2.5k citations · 6.9k across the 23 of their papers we have counts for
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physics.comp-ph2021★ 28 cited
A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data
Lu Lu, Xuhui Meng, Shengze Cai +4
Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applica…
cs.LG2021★ 714 cited
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
Jeremy Yu, Lu Lu, Xuhui Meng +1
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual…
cs.LG2021★ 61 cited
Learning Functional Priors and Posteriors from Data and Physics
Xuhui Meng, Liu Yang, Zhiping Mao +2
We develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both nois…