3.4k citations · 4.7k across the 10 of their papers we have counts for
10 papers
FrFNO:Injecting the analytic Mittag-Leffler propagator into a resolution-robust neural operator for space-time fractional PDEs
Guofei Pang
Fractional partial differential equations couple a memory-dependent time derivative with a nonlocal fractional Laplacian, and their repeated solution under varying fractional order…
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
Guofei Pang, Marta D'Elia, Michael Parks +1
Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integral equations with sparse, noisy, unstructured, and multi-fidelity…
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…
Stochastic Solution of Elliptic and Parabolic Boundary Value Problems for the Spectral Fractional Laplacian
Mamikon Gulian, Guofei Pang
We prove and implement stochastic solution (or Feynman-Kac) formulas for boundary value problems involving the spectral fractional Laplacian with nonzero Dirichlet boundary conditi…
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…
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…