multiscale methods

Physics-informed Neural Networks for Learning the Homogenized Coefficients of Multiscale Elliptic Equations

Dr. Jun Sur Richard Park, Korea Institute for Advanced Study

Jan 10, 10:00 - 11:00

KAUST

Physics-informed Neural Networks multiscale methods Homogenization

Abstract Multiscale elliptic equations with scale separation are often approximated by the corresponding homogenized equations with slowly varying homogenized coefficients (the G-limit). The traditional homogenization techniques typically rely on the periodicity of the multiscale coefficients, thus finding the G-limits often requires sophisticated techniques in more general settings even when multiscale coefficient is known, if possible. Alternatively, we propose a simple approach to estimate the G-limits from (noisy-free or noisy) multiscale solution data, either from the existing forward