3.4k citations · 27.2k across the 213 of their papers we have counts for
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A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data
Lu Lu, Xuhui Meng, Shengze Cai +4
Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applica…
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
Jeremy Yu, Lu Lu, Xuhui Meng +1
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual…
DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs
Mengjia Xu, Apoorva Vikram Singh, George Em Karniadakis
Dynamic graph embedding has gained great attention recently due to its capability of learning low dimensional graph representations for complex temporal graphs with high accuracy.…
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis +1
Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power…
Physics-informed Neural Networks (PINNs) for Wave Propagation and Full Waveform Inversions
Majid Rasht-Behesht, Christian Huber, Khemraj Shukla +1
We propose a new approach to the solution of the wave propagation and full waveform inversions (FWIs) based on a recent advance in deep learning called Physics-Informed Neural Netw…
Meta-learning PINN loss functions
Apostolos F Psaros, Kenji Kawaguchi, George Em Karniadakis
We propose a meta-learning technique for offline discovery of physics-informed neural network (PINN) loss functions. We extend earlier works on meta-learning, and develop a gradien…