Fetching the paper…
Reading the bibliography…
The use of deep learning methods for solving PDEs is a field in full expansion.
Informed Machine Learning – A Taxonomy and Survey of Integrating Knowledge into Learning Systems
Laura von Rueden, Sebastian Mayer, Katharina Beckh, Bogdan Georgiev, Sven Giesselbach, Raoul Heese, Birgit Kirsch, Julius Pfrommer, Annika Pick, Rajkumar Ramamurthy, Michal Walczak, Jochen Garcke, Christian Bauckhage, and Jannis Schuecker · 1903
Earlier work this paper cites.
D3M: A deep domain decomposition method for partial differential equations
Ke Li, Kejun Tang, Tianfan Wu, and Qifeng Liao · 1909
Earlier work this paper cites.
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs
Xuhui Meng, Zhen Li, Dongkun Zhang, and George Em Karniadakis · 1909
Earlier work this paper cites.
Deep Domain Decomposition Method: Elliptic Problems
Wuyang Li, Xueshuang Xiang, and Yingxiang Xu · 2004
Earlier work this paper cites.
Domain decomposition methods–algorithms and theory
Andrea Toselli and Olof B. Widlund · 2005
Earlier work this paper cites.
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers
Kiwon Um, Robert Brand, Yun, Fei, Philipp Holl, and Nils Thuerey · 2007
Earlier work this paper cites.
The Development of Coarse Spaces for Domain Decomposition Algorithms
Olof B. Widlund · 2009
Earlier work this paper cites.
An Introduction to Domain Decomposition Methods
Victorita Dolean, Pierre Jolivet, and Frédéric Nataf · 2015
Cited alongside, same era.
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems
Weinan E and Bing Yu · 2017
Cited alongside, same era.
Adam: A Method for Stochastic Optimization
Diederik P. Kingma and Jimmy Ba · 2017
Cited alongside, same era.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2019
Cited alongside, same era.
Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
Ameya D. Jagtap, Ehsan Kharazmi, and George Em Karniadakis · 2020
Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
Ameya D. Jagtap & George Em Karniadakis · 2020
Later among the works it cites.
Physics-informed deep learning for incompressible laminar flows
Chengping Rao, Hao Sun, and Yang Liu · 2020
Later among the works it cites.
On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
Yeonjong Shin · 2020
Later among the works it cites.
Combining Machine Learning and Simulation to a Hybrid Modelling Approach: Current and Future Directions
Laura von Rueden, Sebastian Mayer, Rafet Sifa, Christian Bauckhage, and Jochen Garcke · 2020
Later among the works it cites.
Combining machine learning and domain decomposition methods for the solution of partial differential equations—A review
Alexander Heinlein, Axel Klawonn, Martin Lanser, and Janine Weber · 2021
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Physics-informed neural networks for solving nonlinear diffusivity and Biot’s equations
Teeratorn Kadeethum, Thomas M. Jørgensen, and Hamidreza M. Nick · 2020
Cited alongside, same era.
Ueber einen Grenzübergang durch alternirendes Verfahren
Hermann Amandus Schwarz
Cited in the paper.
Closest in time.
Parallel Physics-Informed Neural Networks via Domain Decomposition
Khemraj Shukla, Ameya D. Jagtap, and George Em Karniadakis · 2021
Closest in time.