A framework for fitting quadratic-bilinear systems with applications to models of electrical circuits

TL;DR

This paper introduces a data-driven framework for fitting quadratic-bilinear surrogate models to nonlinear electrical circuit dynamics by embedding original models into a quadratic-bilinear form using lifting techniques and transfer function data.

Contribution

It extends existing bilinear and quadratic inference methods by combining them into a unified approach for nonlinear model approximation from transfer function data.

Findings

Effective in modeling electrical circuits with nonlinear components.

Accurate approximation demonstrated on various test cases.

Framework leverages classical linear fitting and nonlinear operator inference.

Abstract

In this contribution, we propose a data-driven procedure to fit quadratic-bilinear surrogate models from data. Although the dynamics characterizing the original model are strongly nonlinear, we rely on lifting techniques to embed the original model into a quadratic-bilinear format. Here, data represent generalized transfer function values. This method is an extension of methods that do bilinear, or quadratic inference, separately. It is based on first fitting a linear model with the classical Loewner framework, and then on inferring the best supplementing nonlinear operators, in a least-squares sense. The application scope of this method is given by electrical circuits with nonlinear components (such as diodes). We propose various test cases to illustrate the performance of the method.