Dynamics-Encoded Deep Learning for Robust System Identification and Parameter Estimation

TL;DR

This paper introduces a deep learning framework that integrates physics knowledge and numerical methods to improve system identification and parameter estimation in dynamical systems, especially under noisy observations.

Contribution

It combines deep learning with classical numerical schemes to enhance robustness and interpretability in discovering system dynamics and estimating parameters.

Findings

Effective data-driven predictions on oscillatory and chaotic systems.

Numerical scheme choices significantly impact prediction accuracy.

Promising results with Runge-Kutta and linear multistep methods.

Abstract

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two challenging missing physics problems in dynamical systems theory: dynamics discovery and parameter estimation. The presented methods encode available information relating to the system dynamics into deep learning architectures, incorporating different assumptions on the known inputs and desired outputs in each case. Results demonstrate the effectiveness of the proposed approaches in making data-driven model predictions given corrupt system observations on a suite of test problems exhibiting oscillatory and chaotic dynamics. When comparing the performance of various numerical schemes, such as the Runge-Kutta and linear multistep families of methods, we observe promising results in predicting the system dynamics and estimating physical parameters, given appropriate choices of spatial and temporal discretization schemes and numerical method orders.