Recovering the state and dynamics of autonomous system with partial states solution using neural networks

TL;DR

This paper demonstrates that neural networks can effectively recover the states and dynamics of autonomous systems described by differential equations, even with partial state information, using deep hidden physics models.

Contribution

It applies deep hidden physics models to estimate states and dynamics of autonomous systems with incomplete data, extending their use to new types of systems.

Findings

Neural networks can estimate unknown states in autonomous systems.

Partial state information suffices to recover system dynamics.

The approach works on linear, nonlinear, and Lorenz systems.

Abstract

In this paper we explore the performance of deep hidden physics model (M. Raissi 2018) for autonomous systems. These systems are described by set of ordinary differential equations which do not explicitly depend on time. Such systems can be found in nature and have applications in modeling chemical concentrations, population dynamics, n-body problems in physics etc. In this work we consider dynamics of states, which explain how the states will evolve are unknown to us. We approximate state and dynamics both using neural networks. We have considered examples of 2D linear/nonlinear and Lorenz systems. We observe that even without knowing all the states information, we can estimate dynamics of certain states whose state information are known.