Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains

• URL: http://arxiv.org/abs/2410.11480v1
• Date: Tue, 15 Oct 2024 10:31:22 GMT
• Title: Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domains
• Authors: Razmik Arman Khosrovian, Takaharu Yaguchi, Hiroaki Yoshimura, Takashi Matsubara,
• Abstract summary: We propose a novel framework based on the Dirac structure that unifies the port-Hamiltonian and Poisson formulations from geometric mechanics. PoDiNNs offer improved accuracy and interpretability in modeling unknown coupled dynamical systems from data.
• Score: 13.499500088995463
• License:
• Abstract: Deep learning has achieved great success in modeling dynamical systems, providing data-driven simulators to predict complex phenomena, even without known governing equations. However, existing models have two major limitations: their narrow focus on mechanical systems and their tendency to treat systems as monolithic. These limitations reduce their applicability to dynamical systems in other domains, such as electrical and hydraulic systems, and to coupled systems. To address these limitations, we propose Poisson-Dirac Neural Networks (PoDiNNs), a novel framework based on the Dirac structure that unifies the port-Hamiltonian and Poisson formulations from geometric mechanics. This framework enables a unified representation of various dynamical systems across multiple domains as well as their interactions and degeneracies arising from couplings. Our experiments demonstrate that PoDiNNs offer improved accuracy and interpretability in modeling unknown coupled dynamical systems from data.

Related papers

• Learning Subsystem Dynamics in Nonlinear Systems via Port-Hamiltonian Neural Networks [0.0]
  Port-Hamiltonian neural networks (pHNNs) are emerging as a powerful modeling tool that integrates physical laws with deep learning techniques. This study introduces a novel method for using pHNNs to identify such subsystems based solely on input-output measurements.
  arXiv  Detail & Related papers  (2024-11-08T17:41:51Z)
• Discovering Governing equations from Graph-Structured Data by Sparse Identification of Nonlinear Dynamical Systems [0.27624021966289597]
  We develop a new method called Sparse Identification of Dynamical Systems from Graph-structured data (SINDyG) SINDyG incorporates the network structure into sparse regression to identify model parameters that explain the underlying network dynamics.
  arXiv  Detail & Related papers  (2024-09-02T17:51:37Z)
• 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)
• Learning Governing Equations of Unobserved States in Dynamical Systems [0.0]
  We employ a hybrid neural ODE structure to learn governing equations of partially-observed dynamical systems. We demonstrate that the method is capable of successfully learning the true underlying governing equations of unobserved states within these systems.
  arXiv  Detail & Related papers  (2024-04-29T10:28:14Z)
• 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)
• Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs [70.51212431290611]
  Partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. We propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d Navier-Stokes equation.
  arXiv  Detail & Related papers  (2022-04-13T08:53:41Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• 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)
• Physics-guided Deep Markov Models for Learning Nonlinear Dynamical Systems with Uncertainty [6.151348127802708]
  We propose a physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM) The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system.
  arXiv  Detail & Related papers  (2021-10-16T16:35:12Z)
• Learning Stable Deep Dynamics Models [91.90131512825504]
  We propose an approach for learning dynamical systems that are guaranteed to be stable over the entire state space. We show that such learning systems are able to model simple dynamical systems and can be combined with additional deep generative models to learn complex dynamics.
  arXiv  Detail & Related papers  (2020-01-17T00:04:45Z)

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.