chebgreen: Learning and interpolating continuous Empirical Green's Functions from data

In this work, we present a mesh-independent, data-driven library, chebgreen, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is unknown. The proposed method learns an Empirical Green's Function for th...

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Vydáno v:Computer physics communications Ročník 317; s. 109867
Hlavní autoři: Praveen, Harshwardhan, Brown, Jacob, Earls, Christopher
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.12.2025
Témata:
Chebyshev polynomials
Green's function
Manifold interpolation
PDE learning
Singular value expansion
Singular value expansion
Green's function
Manifold interpolation
PDE learning
Chebyshev polynomials
ISSN:0010-4655
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Shrnutí:In this work, we present a mesh-independent, data-driven library, chebgreen, to mathematically model one-dimensional systems, possessing an associated control parameter, and whose governing partial differential equation is unknown. The proposed method learns an Empirical Green's Function for the associated, but hidden, boundary value problem, in the form of a Rational Neural Network from which we subsequently construct a bivariate representation in a Chebyshev basis. We uncover the Green's function, at an unseen control parameter value, by interpolating the left and right singular functions within a suitable library, expressed as points on a manifold of Quasimatrices, while the associated singular values are interpolated with Lagrange polynomials. This work improves upon prior work by extending the scope of applicability to non-self-adjoint operators and improves data efficiency.
ISSN:0010-4655
DOI:10.1016/j.cpc.2025.109867