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AmeyaJagtap authored Apr 14, 2021
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Expand Up @@ -9,13 +9,56 @@ References: For Domain Decomposition based PINN framework

1. A.D.Jagtap, G.E.Karniadakis, Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations, Commun. Comput. Phys., Vol.28, No.5, 2002-2041, 2020. (https://doi.org/10.4208/cicp.OA-2020-0164)

@article{jagtap2020extended,
title={Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations},
author={Jagtap, Ameya D and Karniadakis, George Em},
journal={Communications in Computational Physics},
volume={28},
number={5},
pages={2002--2041},
year={2020},
publisher={GLOBAL SCIENCE PRESS ROOM 3208, CENTRAL PLAZA, 18 HARBOUR RD, WANCHAI, HONG~…}
}

2. A.D.Jagtap, E. Kharazmi, G.E.Karniadakis, Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems, Computer Methods in Applied Mechanics and Engineering, 365, 113028 (2020). (https://doi.org/10.1016/j.cma.2020.113028)

@article{jagtap2020conservative,
title={Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems},
author={Jagtap, Ameya D and Kharazmi, Ehsan and Karniadakis, George Em},
journal={Computer Methods in Applied Mechanics and Engineering},
volume={365},
pages={113028},
year={2020},
publisher={Elsevier}
}


References: For adaptive activation functions

3. A.D.Jagtap, K.Kawaguchi, G.E.Karniadakis, Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 20200334, 2020. (http://dx.doi.org/10.1098/rspa.2020.0334).

@article{jagtap2020locally,
title={Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks},
author={Jagtap, Ameya D and Kawaguchi, Kenji and Em Karniadakis, George},
journal={Proceedings of the Royal Society A},
volume={476},
number={2239},
pages={20200334},
year={2020},
publisher={The Royal Society}
}

4. A.D. Jagtap, K.Kawaguchi, G.E.Karniadakis, Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, Journal of Computational Physics, 404 (2020) 109136. (https://doi.org/10.1016/j.jcp.2019.109136)

@article{jagtap2020adaptive,
title={Adaptive activation functions accelerate convergence in deep and physics-informed neural networks},
author={Jagtap, Ameya D and Kawaguchi, Kenji and Karniadakis, George Em},
journal={Journal of Computational Physics},
volume={404},
pages={109136},
year={2020},
publisher={Elsevier}
}


For any queries regarding the XPINN code, feel free to contact me : [email protected], [email protected]

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