Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversion

TL;DR

This paper explores the use of ensemble Kalman inversion, a gradient-free method, for training neural ODEs in system identification and control, showing competitive efficiency and solution quality.

Contribution

It introduces a novel application of EKI to neural ODE training for control and identification, including regularization techniques for optimal control problems.

Findings

EKI is effective for neural ODE training in system identification.

EKI achieves competitive runtime and solution quality compared to gradient-based methods.

The method is applicable to inverse problems with regularization in control tasks.

Abstract

Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to solve inverse problems within a Bayesian framework. Unlike backpropagation, EKI is a gradient-free optimization method that only necessitates the evaluation of artificial neural networks in forward passes. In this study, we examine the effectiveness of EKI in training neural ordinary differential equations (neural ODEs) for system identification and control tasks. To apply EKI to optimal control problems, we formulate inverse problems that incorporate a Tikhonov-type regularization term. Our numerical results demonstrate that EKI is an efficient method for training neural ODEs in system identification and optimal control problems, with runtime and quality of solutions that are competitive with commonly used gradient-based optimizers.