Meta-State-Space Learning: An Identification Approach for Stochastic Dynamical Systems

TL;DR

This paper introduces a novel neural network-based method for identifying stochastic dynamical systems by representing them in a deterministic meta-state-space form, enabling accurate modeling of time-varying output distributions without restrictive assumptions.

Contribution

The paper presents a new exact meta-state-space representation for nonlinear stochastic systems and an ANN-based identification method that captures their dynamics efficiently.

Findings

Achieves high log-likelihood close to the theoretical limit.

Effectively models highly nonlinear and stochastic systems.

Provides a deterministic framework for stochastic system identification.

Abstract

Available methods for identification of stochastic dynamical systems from input-output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability distributions. In this paper, we introduce a novel identification method of such systems, which results in a dynamical model that is able to produce the time-varying output distribution accurately without taking restrictive assumptions on the data-generating process. The method is formulated by first deriving a novel and exact representation of a wide class of nonlinear stochastic systems in a so-called meta-state-space form, where the meta-state can be interpreted as a parameter vector of a state probability function space parameterization. As the resulting representation of the meta-state dynamics is deterministic, we can capture the stochastic system based on a deterministic model, which is highly attractive for identification. The meta-state-space representation often involves unknown and heavily nonlinear functions, hence, we propose an Artificial Neural Network (ANN)-based identification method capable of efficiently learning nonlinear meta-state-space models. We demonstrate that the proposed identification method can obtain models with a log-likelihood close to the theoretical limit even for highly nonlinear, highly stochastic systems.