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Applications · Physics

Bocheng Zeng, Qi Wang, Mengtao Yan, Yang Liu, Ruizhi Chengze, Yi Zhang, Hongsheng Liu, Zidong Wang, Hao Sun

Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics (e.g., tremendous speedup gain compared with classical numerical methods). However, most existing neural models rely on rich training data, have limited extrapolation and generalization abilities, and suffer to produce precise or reliable physical prediction under intricate conditions (e.g., irregular mesh or geometry, complex boundary conditions, diverse PDE parameters, etc.). To this end, we propose a new graph learning approach, namely, Physics-encoded Message Passing Graph Network (PhyMPGN), to model spatiotemporal PDE systems on irregular meshes given small training datasets. Specifically, we incorporate a GNN into a numerical integrator to approximate the temporal marching of spatiotemporal dynamics for a given PDE system. Considering that many physical phenomena are governed by diffusion processes, we further design a learnable Laplace block, which encodes the discrete Laplace-Beltrami operator, to aid and guide the GNN learning in a physically feasible solution space. A boundary condition padding strategy is also designed to improve the model convergence and accuracy. Extensive experiments demonstrate that PhyMPGN is capable of accurately predicting various types of spatiotemporal dynamics on coarse unstructured meshes, consistently achieves the state-of-the-art results, and outperforms other baselines with considerable gains.

Applications · Chemistry and Drug Discovery

Zhengxi Lu, Shizhuo Cheng, Yuru Jiang, Yan Zhang, Min Zhang

Recent advances in protein backbone generation have achieved promising results under structural, functional, or physical constraints. However, existing methods lack the flexibility for precise topology control, limiting navigation of the backbone space. We present $\textbf{ProtPainter}$, a diffusion-based approach for generating protein backbones conditioned on 3D curves. ProtPainter follows a two-stage process: curve-based sketching and sketch-guided backbone generation. For the first stage, we propose $\textbf{CurveEncoder}$, which predicts secondary structure annotations from a curve to parametrize sketch generation. For the second stage, the sketch guides the generative process in Denoising Diffusion Probabilistic Modeling (DDPM) to generate backbones. During the process, we further introduce a fusion scheduling scheme, Helix-Gating, to control the scaling factors. To evaluate, we propose the first benchmark for topology-conditioned protein generation, introducing Protein Restoration Task and a new metric, self-consistency Topology Fitness (scTF). Experiments demonstrate ProtPainter's ability to generate topology-fit (scTF $>$ 0.8) and designable (scTM $>$ 0.5) backbones, with drawing and dragging tasks showcasing its flexibility and versatility.

Applications · Physics

Nils Wandel, Stefan Schulz, Reinhard Klein

Efficient physics simulations are essential for numerous applications, ranging from realistic cloth animations in video games, to analyzing pollutant dispersion in environmental sciences, to calculating vehicle drag coefficients in engineering applications. Unfortunately, analytical solutions to the underlying physical equations are rarely available, and numerical solutions are computationally demanding. Latest developments in the field of physics-based Deep Learning have led to promising efficiency gains but still suffer from limited generalization capabilities across multiple different PDEs. Thus, in this work, we introduce **Metamizer**, a novel neural optimizer that iteratively solves a wide range of physical systems without retraining by minimizing a physics-based loss function. To this end, our approach leverages a scale-invariant architecture that enhances gradient descent updates to accelerate convergence. Since the neural network itself acts as an optimizer, training this neural optimizer falls into the category of meta-optimization approaches. We demonstrate that Metamizer achieves high accuracy across multiple PDEs after training on the Laplace, advection-diffusion and incompressible Navier-Stokes equation as well as on cloth simulations. Remarkably, the model also generalizes to PDEs that were not covered during training such as the Poisson, wave and Burgers equation.

Applications · Physics

Long Wei, Haodong Feng, Yuchen Yang, Ruiqi Feng, Peiyan Hu, Xiang Zheng, Tao Zhang, Dixia Fan, Tailin Wu

The control problems of complex physical systems have broad applications in science and engineering. Previous studies have shown that generative control methods based on diffusion models offer significant advantages for solving these problems. However, existing generative control approaches face challenges in both performance and efficiency when extended to the closed-loop setting, which is essential for effective control. In this paper, we propose an efficient Closed-Loop Diffusion method for Physical systems Control (CL-DiffPhyCon). By employing an asynchronous denoising framework for different physical time steps, CL-DiffPhyCon generates control signals conditioned on real-time feedback from the system with significantly reduced computational cost during sampling. Additionally, the control process could be further accelerated by incorporating fast sampling techniques, such as DDIM. We evaluate CL-DiffPhyCon on two tasks: 1D Burgers' equation control and 2D incompressible fluid control. The results demonstrate that CL-DiffPhyCon achieves superior control performance with significant improvements in sampling efficiency. The code can be found at https://github.com/AI4Science-WestlakeU/CL_DiffPhyCon.

Applications · Physics

Peiyan Hu, Rui Wang, Xiang Zheng, Tao Zhang, Haodong Feng, Ruiqi Feng, Long Wei, Yue Wang, Zhi-Ming Ma, Tailin Wu

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 33.2% compared to the second-best baseline.

Applications · Genetics, Cell Biology, Health, etc

Ziwei Yang, Zheng Chen, XIN LIU, Rikuto Kotoge, Peng Chen, Yasuko Matsubara, Yasushi Sakurai, Jimeng Sun

Retrieving gene functional networks from knowledge databases presents a challenge due to the mismatch between disease networks and subtype-specific variations. Current solutions, including statistical and deep learning methods, often fail to effectively integrate gene interaction knowledge from databases or explicitly learn subtype-specific interactions. To address this mismatch, we propose GeSubNet, which learns a unified representation capable of predicting gene interactions while distinguishing between different disease subtypes. Graphs generated by such representations can be considered subtype-specific networks. GeSubNet is a multi-step representation learning framework with three modules: First, a deep generative model learns distinct disease subtypes from patient gene expression profiles. Second, a graph neural network captures representations of prior gene networks from knowledge databases, ensuring accurate physical gene interactions. Finally, we integrate these two representations using an inference loss that leverages graph generation capabilities, conditioned on the patient separation loss, to refine subtype-specific information in the learned representation. GeSubNet consistently outperforms traditional methods, with average improvements of 30.6%, 21.0%, 20.1%, and 56.6% across four graph evaluation metrics, averaged over four cancer datasets. Particularly, we conduct a biological simulation experiment to assess how the behavior of selected genes from over 11,000 candidates affects subtypes or patient distributions. The results show that the generated network has the potential to identify subtype-specific genes with an 83% likelihood of impacting patient distribution shifts.

Applications · Computer Vision

Jingnan Gao, Zhuo Chen, Xiaokang Yang, Yichao Yan

Neural radiance fields have recently revolutionized novel-view synthesis and achieved high-fidelity renderings. However, these methods sacrifice the geometry for the rendering quality, limiting their further applications including relighting and deformation. How to synthesize photo-realistic rendering while reconstructing accurate geometry remains an unsolved problem. In this work, we present AniSDF, a novel approach that learns fused-granularity neural surfaces with physics-based encoding for high-fidelity 3D reconstruction. Different from previous neural surfaces, our fused-granularity geometry structure balances the overall structures and fine geometric details, producing accurate geometry reconstruction. To disambiguate geometry from reflective appearance, we introduce blended radiance fields to model diffuse and specularity following the anisotropic spherical Gaussian encoding, a physics-based rendering pipeline. With these designs, AniSDF can reconstruct objects with complex structures and produce high-quality renderings. Furthermore, our method is a unified model that does not require complex hyperparameter tuning for specific objects. Extensive experiments demonstrate that our method boosts the quality of SDF-based methods by a great scale in both geometry reconstruction and novel-view synthesis.

Probabilistic Methods · Monte Carlo and Sampling Methods

Rishal Aggarwal, Daniel Penaherrera, Justin Shao, Minhyek Jeon, David Koes

Training a generative model with energy or unnormalized density functions is considered an important problem for physical systems such as molecules. This provides a path to train generative models to sample from the much desired Boltzmann distribution in situations of data scarcity. As of late, several generative frameworks have been proposed to target this problem. However, as we show in the following blog post, these methods have not been benchmarked sufficiently well against traditional Markov Chain Monte Carlo (MCMC) methods that are used to sample from energy functions. We take the example of two recent methods (IDEM and IEFM) and show that MCMC outperforms both methods in terms of number of energy evaluations and wall clock time on established baselines. With this, we suggest a “course correction” on the benchmarking of these models and comment on the utility and potential of generative models on these tasks.

Applications · Physics

Jindou Chen, Jidong Tian, Liang Wu, ChenXinWei, Xiaokang Yang, Yaohui Jin, Yanyan Xu

Modeling kinetic equations is essential for understanding the mechanisms of chemical reactions, yet a complex and time-consuming task. Kinetic equation prediction is formulated as a problem of dynamical symbolic regression (DSR) subject to physical chemistry constraints. Deep learning (DL) holds the potential to capture reaction patterns and predict kinetic equations from data of chemical species, effectively avoiding empirical bias and improving efficiency compared with traditional analytical methods. Despite numerous studies focusing on DSR and the introduction of Transformers to predict ordinary differential equations, the corresponding models lack generalization abilities across diverse categories of reactions. In this study, we propose KinFormer, a generalizable kinetic equation prediction model. KinFormer utilizes a conditional Transformer to model DSR under physical constraints and employs Monte Carlo Tree Search to apply the model to new types of reactions. Experimental results on 20 types of organic reactions demonstrate that KinFormer not only outperforms classical baselines, but also exceeds Transformer baselines in out-of-domain evaluations, thereby proving its generalization ability.

Applications · Genetics, Cell Biology, Health, etc

Ziwei Yang, Zheng Chen, XIN LIU, Rikuto Kotoge, Peng Chen, Yasuko Matsubara, Yasushi Sakurai, Jimeng Sun

Retrieving gene functional networks from knowledge databases presents a challenge due to the mismatch between disease networks and subtype-specific variations. Current solutions, including statistical and deep learning methods, often fail to effectively integrate gene interaction knowledge from databases or explicitly learn subtype-specific interactions. To address this mismatch, we propose GeSubNet, which learns a unified representation capable of predicting gene interactions while distinguishing between different disease subtypes. Graphs generated by such representations can be considered subtype-specific networks. GeSubNet is a multi-step representation learning framework with three modules: First, a deep generative model learns distinct disease subtypes from patient gene expression profiles. Second, a graph neural network captures representations of prior gene networks from knowledge databases, ensuring accurate physical gene interactions. Finally, we integrate these two representations using an inference loss that leverages graph generation capabilities, conditioned on the patient separation loss, to refine subtype-specific information in the learned representation. GeSubNet consistently outperforms traditional methods, with average improvements of 30.6%, 21.0%, 20.1%, and 56.6% across four graph evaluation metrics, averaged over four cancer datasets. Particularly, we conduct a biological simulation experiment to assess how the behavior of selected genes from over 11,000 candidates affects subtypes or patient distributions. The results show that the generated network has the potential to identify subtype-specific genes with an 83% likelihood of impacting patient distribution shifts.

Reinforcement Learning · Deep RL

Eliot Xing, Vernon Luk, Jean Oh

Recent advances in GPU-based parallel simulation have enabled practitioners to collect large amounts of data and train complex control policies using deep reinforcement learning (RL), on commodity GPUs. However, such successes for RL in robotics have been limited to tasks sufficiently simulated by fast rigid-body dynamics. Simulation techniques for soft bodies are comparatively several orders of magnitude slower, thereby limiting the use of RL due to sample complexity requirements. To address this challenge, this paper presents both a novel RL algorithm and a simulation platform to enable scaling RL on tasks involving rigid bodies and deformables. We introduce Soft Analytic Policy Optimization (SAPO), a maximum entropy first-order model-based actor-critic RL algorithm, which uses first-order analytic gradients from differentiable simulation to train a stochastic actor to maximize expected return and entropy. Alongside our approach, we develop Rewarped, a parallel differentiable multiphysics simulation platform that supports simulating various materials beyond rigid bodies. We re-implement challenging manipulation and locomotion tasks in Rewarped, and show that SAPO outperforms baselines over a range of tasks that involve interaction between rigid bodies, articulations, and deformables. Additional details at https://rewarped.github.io/.

Applications · Physics

Yan Xie, Minrui Lv, Chen-Song Zhang

Solving high wavenumber Helmholtz equations is notoriously challenging. Traditional solvers have yet to yield satisfactory results, and most neural network methods struggle to accurately solve cases with extremely high wavenumbers within heterogeneous media. This paper presents an advanced multigrid-hierarchical AI solver, tailored specifically for high wavenumber Helmholtz equations. We adapt the MGCNN architecture to align with the problem setting and incorporate a novel Fourier neural network (FNN) to match the characteristics of Helmholtz equations. FNN, mathematically akin to the convolutional neural network (CNN), enables faster propagation of source influence during the solve phase, making it particularly suitable for handling large size, high wavenumber problems. We conduct supervised learning tests against numerous neural operator learning methods to demonstrate the superior learning capabilities of our solvers. Additionally, we perform scalability tests using an unsupervised strategy to highlight our solvers' significant speedup over the most recent specialized AI solver and AI-enhanced traditional solver for high wavenumber Helmholtz equations. We also carry out an ablation study to underscore the effectiveness of the multigrid hierarchy and the benefits of introducing FNN. Notably, our solvers exhibit optimal convergence of $\mathcal{O}(k)$ up to $k \approx 2000$.

Deep Learning · Large Language Models

Santhosh Kumar Ramakrishnan, Erik Wijmans, Philipp Krähenbühl, Vladlen Koltun

Not yet. We present SPACE, a benchmark that systematically evaluates spatial cognition in frontier models. Our benchmark builds on decades of research in cognitive science. It evaluates large-scale mapping abilities that are brought to bear when an organism traverses physical environments, smaller-scale reasoning about object shapes and layouts, and cognitive infrastructure such as spatial attention and memory. For many tasks, we instantiate parallel presentations via text and images, allowing us to benchmark both large language models and large multimodal models. Results suggest that contemporary frontier models fall short of the spatial intelligence of animals, performing near chance level on a number of classic tests of animal cognition.

Deep Learning · Self-Supervised Learning

Manuel Cherep, Nikhil Singh

Learning robust audio representations currently demands extensive datasets of real-world sound recordings. By applying artificial transformations to these recordings, models can learn to recognize similarities despite subtle variations through techniques like contrastive learning. However, these transformations are only approximations of the true diversity found in real-world sounds, which are generated by complex interactions of physical processes, from vocal cord vibrations to the resonance of musical instruments. We propose a solution to both the data scale and transformation limitations, leveraging synthetic audio. By randomly perturbing the parameters of a sound synthesizer, we generate audio doppelgängers—synthetic positive pairs with causally manipulated variations in timbre, pitch, and temporal envelopes. These variations, difficult to achieve through augmentations of existing audio, provide a rich source of contrastive information. Despite the shift to randomly generated synthetic data, our method produces strong representations, outperforming real data on several standard audio classification tasks. Notably, our approach is lightweight, requires no data storage, and has only a single hyperparameter, which we extensively analyze. We offer this method as a complement to existing strategies for contrastive learning in audio, using synthesized sounds to reduce the data burden on practitioners.

Social Aspects · Trustworthy Machine Learning

Yanjie Li, Kaisheng Liang, Bin Xiao

Recent works have attacked person detectors using adversarial patches or static-3D-model-based texture modifications. However, these methods suffer from low attack success rates when faced with significant human movements. The primary challenge stems from the highly non-rigid nature of the human body and clothing. Current attacks fail to model these 3D non-rigid deformations caused by varied actions.Fortunately, recent research has shown significant progress in using NeRF for dynamic human modeling. In this paper, we introduce \texttt{UV-Attack}, a novel physical adversarial attack achieving high attack success rates in scenarios involving extensive and unseen actions. We address the challenges above by leveraging dynamic-NeRF-based UV mapping. Our method can generate human images across diverse actions and viewpoints and even create novel unseen actions by sampling from the SMPL parameter space. While dynamic NeRF models are capable of modeling human bodies, modifying their clothing textures is challenging due to the texture being embedded within neural network parameters.To overcome this, \texttt{UV-Attack} generates UV maps instead of RGB images and modifies the texture stacks. This approach enables real-time texture edits and makes attacks more practical. Finally, we propose a novel Expectation over Pose Transformation loss (EoPT) to improve the evasion success rate on unseen poses and views.Our experiments show that \texttt{UV-Attack} achieves a 92.7\% attack success rate against the FastRCNN model across varied poses in dynamic video settings, significantly outperforming the state-of-the-art AdvCaT attack, which only had a 28.5\% ASR. Moreover, we achieve 49.5\% ASR on the latest YOLOv8 detector in black-box settings. The code is available at https://github.com/PolyLiYJ/UV-Attack

Applications · Computer Vision

Hritik Bansal, Zongyu Lin, Tianyi Xie, Zeshun Zong, Michal Yarom, Yonatan Bitton, Chenfanfu Jiang, Yizhou Sun, Kai-Wei Chang, Aditya Grover

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. The code is available here: https://github.com/Hritikbansal/videophy.

Applications · Computer Vision

Xiaoyu Xiong, Changyu Hu, Chunru Lin, Pingchuan Ma, Chuang Gan, Tao Du

We present TopoGaussian, a holistic, particle-based pipeline for inferring the interior structure of an opaque object from easily accessible photos and videos as input. Traditional mesh-based approaches require tedious and error-prone mesh filling and fixing process, while typically output rough boundary surface. Our pipeline combines Gaussian Splatting with a novel, versatile particle-based differentiable simulator that simultaneously accommodates constitutive model, actuator, and collision, without interference with mesh. Based on the gradients from this simulator, we provide flexible choice of topology representation for optimization, including particle, neural implicit surface, and quadratic surface. The resultant pipeline takes easily accessible photos and videos as input and outputs the topology that matches the physical characteristics of the input. We demonstrate the efficacy of our pipeline on a synthetic dataset and four real-world tasks with 3D-printed prototypes. Compared with existing mesh-based method, our pipeline is 5.26x faster on average with improved shape quality. These results highlight the potential of our pipeline in 3D vision, soft robotics, and manufacturing applications.

Maxence Faldor, Antoine Cully

Cellular automata have become a cornerstone for investigating emergence and self-organization across diverse scientific disciplines, spanning neuroscience, artificial life, and theoretical physics. However, the absence of a hardware-accelerated cellular automata library limits the exploration of new research directions, hinders collaboration, and impedes reproducibility. In this work, we introduce CAX (Cellular Automata Accelerated in JAX), a high-performance and flexible open-source library designed to accelerate cellular automata research. CAX offers cutting-edge performance and a modular design through a user-friendly interface, and can support both discrete and continuous cellular automata with any number of dimensions. We demonstrate CAX's performance and flexibility through a wide range of benchmarks and applications. From classic models like elementary cellular automata and Conway's Game of Life to advanced applications such as growing neural cellular automata and self-classifying MNIST digits, CAX speeds up simulations up to 2,000 times faster. Furthermore, we demonstrate CAX's potential to accelerate research by presenting a collection of three novel cellular automata experiments, each implemented in just a few lines of code thanks to the library's modular architecture. Notably, we show that a simple one-dimensional cellular automaton can outperform GPT-4 on the 1D-ARC challenge.

Applications · Computer Vision

Hongze CHEN, Zehong Lin, Jun Zhang

We present GI-GS, a novel inverse rendering framework that leverages 3D Gaussian Splatting (3DGS) and deferred shading to achieve photo-realistic novel view synthesis and relighting. In inverse rendering, accurately modeling the shading processes of objects is essential for achieving high-fidelity results. Therefore, it is critical to incorporate global illumination to account for indirect lighting that reaches an object after multiple bounces across the scene. Previous 3DGS-based methods have attempted to model indirect lighting by characterizing indirect illumination as learnable lighting volumes or additional attributes of each Gaussian, while using baked occlusion to represent shadow effects. These methods, however, fail to accurately model the complex physical interactions between light and objects, making it impossible to construct realistic indirect illumination during relighting. To address this limitation, we propose to calculate indirect lighting using efficient path tracing with deferred shading. In our framework, we first render a G-buffer to capture the detailed geometry and material properties of the scene. Then, we perform physically-based rendering (PBR) only for direct lighting. With the G-buffer and previous rendering results, the indirect lighting can be calculated through a lightweight path tracing. Our method effectively models indirect lighting under any given lighting conditions, thereby achieving better novel view synthesis and competitive relighting. Quantitative and qualitative results show that our GI-GS outperforms existing baselines in both rendering quality and efficiency. Project page: https://stopaimme.github.io/GI-GS-site/.

Optimization · Everything Else

Qiang Liu, Mengyu Chu, Nils Thuerey

The loss functions of many learning problems contain multiple additive terms that can disagree and yield conflicting update directions. For Physics-Informed Neural Networks (PINNs), loss terms on initial/boundary conditions and physics equations are particularly interesting as they are well-established as highly difficult tasks. To improve learning the challenging multi-objective task posed by PINNs, we propose the ConFIG method, which provides conflict-free updates by ensuring a positive dot product between the final update and each loss-specific gradient. It also maintains consistent optimization rates for all loss terms and dynamically adjusts gradient magnitudes based on conflict levels. We additionally leverage momentum to accelerate optimizations by alternating the back-propagation of different loss terms. We provide a mathematical proof showing the convergence of the ConFIG method, and it is evaluated across a range of challenging PINN scenarios. ConFIG consistently shows superior performance and runtime compared to baseline methods. We also test the proposed method in a classic multi-task benchmark, where the ConFIG method likewise exhibits a highly promising performance. Source code is available at https://tum-pbs.github.io/ConFIG