Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
By Sifan Wang, Yujun Teng, Paris Perdikaris. SIAM Journal on Scientific Computing, 2021
1,561 citations recorded by the source corpus.
Subfields: Computational Mechanics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/bdd29cf7f30cfa7991c8259a0d27217c9eafb3bd
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- G. Em Karniadakis
- Zhiping Mao
- Ameya Dilip Jagtap
- Maizar Raissi
- Nikolaus A. Adams
- Gianluigi Rozza
- Vipin Kumar
- Michael S. Steinbach
In Statistical and Nonlinear Physics
- G. Em Karniadakis
- Zhiping Mao
- Ameya Dilip Jagtap
- Maizar Raissi
- Gianluigi Rozza
- Fabio Giampaolo
- Salvatore Cuomo
- Francesco Piccialli
Citations in the corpus
- Physics-Informed Neural Operator for Learning Partial Differential Equations (2021, neutral): “Empirically, PINNs often fail to solve challenging PDEs when the solution exhibits high-frequency or multi-scale structure [40, 42, 7, 36].”
- Physics-informed neural networks for inverse problems in supersonic flows (2022, methodology): “We also employ dynamic weights [44] denoted as ωi, i = 1, 2, · · · in front of all the MSE terms in the loss function.”
- A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks (2022, methodology): “In PINNs, the total loss is a weighted summation of multiple loss terms corresponding to the PDE and initial/boundary conditions, and different methods have been developed to automatically tune these weights and balance the losses [13, 14, 15].”
- Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next (2022, methodology): “AE architecture of the convolutional neural network (CNN) is also used in Wang et al (2021a).”
- Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “Many of the foundational works on physics-guided loss functions also include open source code that could be adapted to new applications (e.g. Raissi et al. [226], Read et al. [231], Wang et al. [282]).”
- Choose a Transformer: Fourier or Galerkin (2021, methodology): “[90, 91] proposed a DeepONet roughly equivalent to an additive attention, similar to the one in the Neural Turing Machine (NMT) in [7].”