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20092026
most citedDeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

3.4k citations · 27.2k across the 213 of their papers we have counts for

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Showing 2017 · math.NAShow all

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math.NA2017★ 44 cited

A Riesz basis Galerkin method for the tempered fractional Laplacian

Zhijiang Zhang, Weihua Deng, George Em Karniadakis

The fractional Laplacian is the generator of -stable Lévy process, which is the scaling limit of the Lévy fight. Due to the divergence of the second moment of the jump…

math.NA2017★ 140 cited

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

Fanhai Zeng, Zhongqiang Zhang, George Em Karniadakis

Starting with the asymptotic expansion of the error equation of the shifted Grünwald--Letnikov formula, we derive a new modified weighted shifted Grünwald--Letnikov (WSGL) formula…