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A neural surrogate with analytic derivatives is used to detect separability, recursively reducing multivariate problems to simpler neural atoms, and provides a practical route from neural surrogates to interpretable closed-form empirical laws.
NestyNet, a coupled model-and-optimizer framework capable of fitting difficult scientific surrogates to high accuracy while also delivering their gradients, Hessians, Laplacians, and antiderivatives analytically and at low cost, is presented.
NestyNet-DE addresses differential-equation discovery via two complementary DE search strategies, both employing analytic derivatives from segmented neural surrogates: a sparse-library route linear in the outer coefficients, and a new operator-factorized route that searches directly over equation structure rather than...
Tabular foundation models (TFMs) learn to fill in tables the way language models fill in text, and tables are arguably the format in which most physical measurement arrives. Did they learn any physics in the process? They are Bayesian by construction, so the question is what their prior contains. We probe it directly,...
A low-dimensional posterior for the fitted function itself, for scientific neural surrogates trained with second-order optimization, provides a highly efficient route to uncertainty propagation for derivative-dependent scientific inference.
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