Dynamics-Encoded Deep Learning for Robust System Identification and Parameter Estimation
It provides a method for robust system identification and parameter estimation in dynamical systems, which is important for scientific modeling but is incremental in combining existing techniques.
The paper combines deep learning with numerical methods for differential equations to address dynamics discovery and parameter estimation in dynamical systems, achieving robust predictions on oscillatory and chaotic test problems with corrupt observations.
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.