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20182023
most citedB-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data

1.2k citations · 1.5k across the 15 of their papers we have counts for

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stat.ML2018★ 59 cited

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

Liu Yang, Dongkun Zhang, George Em Karniadakis

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve in a unified manner forward, inverse and mixed stochastic problems based on a limite…

cs.LG2018★ 77 cited

Neural-net-induced Gaussian process regression for function approximation and PDE solution

Guofei Pang, Liu Yang, George Em Karniadakis

Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of G…