DL with black box. Codes are available at https://github.com/OPTML-Group/DeepZero.
Fourier Neural Operator (FNO) is a popular operator learning framework. It not only achieves the state-of-the-art performance in many tasks, but also is efficient in training and prediction. However, collecting training data for the FNO can be a costly bottleneck in practice, because it often demands expensive physical simulations. To overcome this problem, we propose Multi-Resolution Active learning of FNO (MRA-FNO), which can dynamically select the input functions and resolutions to lower the data cost as much as possible while optimizing the learning efficiency. Specifically, we propose a probabilistic multi-resolution FNO and use ensemble Monte-Carlo to develop an effective posterior inference algorithm. To conduct active learning, we maximize a utility-cost ratio as the acquisition function to acquire new examples and resolutions at each step. We use moment matching and the matrix determinant lemma to enable tractable, efficient utility computation. Furthermore, we develop a cost annealing framework to avoid over-penalizing high-resolution queries at the early stage. The over-penalization is severe when the cost difference is significant between the resolutions, which renders active learning often stuck at low-resolution queries and inferior performance. Our method overcomes this problem and applies to general multi-fidelity active learning and optimization problems. We have shown the advantage of our method in several benchmark operator learning tasks. The code is available at https://github.com/shib0li/MRA-FNO.
Predicting potential risks associated with the fatigue of key structural components is crucial in engineering design. However, fatigue often involves entangled complexities of material microstructures and service conditions, making diagnosis and prognosis of fatigue damage challenging. We report a statistical learning framework to predict the growth of fatigue cracks and the life-to-failure of the components under loading conditions with uncertainties. Digital libraries of fatigue crack patterns and the remaining life are constructed by high-fidelity physical simulations. Dimensionality reduction and neural network architectures are then used to learn the history dependence and nonlinearity of fatigue crack growth. Path-slicing and re-weighting techniques are introduced to handle the statistical noises and rare events. The predicted fatigue crack patterns are self-updated and self-corrected by the evolving crack patterns. The end-to-end approach is validated by representative examples with fatigue cracks in plates, which showcase the digital-twin scenario in real-time structural health monitoring and fatigue life prediction for maintenance management decision-making.
This paper presents Sim-Suction, a robust object-aware suction grasp policy for mobile manipulation platforms with dynamic camera viewpoints, designed to pick up unknown objects from cluttered environments. Suction grasp policies typically employ data-driven approaches, necessitating large-scale, accurately-annotated suction grasp datasets. However, the generation of suction grasp datasets in cluttered environments remains underexplored, leaving uncertainties about the relationship between the object of interest and its surroundings. To address this, we propose a benchmark synthetic dataset, Sim-Suction-Dataset, comprising 500 cluttered environments with 3.2 million annotated suction grasp poses. The efficient Sim-Suction-Dataset generation process provides novel insights by combining analytical models with dynamic physical simulations to create fast and accurate suction grasp pose annotations. We introduce Sim-Suction-Pointnet to generate robust 6D suction grasp poses by learning point-wise affordances from the Sim-Suction-Dataset, leveraging the synergy of zero-shot text-to-segmentation. Real-world experiments for picking up all objects demonstrate that Sim-Suction-Pointnet achieves success rates of 96.76%, 94.23%, and 92.39% on cluttered level 1 objects (prismatic shape), cluttered level 2 objects (more complex geometry), and cluttered mixed objects, respectively. The Sim-Suction policies outperform state-of-the-art benchmarks tested by approximately 21% in cluttered mixed scenes.
Physical simulations that accurately model reality are crucial for many engineering disciplines such as mechanical engineering and robotic motion planning. In recent years, learned Graph Network Simulators produced accurate mesh-based simulations while requiring only a fraction of the computational cost of traditional simulators. Yet, the resulting predictors are confined to learning from data generated by existing mesh-based simulators and thus cannot include real world sensory information such as point cloud data. As these predictors have to simulate complex physical systems from only an initial state, they exhibit a high error accumulation for long-term predictions. In this work, we integrate sensory information to ground Graph Network Simulators on real world observations. In particular, we predict the mesh state of deformable objects by utilizing point cloud data. The resulting model allows for accurate predictions over longer time horizons, even under uncertainties in the simulation, such as unknown material properties. Since point clouds are usually not available for every time step, especially in online settings, we employ an imputation-based model. The model can make use of such additional information only when provided, and resorts to a standard Graph Network Simulator, otherwise. We experimentally validate our approach on a suite of prediction tasks for mesh-based interactions between soft and rigid bodies. Our method results in utilization of additional point cloud information to accurately predict stable simulations where existing Graph Network Simulators fail.
We present a general framework for the garment animation problem through unsupervised deep learning inspired in physically based simulation. Existing trends in the literature already explore this possibility. Nonetheless, these approaches do not handle cloth dynamics. Here, we propose the first methodology able to learn realistic cloth dynamics unsupervisedly, and henceforth, a general formulation for neural cloth simulation. The key to achieve this is to adapt an existing optimization scheme for motion from simulation based methodologies to deep learning. Then, analyzing the nature of the problem, we devise an architecture able to automatically disentangle static and dynamic cloth subspaces by design. We will show how this improves model performance. Additionally, this opens the possibility of a novel motion augmentation technique that greatly improves generalization. Finally, we show it also allows to control the level of motion in the predictions. This is a useful, never seen before, tool for artists. We provide of detailed analysis of the problem to establish the bases of neural cloth simulation and guide future research into the specifics of this domain.
We propose a method that leverages graph neural networks, multi-level message passing, and unsupervised training to enable real-time prediction of realistic clothing dynamics. Whereas existing methods based on linear blend skinning must be trained for specific garments, our method is agnostic to body shape and applies to tight-fitting garments as well as loose, free-flowing clothing. Our method furthermore handles changes in topology (e.g., garments with buttons or zippers) and material properties at inference time. As one key contribution, we propose a hierarchical message-passing scheme that efficiently propagates stiff stretching modes while preserving local detail. We empirically show that our method outperforms strong baselines quantitatively and that its results are perceived as more realistic than state-of-the-art methods.