Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling

2021/09/11 by Kookjin Lee, Lee, Kookjin, Nathaniel Trask +3 · 11 citations
Computer Science · Engineering · Physics and Astronomy · #Control Systems and Identification #Model Reduction and Neural Networks #Structural Health Monitoring Techniques #cs.LG #physics.comp-ph

paper · pdf · doi:10.48550/arxiv.2109.05364

arxiv created 2021/09/11 · arxiv updated 2021/09/14

Abstract

Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability guarantees. We present here a unification of the Sparse Identification of Nonlinear Dynamics (SINDy) formalism with neural ordinary differential equations. The resulting framework allows learning of both "black-box" dynamics and learning of structure preserving bracket formalisms for both reversible and irreversible dynamics. We present a suite of benchmarks demonstrating effectiveness and structure preservation, including for chaotic systems.

Citations

• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Data-Driven multiscale modeling in mechanics

Cited by

• Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches
• Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurements
• Neural non-canonical Hamiltonian dynamics for long-time simulations
• Function Spaces Without Kernels: Learning Compact Hilbert Space Representations
• Parameter Robustness in Data-Driven Estimation of Dynamical Systems
• Data-driven Discovery of Digital Twins in Biomedical Research
• Meta-learning Structure-Preserving Dynamics
• Reversible and irreversible bracket-based dynamics for deep graph neural networks
• Discovering Symbolic Differential Equations with Symmetry Invariants
• Think like a Scientist: Physics-guided LLM Agent for Equation Discovery
• Equilibrium Conserving Neural Operators for Super-Resolution Learning

Related

• LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification
• SINDyG: Sparse Identification of Nonlinear Dynamical Systems from Graph-Structured Data, with Applications to Stuart-Landau Oscillator Networks
• Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI)
• Deep Generative Modeling for Identification of Noisy, Non-Stationary Dynamical Systems
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems