mlsanityData to 14 Oct 2026

chebgreen: Learning and Interpolating Continuous Empirical Green's Functions from Data

arXiv 2501.18715 ↗First posted 30 Jan 2025cs.LG cs.NA math.NAcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 23 of its 54 references that are in the map. First posted on arXiv 30 Jan 2025.

Builds on

23 of 54 references.

References · 23

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11 more
  1. 2020Rational neural networkscited by 75
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Learning PDE Dynamics between Submanifolds Using Green's Observation Operatorscited by 0