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Sifan Wang, Hanwen Wang, Paris G. Perdikaris
Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.
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Wang, S., Wang, H., & Perdikaris, P. G. (2021). Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. Science Advances, 7(40), eabi8605. https://doi.org/10.1126/sciadv.abi8605
Wang, Sifan, et al. "Learning the solution operator of parametric partial differential equations with physics-informed DeepONets." Science Advances, vol. 7, no. 40, 2021, pp. eabi8605, https://doi.org/10.1126/sciadv.abi8605.
Wang, Sifan, Hanwen Wang, and Paris G. Perdikaris. "Learning the solution operator of parametric partial differential equations with physics-informed DeepONets." Science Advances 7, no. 40 (2021): eabi8605. https://doi.org/10.1126/sciadv.abi8605.
Wang S., Wang H., Perdikaris P. G. Learning the solution operator of parametric partial differential equations with physics-informed DeepONets // Science Advances. — 2021. — Vol. 7, № 40. — P. eabi8605. — URL: https://doi.org/10.1126/sciadv.abi8605
@article{wang2021learning,
title = {{Learning the solution operator of parametric partial differential equations with physics-informed DeepONets}},
author = {Sifan Wang and Hanwen Wang and Paris G. Perdikaris},
journal = {Science Advances},
year = {2021},
volume = {7},
number = {40},
pages = {eabi8605},
doi = {10.1126/sciadv.abi8605},
url = {https://doi.org/10.1126/sciadv.abi8605}
}TY - JOUR AU - Wang, Sifan AU - Wang, Hanwen AU - Perdikaris, Paris G. TI - Learning the solution operator of parametric partial differential equations with physics-informed DeepONets JO - Science Advances VL - 7 IS - 40 SP - eabi8605 PY - 2021 DA - 2021/09/29 DO - 10.1126/sciadv.abi8605 UR - https://doi.org/10.1126/sciadv.abi8605 ER -
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