Gauss-Jacobi-type quadrature rules for fractional directional integrals. - Guofei Pang; Wen Chen 003; Kam-Yim Sze (Comput. Math. Appl., 2013)

Space-fractional advection-dispersion equations by the Kansa method. - Guofei Pang; Wen Chen 003; Zhuo-Jia Fu (J. Comput. Phys., 2015)

Singular boundary method for acoustic eigenanalysis. - Weiwei Li; Wen Chen 003; Guofei Pang (Comput. Math. Appl., 2016)

A new definition of fractional Laplacian with application to modeling three-dimensional nonlocal heat conduction. - Wen Chen 003; Guofei Pang (J. Comput. Phys., 2016)

Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization. - Guofei Pang; Paris Perdikaris; Wei Cai 003; George E. Karniadakis (J. Comput. Phys., 2017)

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation. - Hongguang Sun; Xiaoting Liu; Yong Zhang 013; Guofei Pang; Rhiannon Garrard (J. Comput. Phys., 2017)

Radial basis function collocation method for decoupled fractional Laplacian wave equations. - Yiran Xu; Jingye Li; Guofei Pang; Zhikai Wang; Xiaohong Chen 003 (CoRR, 2018)

Neural-net-induced Gaussian process regression for function approximation and PDE solution. - Guofei Pang; Liu Yang; George E. Karniadakis (J. Comput. Phys., 2019)

fPINNs: Fractional Physics-Informed Neural Networks. - Guofei Pang; Lu Lu 010; George Em Karniadakis (SIAM J. Sci. Comput., 2019)

Nonlocal Physics-Informed Neural Networks - A Unified Theoretical and Computational Framework for Nonlocal Models. - Marta D'Elia; George E. Karniadakis; Guofei Pang; Michael L. Parks (AAAI Spring Symposium: MLPS, 2020)

Solving fractional Laplacian visco-acoustic wave equations on complex-geometry domains using Grünwald-formula based radial basis collocation method. - Yiran Xu; Jingye Li; Xiaohong Chen 003; Guofei Pang (Comput. Math. Appl., 2020)

What is the fractional Laplacian? A comparative review with new results. - Anna Lischke; Guofei Pang; Mamikon A. Gulian; Fangying Song; Christian Glusa; Xiaoning Zheng; Zhiping Mao; Wei Cai 003; Mark M. Meerschaert; Mark Ainsworth; George Em Karniadakis (J. Comput. Phys., 2020)

nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications. - Guofei Pang; Marta D'Elia; Michael L. Parks; George E. Karniadakis (J. Comput. Phys., 2020)

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. - Lu Lu 010; Pengzhan Jin; Guofei Pang; Zhongqiang Zhang; George Em Karniadakis (Nat. Mach. Intell., 2021)

On numerical methods to second-order singular initial value problems with additive white noise. - Nan Deng; Wanrong Cao; Guofei Pang (J. Comput. Appl. Math., 2022)