Discovering Sparse Interpretable Dynamics from Partial Observations
This addresses the challenge of modeling complex systems with incomplete data, which is incremental as it builds on existing sparse symbolic methods by incorporating partial observations.
The authors tackled the problem of identifying governing equations of nonlinear dynamical systems from partial observations, proposing a framework that combines an encoder for state reconstruction with a sparse symbolic model, and demonstrated successful reconstruction and identification for various ODE and PDE systems.
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.