3.4k citations · 27.2k across the 213 of their papers we have counts for
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Linking Gaussian Process regression with data-driven manifold embeddings for nonlinear data fusion
Seungjoon Lee, Felix Dietrich, George E. Karniadakis +1
In statistical modeling with Gaussian Process regression, it has been shown that combining (few) high-fidelity data with (many) low-fidelity data can enhance prediction accuracy, c…
Efficient multistep methods for tempered fractional calculus: Algorithms and Simulations
Ling Guo, Fanhai Zeng, Ian Turner +2
In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative opera…
fPINNs: Fractional Physics-Informed Neural Networks
Guofei Pang, Lu Lu, George Em Karniadakis
Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedf…
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…
Self-cleaning of hydrophobic rough surfaces by coalescence-induced wetting transition
Kaixuan Zhang, Zhen Li, Martin Maxey +2
The superhydrophobic leaves of a lotus plant and other natural surfaces with self-cleaning function have been studied intensively for the development of artificial biomimetic surfa…
Nonlocal flocking dynamics: Learning the fractional order of PDEs from particle simulations
Zhiping Mao, Zhen Li, George Em Karniadakis
Flocking refers to collective behavior of a large number of interacting entities, where the interactions between discrete individuals produce collective motion on the large scale.…