Kalman-Bucy-Informed Neural Network for System Identification

TL;DR

This paper introduces a novel neural network approach that integrates Kalman filtering principles to accurately identify parameters in stochastic continuous-time systems with noisy data, demonstrated on a double pendulum.

Contribution

It combines physics-informed neural networks with Kalman filter techniques to improve parameter estimation in noisy, nonlinear systems, a novel integration in system identification.

Findings

Successfully identified parameters of a double pendulum system.

Estimated system state mean and covariance alongside parameters.

Effective in noisy measurement scenarios.

Abstract

Identifying parameters in a system of nonlinear, ordinary differential equations is vital for designing a robust controller. However, if the system is stochastic in its nature or if only noisy measurements are available, standard optimization algorithms for system identification usually fail. We present a new approach that combines the recent advances in physics-informed neural networks and the well-known achievements of Kalman filters in order to find parameters in a continuous-time system with noisy measurements. In doing so, our approach allows estimating the parameters together with the mean value and covariance matrix of the system's state vector. We show that the method works for complex systems by identifying the parameters of a double pendulum.