DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization

Abstract

Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon Optimization (DySMHO), a scalable machine learning framework for identifying governing laws in the form of differential equations from large-scale noisy experimental data sets. DySMHO consists of a novel moving horizon dynamic optimization strategy that sequentially learns the underlying governing equations from a large dictionary of basis functions. The sequential nature of DySMHO allows leveraging statistical arguments for eliminating irrelevant basis functions, avoiding overfitting to recover accurate and parsimonious forms of the governing equations. Canonical nonlinear dynamical system examples are used to demonstrate that DySMHO can accurately recover the governing laws, is robust to high levels of measurement noise and that it can handle challenges such as multiple time scale dynamics.

References in corpus (15)

• Scikit-learn: Machine Learning in Python
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
• fPINNs: Fractional Physics-Informed Neural Networks
• Explainable Machine Learning for Scientific Insights and Discoveries
• Data-driven discovery of coordinates and governing equations
• PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs
• PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
• Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
• Weak SINDy: Galerkin-Based Data-Driven Model Selection
• Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics
• Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression
• DLGA-PDE: Discovery of PDEs with incomplete candidate library via combination of deep learning and genetic algorithm
• Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach

Cited by in corpus (5)

• Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion
• Data-driven sparse modeling of oscillations in plasma space propulsion
• Enhancing model identification with SINDy via nullcline reconstruction
• Testing topological conjugacy of time series
• Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering