Continuous-time identification of dynamic state-space models by deep subspace encoding

TL;DR

This paper introduces SUBNET, a novel continuous-time nonlinear state-space model identification method using deep subspace encoding, which improves robustness, stability, and efficiency in modeling physical systems with external inputs and noise.

Contribution

It proposes a new estimation approach that combines subsections, an encoder, and state-derivative normalization for accurate CT NL-SS model identification.

Findings

Achieves state-of-the-art results on multiple benchmarks.

Ensures stability and numerical conditioning in training.

Demonstrates effectiveness with compact neural networks.

Abstract

Continuous-time (CT) modeling has proven to provide improved sample efficiency and interpretability in learning the dynamical behavior of physical systems compared to discrete-time (DT) models. However, even with numerous recent developments, the CT nonlinear state-space (NL-SS) model identification problem remains to be solved in full, considering common experimental aspects such as the presence of external inputs, measurement noise, latent states, and general robustness. This paper presents a novel estimation method that addresses all these aspects and that can obtain state-of-the-art results on multiple benchmarks with compact fully connected neural networks capturing the CT dynamics. The proposed estimation method called the subspace encoder approach (SUBNET) ascertains these results by efficiently approximating the complete simulation loss by evaluating short simulations on subsections of the data, by using an encoder function to estimate the initial state for each subsection and a novel state-derivative normalization to ensure stability and good numerical conditioning of the training process. We prove that the use of subsections increases cost function smoothness together with the necessary requirements for the existence of the encoder function and we show that the proposed state-derivative normalization is essential for reliable estimation of CT NL-SS models.