SINDy-BVP: Sparse Identification of Nonlinear Dynamics for Boundary Value Problems

TL;DR

This paper introduces SINDy-BVP, a novel data-driven method that combines sparse identification and regression techniques to discover models of boundary value problems with spatially-dependent dynamics, applicable to various physical systems.

Contribution

The paper presents a new framework, SINDy-BVP, for system identification of boundary value problems using sparse regression, capable of inferring operators and parameters from data.

Findings

Successfully applied to Sturm-Liouville and elasticity problems

Able to infer spatially-dependent parameters and operators

Demonstrates broad applicability to nonlinear BVPs

Abstract

We develop a data-driven model discovery and system identification technique for spatially-dependent boundary value problems (BVPs). Specifically, we leverage the sparse identification of nonlinear dynamics (SINDy) algorithm and group sparse regression techniques with a set of forcing functions and corresponding state variable measurements to yield a parsimonious model of the system. The approach models forced systems governed by linear or nonlinear operators of the form $L[u(x)] = f(x)$ on a prescribed domain $x \in [a, b]$. We demonstrate the approach on a range of example systems, including Sturm-Liouville operators, beam theory (elasticity), and a class of nonlinear BVPs. The generated data-driven model is used to infer both the operator and/or spatially-dependent parameters that describe the heterogenous, physical quantities of the system. Our SINDy-BVP framework will enables the characterization of a broad range of systems, including for instance, the discovery of anisotropic materials with heterogeneous variability.