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arXiv Machine Learning By Jan Tauberschmidt, Jephte Abijuru, Samuel Okon, Naukshatro Bose, Sophie Fellenz, Marius Kloft, Jonas Latz, Sebastian Josef Vollmer

Learning PDE Dynamics between Submanifolds Using Green's Observation Operators

Read the original on arXiv Machine Learning →

The paper introduces the Green's Observation Operator (GObO), a method that maps the ambient medium to the Green's kernel of a linear PDE restricted to source and observation submanifolds. This approach allows new sources to be evaluated with a single lower-dimensional integral, avoiding full-domain solvers and black-box surrogate evaluations. Experiments on 3‑D heat conduction and advection–diffusion show that GObO, trained on static sources, can predict moving-source responses with 4–8× lower error than black-box surrogates, achieving 1.4 ms per query after a single conditioning pass.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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