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B. C. Daniels, I. Nemenman, Efficient inference of parsimonious phenomenological models of cellular dynamics using S-systems and alternating regression , PloS one, 10 (3)
2015
Earlier work this paper cites.
M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations , arXiv preprint arXiv:1711.10566 (2017)
Original
2017
Earlier work this paper cites.
M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations , arXiv preprint arXiv:1711.10561 (2017)
Original
2017
Earlier work this paper cites.
M. Raissi, P. Perdikaris, G. E. Karniadakis, Multistep neural networks for data-driven discovery of nonlinear dynamical systems , arXiv preprint arXiv:1801.01236, (2018)
Original
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
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
Earlier work this paper cites.

Similar

L. McClenny, U. Braga-Neto, Self-adaptive physics-informed neural networks using a soft attention mechanism , arXiv preprint arXiv:2009.04544 (2020)
Original
2020
Cited alongside, same era.
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
Cited alongside, same era.
L. Yang, D. Zhang, G. E. Karniadakis, Physics-informed generative adversarial networks for stochastic differential equations , SIAM Journal on Scientific Computing, 42 (1)
2020
Cited alongside, same era.
Y. Shin, J. Darbon, G. E. Karniadakis, On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs , arXiv preprint arXiv:2004.01806, (2020)
Original
2020
Cited alongside, same era.

Then

S. Wang, X. Yu, P. Perdikaris, When and why PINNs fail to train: A neural tangent kernel perspective , Journal of Computational Physics, 449
2022
Later among the works it cites.
S. Anagnostopoulos, J. D. Toscano, N. Stergiopulos, G. E. Karniadakis Residual-based attention and connection to information bottleneck theory in PINNs , arXiv preprint arXiv:2307.00379 (2023)
Original
2023
Later among the works it cites.
M. Penwarden, A. D. Jagtap, S. Zhe, G. E. Karniadakis, R.M. Kirby, A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions , arXiv preprint arXiv:2302.14227, (2023)
Original
2023
Later among the works it cites.
S. Mishra, R. Molinaro, Estimates on the generalization error of physics-informed neural networks for approximating PDEs , IMA Journal of Numerical Analysis, 43 (1)
2023
Later among the works it cites.

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2024

Physics-Informed Neural Networks and Extensions

Raissi, Maziar, Perdikaris, Paris, Ahmadi, Nazanin et al.

Understand

In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensions, and provide a specific example in data-driven discovery of governing differential equations.

Built on

B. C. Daniels, I. Nemenman, Efficient inference of parsimonious phenomenological models of cellular dynamics using S-systems and alternating regression , PloS one, 10 (3)
2015
Earlier work this paper cites.
M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations , arXiv preprint arXiv:1711.10566 (2017)
Original
2017
Earlier work this paper cites.
M. Raissi, P. Perdikaris, G. E. Karniadakis, Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations , arXiv preprint arXiv:1711.10561 (2017)
Original
2017
Earlier work this paper cites.
M. Raissi, P. Perdikaris, G. E. Karniadakis, Multistep neural networks for data-driven discovery of nonlinear dynamical systems , arXiv preprint arXiv:1801.01236, (2018)
Original
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
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
Earlier work this paper cites.

Similar

L. McClenny, U. Braga-Neto, Self-adaptive physics-informed neural networks using a soft attention mechanism , arXiv preprint arXiv:2009.04544 (2020)
Original
2020
Cited alongside, same era.
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
Cited alongside, same era.
L. Yang, D. Zhang, G. E. Karniadakis, Physics-informed generative adversarial networks for stochastic differential equations , SIAM Journal on Scientific Computing, 42 (1)
2020
Cited alongside, same era.
Y. Shin, J. Darbon, G. E. Karniadakis, On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs , arXiv preprint arXiv:2004.01806, (2020)
Original
2020
Cited alongside, same era.

Then

S. Wang, X. Yu, P. Perdikaris, When and why PINNs fail to train: A neural tangent kernel perspective , Journal of Computational Physics, 449
2022
Later among the works it cites.
S. Anagnostopoulos, J. D. Toscano, N. Stergiopulos, G. E. Karniadakis Residual-based attention and connection to information bottleneck theory in PINNs , arXiv preprint arXiv:2307.00379 (2023)
Original
2023
Later among the works it cites.
M. Penwarden, A. D. Jagtap, S. Zhe, G. E. Karniadakis, R.M. Kirby, A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions , arXiv preprint arXiv:2302.14227, (2023)
Original
2023
Later among the works it cites.
S. Mishra, R. Molinaro, Estimates on the generalization error of physics-informed neural networks for approximating PDEs , IMA Journal of Numerical Analysis, 43 (1)
2023
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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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. , AAAI spring symposium: MLPS, 10

2021

Cited alongside, same era.

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

Cited alongside, same era.

N. Ahmadi Daryakenari, M. De Florio, K. Shukla, G. E. Karniadakis AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification , arXiv preprint arXiv:2310.01433 (2023)

Original

2023

Later among the works it cites.

M. Cranmer, Interpretable machine learning for science with PySR and SymbolicRegression. jl , arXiv preprint arXiv:2305.01582, (2023)

Original

2023

Later among the works it cites.