Coarse-Grained Nonlinear System Identification

TL;DR

This paper introduces a novel, efficient parameterization method for nonlinear system identification based on coarse-graining and Volterra series, significantly reducing parameters needed and enabling accurate modeling with minimal data.

Contribution

It presents a new coarse-grained nonlinear dynamics model that drastically reduces parameter complexity and improves data efficiency in system identification.

Findings

Achieves superpolynomial reduction in parameters with high-order Volterra series

Demonstrates accurate modeling of nonlinear voltage-luminosity dynamics with less than a second of data

Validates the approach on synthetic and real-world nonlinear systems

Abstract

We introduce Coarse-Grained Nonlinear Dynamics, an efficient and universal parameterization of nonlinear system dynamics based on the Volterra series expansion. These models require a number of parameters only quasilinear in the system's memory regardless of the order at which the Volterra expansion is truncated; this is a superpolynomial reduction in the number of parameters as the order becomes large. This efficient parameterization is achieved by coarse-graining parts of the system dynamics that depend on the product of temporally distant input samples; this is conceptually similar to the coarse-graining that the fast multipole method uses to achieve $\mathcal{O}(n)$ simulation of n-body dynamics. Our efficient parameterization of nonlinear dynamics can be used for regularization, leading to Coarse-Grained Nonlinear System Identification, a technique which requires very little experimental data to identify accurate nonlinear dynamic models. We demonstrate the properties of this approach on a simple synthetic problem. We also demonstrate this approach experimentally, showing that it identifies an accurate model of the nonlinear voltage to luminosity dynamics of a tungsten filament with less than a second of experimental data.