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20162026
most citedDeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

3.4k citations · 4.7k across the 10 of their papers we have counts for

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cs.LG2019★ 3.4k cited

DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Lu Lu, Pengzhan Jin, George Em Karniadakis

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a sin…

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…