Coarse-Grained Nonlinear System Identification
This addresses the challenge of data-efficient nonlinear system identification for applications like physical modeling, though it appears incremental as it builds on Volterra series expansions.
The paper tackles the problem of efficiently identifying nonlinear dynamic systems by introducing Coarse-Grained Nonlinear Dynamics, which reduces the number of parameters to quasilinear in system memory, enabling accurate modeling with less than a second of experimental data for a tungsten filament.
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.