PINN-AFE uses multi-head attention and input convex networks to solve Monge-Ampère equations with claimed accuracy, efficiency, and extensions to image enhancement and medical registration.
PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network , volume=
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SINO learns PDE operators from limited data using spectral features from frequency indices, a Pi-block for nonlinearities, and a low-pass filter, achieving 1-2 orders of magnitude better accuracy than prior methods on 2D/3D benchmarks.
Data-driven equation discovery applied to liquid film flows identifies identifiability issues from multi-collinearity in monomial bases and early-time transients with large residuals.
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Spectral-inspired Operator Learning with Limited Data and Unknown Physics
SINO learns PDE operators from limited data using spectral features from frequency indices, a Pi-block for nonlinearities, and a low-pass filter, achieving 1-2 orders of magnitude better accuracy than prior methods on 2D/3D benchmarks.