A data-driven library, chebgreen, learns continuous empirical Green's functions for unknown 1D linear PDEs and interpolates them across control parameters using manifold-based interpolation of singular functions.
Exponential map of a weak Riemannian Hilbert manifold
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We prove the Focal Index Lemma and the Rauch and Berger comparison theorems on a weak Riemannian Hilbert manifold with a smooth Levi-Civita connection and we apply these results to the free loop spaces of a compact manifold with the L^2 metrics
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chebgreen: Learning and Interpolating Continuous Empirical Green's Functions from Data
A data-driven library, chebgreen, learns continuous empirical Green's functions for unknown 1D linear PDEs and interpolates them across control parameters using manifold-based interpolation of singular functions.