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NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations [article]

Kirill Zubov, Zoe McCarthy, Yingbo Ma, Francesco Calisto, Valerio Pagliarino, Simone Azeglio, Luca Bottero, Emmanuel Luján, Valentin Sulzer, Ashutosh Bharambe, Nand Vinchhi, Kaushik Balakrishnan (+2 others)
2021 arXiv   pre-print
Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models.  ...  We end by focusing on a complex multiphysics example, the Doyle-Fuller-Newman (DFN) Model, and showcase how this PDE can be formulated and solved with NeuralPDE.  ...  Physics-Informed Neural Networks (PINNs) The PINN Training Problem The basis of our physical models will be partial differential equations (PDEs).  ... 
arXiv:2107.09443v1 fatcat:22zfxicti5ed3msl6lcbzmynga

Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next [article]

Salvatore Cuomo, Vincenzo Schiano di Cola, Fabio Giampaolo, Gianluigi Rozza, Maziar Raissi, Francesco Piccialli
2022 arXiv   pre-print
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself.  ...  also attempts to incorporate publications on a larger variety of issues, including physics-constrained neural networks (PCNN), where the initial or boundary conditions are directly embedded in the NN  ...  A deep neural network can reduce approximation error by increasing network expressivity, but it can also produce a large generalization error.  ... 
arXiv:2201.05624v3 fatcat:elmdoax7ongblim3cbvkj2pdxi

Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next [article]

Salvatore Cuomo, Vincenzo Schiano di Cola, Fabio Giampaolo, Gianluigi Rozza, Maizar Raissi, Francesco Piccialli
2022
Physic-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself.  ...  also attempts to incorporate publications on a larger variety of issues, including physics-constrained neural networks (PCNN), where the initial or boundary conditions are directly embedded in the NN  ...  A deep neural network can reduce approximation error by increasing network expressivity, but it can also produce a large generalization error.  ... 
doi:10.48550/arxiv.2201.05624 fatcat:psynxr3k75bwpm437zl7ua5ndy