705 citations · 1.4k across the 22 of their papers we have counts for
4 papers · 1 filter
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
Sifan Wang, Hanwen Wang, Paris Perdikaris
Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cas…
When and why PINNs fail to train: A neural tangent kernel perspective
Sifan Wang, Xinling Yu, Paris Perdikaris
Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial…
Deep learning of free boundary and Stefan problems
Sifan Wang, Paris Perdikaris
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate n…
Understanding and mitigating gradient pathologies in physics-informed neural networks
Sifan Wang, Yujun Teng, Paris Perdikaris
The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowled…