2.5k citations · 6.9k across the 23 of their papers we have counts for
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PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs
Xuhui Meng, Zhen Li, Dongkun Zhang +1
Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accura…
DeepXDE: A deep learning library for solving differential equations
Lu Lu, Xuhui Meng, Zhiping Mao +1
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present…
Discrete effect on the anti-bounce-back boundary condition of lattice Bhatnagar-Gross-Krook model for convection-diffusion equations
Liang Wang, Xuhui Meng, Hao-Chi Wu +2
The discrete effect on the boundary condition has been a fundamental topic for the lattice Boltzmann method in simulating heat and mass transfer problems. In previous works based o…
A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
Xuhui Meng, George Em Karniadakis
We propose a new composite neural network (NN) that can be trained based on multi-fidelity data. It is comprised of three NNs, with the first NN trained using the low-fidelity data…