DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization
This addresses the challenge of understanding physical and chemical systems for scientists and engineers, though it appears incremental as it builds on existing data-driven discovery methods.
The authors tackled the problem of discovering governing differential equations from noisy experimental data by introducing DySMHO, a scalable machine learning framework that uses moving horizon optimization to accurately and parsimoniously recover equations, demonstrating robustness to high noise and multiple time scales.
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.