Equivariant Graph Neural Operator for Modeling 3D Dynamics

• URL: http://arxiv.org/abs/2401.11037v2
• Date: Sun, 2 Jun 2024 04:43:30 GMT
• Title: Equivariant Graph Neural Operator for Modeling 3D Dynamics
• Authors: Minkai Xu, Jiaqi Han, Aaron Lou, Jean Kossaifi, Arvind Ramanathan, Kamyar Azizzadenesheli, Jure Leskovec, Stefano Ermon, Anima Anandkumar,
• Abstract summary: We propose Equivariant Graph Neural Operator (EGNO) to directly models dynamics as trajectories instead of just next-step prediction. EGNO explicitly learns the temporal evolution of 3D dynamics where we formulate the dynamics as a function over time and learn neural operators to approximate it. Comprehensive experiments in multiple domains, including particle simulations, human motion capture, and molecular dynamics, demonstrate the significantly superior performance of EGNO against existing methods.
• Score: 148.98826858078556
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning methods have achieved good success by learning graph neural networks to model spatial interactions. However, these approaches do not faithfully capture temporal correlations since they only model next-step predictions. In this work, we propose Equivariant Graph Neural Operator (EGNO), a novel and principled method that directly models dynamics as trajectories instead of just next-step prediction. Different from existing methods, EGNO explicitly learns the temporal evolution of 3D dynamics where we formulate the dynamics as a function over time and learn neural operators to approximate it. To capture the temporal correlations while keeping the intrinsic SE(3)-equivariance, we develop equivariant temporal convolutions parameterized in the Fourier space and build EGNO by stacking the Fourier layers over equivariant networks. EGNO is the first operator learning framework that is capable of modeling solution dynamics functions over time while retaining 3D equivariance. Comprehensive experiments in multiple domains, including particle simulations, human motion capture, and molecular dynamics, demonstrate the significantly superior performance of EGNO against existing methods, thanks to the equivariant temporal modeling. Our code is available at https://github.com/MinkaiXu/egno.

Related papers

• Trajectory Flow Matching with Applications to Clinical Time Series Modeling [77.58277281319253]
  Trajectory Flow Matching (TFM) trains a Neural SDE in a simulation-free manner, bypassing backpropagation through the dynamics. We demonstrate improved performance on three clinical time series datasets in terms of absolute performance and uncertainty prediction.
  arXiv  Detail & Related papers  (2024-10-28T15:54:50Z)
• Equivariant Spatio-Temporal Attentive Graph Networks to Simulate Physical Dynamics [32.115887916401036]
  We develop an equivariant version of Fourier-temporal GNNs to represent and simulate dynamics of physical systems. We evaluate our model on three real datasets corresponding to the molecular-, protein- and macro-level.
  arXiv  Detail & Related papers  (2024-05-21T15:33:21Z)
• Dynamic Tensor Decomposition via Neural Diffusion-Reaction Processes [24.723536390322582]
  tensor decomposition is an important tool for multiway data analysis. We propose Dynamic EMbedIngs fOr dynamic algorithm dEcomposition (DEMOTE) We show the advantage of our approach in both simulation study and real-world applications.
  arXiv  Detail & Related papers  (2023-10-30T15:49:45Z)
• Learning Lagrangian Fluid Mechanics with E($3$)-Equivariant Graph Neural Networks [2.1401663582288144]
  equivariant graph neural networks have the potential to learn more accurate dynamic-interaction models. We benchmark two well-studied fluid-flow systems, namely 3D decaying Taylor-Green vortex and 3D reverse Poiseuille flow. We find that while currently being rather slow to train and evaluate, equivariant models with our proposed history embeddings learn more accurate physical interactions.
  arXiv  Detail & Related papers  (2023-05-24T22:26:38Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• E($3$) Equivariant Graph Neural Networks for Particle-Based Fluid Mechanics [2.1401663582288144]
  We demonstrate that equivariant graph neural networks have the potential to learn more accurate dynamic-interaction models. We benchmark two well-studied fluid flow systems, namely the 3D decaying Taylor-Green vortex and the 3D reverse Poiseuille flow.
  arXiv  Detail & Related papers  (2023-03-31T21:56:35Z)
• Gait Recognition in the Wild with Multi-hop Temporal Switch [81.35245014397759]
  gait recognition in the wild is a more practical problem that has attracted the attention of the community of multimedia and computer vision. This paper presents a novel multi-hop temporal switch method to achieve effective temporal modeling of gait patterns in real-world scenes.
  arXiv  Detail & Related papers  (2022-09-01T10:46:09Z)
• Equivariant vector field network for many-body system modeling [65.22203086172019]
  Equivariant Vector Field Network (EVFN) is built on a novel equivariant basis and the associated scalarization and vectorization layers. We evaluate our method on predicting trajectories of simulated Newton mechanics systems with both full and partially observed data.
  arXiv  Detail & Related papers  (2021-10-26T14:26:25Z)
• E(n) Equivariant Graph Neural Networks [86.75170631724548]
  This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs) In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance.
  arXiv  Detail & Related papers  (2021-02-19T10:25:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.