Discovering Sparse Interpretable Dynamics from Partial Observations

TL;DR

This paper introduces a machine learning framework that reconstructs full system states and identifies governing equations of nonlinear dynamical systems from partial observations, enhancing understanding and modeling accuracy.

Contribution

It presents a novel approach combining state reconstruction with sparse symbolic modeling to discover dynamics from limited data.

Findings

Successfully reconstructs full states from partial observations.

Accurately identifies underlying dynamics of ODE and PDE systems.

Demonstrates effectiveness across various nonlinear systems.

Abstract

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We propose a machine learning framework for discovering these governing equations using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. Our tests show that this method can successfully reconstruct the full system state and identify the underlying dynamics for a variety of ODE and PDE systems.