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Scientific Computing
PDE and Machine Learning (4): Variational Inference and the Fokker-Planck Equation
Variational inference and Langevin MCMC are two faces of the same Fokker-Planck PDE. We derive the equivalence, build SVGD as an interacting-particle approximation, and quantify convergence under log-Sobolev …
PDE and Machine Learning (2) — Neural Operator Theory
A classical PDE solver — finite difference, finite element, spectral — is a function: feed it one initial condition and one set of coefficients, get back one solution. A PINN is the same kind of …