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

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.

References in corpus (2)

• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics

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