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We develop a distributed framework for the physics-informed neural networks (PINNs) based on two recent extensions, namely conservative PINNs (cPINNs) and extended PINNs (XPINNs), which employ domain decomposition in space and in time-space, respectively.
1912
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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
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M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journal of Computational Physics 378 (2019) 686–707
2019
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Z. Mao, A. D. Jagtap, G. E. Karniadakis, Physics-informed neural networks for high-speed flows, Computer Methods in Applied Mechanics and Engineering 360 (2020) 112789
2020
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K. Shukla, P. C. Di Leoni, J. Blackshire, D. Sparkman, G. E. Karniadakis, Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks, Journal of Nondestructive Evaluation 39 (3) (2020) 1–20
2020
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F. Sahli Costabal, Y. Yang, P. Perdikaris, D. E. Hurtado, E. Kuhl, Physics-informed neural networks for cardiac activation mapping, Frontiers in Physics 8 (2020) 42
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U. Waheed, E. Haghighat, T. Alkhalifah, C. Song, Q. Hao, Eikonal solution using physics-informed neural networks, in: 82nd EAGE Annual Conference & Exhibition, Vol. 2020, European Association of Geoscientists & Engineers, 2020, pp. 1–5
2020
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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 (2020) 113028
2020
Cited alongside, same era.
Cited in the paper.
S. Cai, Z. Wang, F. Fuest, Y. J. Jeon, C. Gray, G. E. Karniadakis, Flow over an espresso cup: inferring 3-d velocity and pressure fields from tomographic background oriented schlieren via physics-informed neural networks, Journal of Fluid Mechanics 915
Cited in the paper.
H. Tang, R. Haynes, G. Houzeaux, A review of domain decomposition methods for simulation of fluid flows: Concepts, algorithms, and applications, Archives of Computational Methods in Engineering (2020) 1–33
2020
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M. Yin, X. Zheng, J. D. Humphrey, G. E. Karniadakis, Non-invasive inference of thrombus material properties with physics-informed neural networks, Computer Methods in Applied Mechanics and Engineering 375 (2021) 113603
2021
Closest in time.
2021
Closest in time.
E. Kharazmi, Z. Zhang, G. E. Karniadakis, hp-vpinns: Variational physics-informed neural networks with domain decomposition, Computer Methods in Applied Mechanics and Engineering 374 (2021) 113547
2021
Closest in time.
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, Communications in Computational Physics 28 (5) (2020) 2002–2041
2041
Closest in time.