Fetching the paper…
Reading the bibliography…
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs).
M. Dissanayake, N. Phan-Thien, Neural-network-based approximations for solving partial differential equations, Communications in Numerical Methods in Engineering 10 (3) (1994) 195–201
1994
Earlier work this paper cites.
I. E. Lagaris, A. Likas, D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE Transactions on Neural Networks 9 (5) (1998) 987–1000
1998
Earlier work this paper cites.
K. S. McFall, J. R. Mahan, Artificial neural network method for solution of boundary value problems with exact satisfaction of arbitrary boundary conditions, IEEE Transactions on Neural Networks 20 (8) (2009) 1221–1233
2009
Earlier work this paper cites.
R. S. Beidokhti, A. Malek, Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques, Journal of the Franklin Institute 346 (9) (2009) 898–913
2009
Earlier work this paper cites.
A. G. Baydin, B. A. Pearlmutter, A. A. Radul, J. M. Siskind, Automatic differentiation in machine learning: a survey, Journal of Machine Learning Research 18 (2018)
2018
Earlier work this paper cites.
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
Earlier work this paper cites.
G. Pang, L. Lu, G. E. Karniadakis, fPINNs: Fractional physics-informed neural networks, SIAM Journal on Scientific Computing 41 (4) (2019) A2603–A2626
2019
Earlier work this paper cites.
D. Zhang, L. Lu, L. Guo, G. E. Karniadakis, Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems, Journal of Computational Physics 397 (2019) 108850
2019
Earlier work this paper cites.
C. C. Margossian, A review of automatic differentiation and its efficient implementation, Wiley interdisciplinary reviews: data mining and knowledge discovery 9 (4) (2019) e1305
2019
Earlier work this paper cites.
J. Bettencourt, M. J. Johnson, D. Duvenaud, Taylor-mode automatic differentiation for higher-order derivatives in JAX (2019)
2019
Earlier work this paper cites.
D. Zhang, L. Guo, G. E. Karniadakis, Learning in modal space: Solving time-dependent stochastic PDEs using physics-informed neural networks, SIAM Journal on Scientific Computing 42 (2) (2020) A639–A665
2020
Earlier work this paper cites.
Y. Chen, L. Lu, G. E. Karniadakis, L. Dal Negro, Physics-informed neural networks for inverse problems in nano-optics and metamaterials, Optics Express 28 (8) (2020) 11618–11633
2020
Earlier work this paper cites.
M. Raissi, A. Yazdani, G. E. Karniadakis, Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, Science 367 (6481) (2020) 1026–1030
2020
Cited alongside, same era.
A. Yazdani, L. Lu, M. Raissi, G. E. Karniadakis, Systems biology informed deep learning for inferring parameters and hidden dynamics, PLoS Computational Biology 16 (11) (2020) e1007575
2020
Cited alongside, same era.
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
2020
Cited alongside, same era.
2020
Cited alongside, same era.
2020
Later among the works it cites.
W. Cai, X. Li, L. Liu, A phase shift deep neural network for high frequency approximation and wave problems, SIAM Journal on Scientific Computing 42 (5) (2020) A3285–A3312
2020
Later among the works it cites.
2020
Later among the works it cites.
2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2020
Cited alongside, same era.
2020
Cited alongside, same era.
2020
Cited alongside, same era.
X. Meng, Z. Li, D. Zhang, G. E. Karniadakis, PPINN: Parareal physics-informed neural network for time-dependent PDEs, Computer Methods in Applied Mechanics and Engineering 370 (2020) 113250
2020
Cited alongside, same era.
V. Dwivedi, B. Srinivasan, Physics informed extreme learning machine (PIELM)–a rapid method for the numerical solution of partial differential equations, Neurocomputing 391 (2020) 96–118
2020
Cited alongside, same era.
2020
Cited alongside, same era.
P. L. Lagari, L. H. Tsoukalas, S. Safarkhani, I. E. Lagaris, Systematic construction of neural forms for solving partial differential equations inside rectangular domains, subject to initial, boundary and interface conditions, International Journal on Artificial Intelligence Tools 29 (5) (2020)
2020
Cited alongside, same era.
2020
Later among the works it cites.
2020
Later among the works it cites.
L. Lu, X. Meng, Z. Mao, G. E. Karniadakis, DeepXDE: A deep learning library for solving differential equations, SIAM Review 63 (1) (2021) 208–228
2021
Closest in time.
2021
Closest in time.
M. A. Nabian, R. J. Gladstone, H. Meidani, Efficient training of physics-informed neural networks via importance sampling, Computer-Aided Civil and Infrastructure Engineering (2021)
2021
Closest in time.
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.