Coarse-Grained Nonlinear System Identification

• URL: http://arxiv.org/abs/2010.06830v1
• Date: Wed, 14 Oct 2020 06:45:51 GMT
• Title: Coarse-Grained Nonlinear System Identification
• Authors: Span Spanbauer, Ian Hunter
• Abstract summary: We introduce Coarse-Grained Dynamics, an efficient and universal parameterization of nonlinear system dynamics based on the Volterra series expansion. 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 dynamics of a tungsten filament with less than a second of experimental data.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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