Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems

• URL: http://arxiv.org/abs/2211.05520v1
• Date: Thu, 10 Nov 2022 12:29:30 GMT
• Title: Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems
• Authors: Abishek Thangamuthu, Gunjan Kumar, Suresh Bishnoi, Ravinder Bhattoo, N M Anoop Krishnan, Sayan Ranu
• Abstract summary: We evaluate the performance of graph neural networks (GNNs) and their variants with explicit constraints and different architectures. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. All the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
• Score: 5.787429262238507
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.

Related papers

• Learning System Dynamics without Forgetting [60.08612207170659]
  Predicting trajectories of systems with unknown dynamics is crucial in various research fields, including physics and biology. We present a novel framework of Mode-switching Graph ODE (MS-GODE), which can continually learn varying dynamics. We construct a novel benchmark of biological dynamic systems, featuring diverse systems with disparate dynamics.
  arXiv  Detail & Related papers  (2024-06-30T14:55:18Z)
• Mechanistic Neural Networks for Scientific Machine Learning [58.99592521721158]
  We present Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential equations as representations. Central to our approach is a novel Relaxed Linear Programming solver (NeuRLP) inspired by a technique that reduces solving linear ODEs to solving linear programs.
  arXiv  Detail & Related papers  (2024-02-20T15:23:24Z)
• Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-time Dynamics [13.912268915939656]
  The prevailing approach of integrating graph neural networks with ordinary differential equations has demonstrated promising performance. We introduce a novel approach: a signed graph neural ordinary differential equation, adeptly addressing the limitations of miscapturing signed information. Our proposed solution boasts both flexibility and efficiency.
  arXiv  Detail & Related papers  (2023-12-18T13:45:33Z)
• SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases [66.61789780666727]
  We show how the second-order continuity can be incorporated into GNNs while maintaining the equivariant property. We also offer theoretical insights into SEGNO, highlighting that it can learn a unique trajectory between adjacent states. Our model yields a significant improvement over the state-of-the-art baselines.
  arXiv  Detail & Related papers  (2023-08-25T07:15:58Z)
• Graph Neural Stochastic Differential Equations for Learning Brownian Dynamics [6.362339104761225]
  We propose a framework namely Brownian graph neural networks (BROGNET) to learn Brownian dynamics directly from the trajectory. We show that BROGNET conserves the linear momentum of the system, which in turn, provides superior performance on learning dynamics.
  arXiv  Detail & Related papers  (2023-06-20T10:30:46Z)
• 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)
• Learning Physical Dynamics with Subequivariant Graph Neural Networks [99.41677381754678]
  Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization. Our model achieves on average over 3% enhancement in contact prediction accuracy across 8 scenarios on Physion and 2X lower rollout MSE on RigidFall.
  arXiv  Detail & Related papers  (2022-10-13T10:00:30Z)
• Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systems [19.634451472032733]
  We present a graph based neural ODE, GNODE, to learn the time evolution of dynamical systems. We show that, similar to LNN and HNN, encoding the constraints explicitly can significantly improve the training efficiency and performance of GNODE. We demonstrate that inducing these biases can enhance the performance of model by orders of magnitude in terms of both energy violation and rollout error.
  arXiv  Detail & Related papers  (2022-09-22T02:20:29Z)
• Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networks [5.560715621814096]
  We present a framework, namely, Lagrangian graph neural network (LGnn), that provides a strong inductive bias to learn the Lagrangian of a particle-based system directly from the trajectory. We show the zero-shot generalizability of the system by simulating systems two orders of magnitude larger than the trained one and also hybrid systems that are unseen by the model.
  arXiv  Detail & Related papers  (2022-09-03T18:38:17Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Continuous-in-Depth Neural Networks [107.47887213490134]
  We first show that ResNets fail to be meaningful dynamical in this richer sense. We then demonstrate that neural network models can learn to represent continuous dynamical systems. We introduce ContinuousNet as a continuous-in-depth generalization of ResNet architectures.
  arXiv  Detail & Related papers  (2020-08-05T22:54:09Z)

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.