Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networks

• URL: http://arxiv.org/abs/2209.01476v1
• Date: Sat, 3 Sep 2022 18:38:17 GMT
• Title: Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networks
• Authors: Ravinder Bhattoo, Sayan Ranu and N. M. Anoop Krishnan
• Abstract summary: 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.
• Score: 5.560715621814096
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physical systems are commonly represented as a combination of particles, the individual dynamics of which govern the system dynamics. However, traditional approaches require the knowledge of several abstract quantities such as the energy or force to infer the dynamics of these particles. Here, 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 test our approach on challenging systems with constraints and drag -- LGnn outperforms baselines such as feed-forward Lagrangian neural network (Lnn) with improved performance. We also 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, a unique feature. The graph architecture of LGnn significantly simplifies the learning in comparison to Lnn with ~25 times better performance on ~20 times smaller amounts of data. Finally, we show the interpretability of LGnn, which directly provides physical insights on drag and constraint forces learned by the model. LGnn can thus provide a fillip toward understanding the dynamics of physical systems purely from observable quantities.

Related papers

• 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)
• 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)
• Discovering Symbolic Laws Directly from Trajectories with Hamiltonian Graph Neural Networks [5.824034325431987]
  We present a Hamiltonian graph neural network (HGNN) that learns the dynamics of systems directly from their trajectory. We demonstrate the performance of HGNN on n-springs, n-pendulums, gravitational systems, and binary Lennard Jones systems.
  arXiv  Detail & Related papers  (2023-07-11T14:43:25Z)
• 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)
• Graph Neural Network-based surrogate model for granular flows [2.153852088624324]
  Granular flow dynamics is crucial for assessing various geotechnical risks, including landslides and debris flows. Traditional continuum and discrete numerical methods are limited by their computational cost in simulating large-scale systems. We develop a graph neural network-based simulator (GNS) that takes the current state of granular flow and predicts the next state using explicit integration by learning the local interaction laws.
  arXiv  Detail & Related papers  (2023-05-09T07:28:12Z)
• Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems [5.787429262238507]
  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.
  arXiv  Detail & Related papers  (2022-11-10T12:29:30Z)
• Learning Rigid Body Dynamics with Lagrangian Graph Neural Network [5.560715621814096]
  We present a Lagrangian graph neural network (LGNN) that can learn the dynamics of rigid bodies by exploiting their topology. We show that the LGNN can be used to model the dynamics of complex real-world structures such as the stability of tensegrity structures.
  arXiv  Detail & Related papers  (2022-09-23T13:41:54Z)
• NeuroFluid: Fluid Dynamics Grounding with Particle-Driven Neural Radiance Fields [65.07940731309856]
  Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids. In this paper, we consider a partially observable scenario known as fluid dynamics grounding. We propose a differentiable two-stage network named NeuroFluid. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities.
  arXiv  Detail & Related papers  (2022-03-03T15:13:29Z)
• 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)
• Learning to Simulate Complex Physics with Graph Networks [68.43901833812448]
  We present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains. Our framework---which we term "Graph Network-based Simulators" (GNS)--represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time.
  arXiv  Detail & Related papers  (2020-02-21T16:44:28Z)

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.