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

TL;DR

DySMHO is a scalable machine learning framework that accurately discovers governing differential equations from large noisy datasets using a moving horizon optimization approach, effectively handling complex dynamics and noise.

Contribution

Introduces DySMHO, a novel moving horizon optimization method for data-driven discovery of differential equations, improving robustness and scalability in noisy, large-scale data.

Findings

Accurately recovers governing laws in nonlinear dynamical systems

Robust to high measurement noise levels

Handles multiple time scale dynamics effectively

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.