SINDy-BVP: Sparse identification of nonlinear dynamics for boundary value problems

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