PCELM overcomes nonconvex optimization difficulties in neural approximations of Stefan problems by using an initial rough fit followed by a perturbation-based convex correction step that improves relative L2 accuracy by 2-6 orders of magnitude.
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Extends a neural pushforward solver to the Wigner equation via operator simplification to finite differences and a signed decomposition to manage negativity.
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PCELM: Perturbation-Correction Extreme Learning Machine for the Stefan problem
PCELM overcomes nonconvex optimization difficulties in neural approximations of Stefan problems by using an initial rough fit followed by a perturbation-based convex correction step that improves relative L2 accuracy by 2-6 orders of magnitude.
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Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation
Extends a neural pushforward solver to the Wigner equation via operator simplification to finite differences and a signed decomposition to manage negativity.