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

arXiv: https://arxiv.org/abs/2005.10756 · HTML: https://mlsanity.com/paper/2005.10756/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2020.

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## Abstract (arXiv)

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 ∈ [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.