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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...
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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