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Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models.
The finite element method , volume 3
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Computational differential equations
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A practical guide to pseudospectral methods
B. Fornberg · 1998
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Artificial neural networks for solving ordinary and partial differential equations
I. E. Lagaris, A. Likas, and D. I. Fotiadis · 1998
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Understanding and mitigating gradient pathologies in physics-informed neural networks
S. Wang, Y. Teng, and P. Perdikaris · 2001
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Solving differential equations with unsupervised neural networks
D. R. Parisi, M. C. Mariani, and M. A. Laborde · 2003
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When and why pinns fail to train: A neural tangent kernel perspective
S. Wang, X. Yu, and P. Perdikaris · 2007
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Curriculum learning
Y. Bengio, J. Louradour, R. Collobert, and J. Weston · 2009
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Multi-scale deep neural network (mscalednn) methods for oscillatory stokes flows in complex domains
B. Wang, W. Zhang, and W. Cai · 2009
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Fundamentals of engineering numerical analysis
P. Moin · 2010
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S. Wang, H. Wang, and P. Perdikaris · 2012
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Imposing hard constraints on deep networks: Promises and limitations
P. Márquez-Neila, M. Salzmann, and P. Fua · 2017
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
E. Weinan, J. Han, and A. Jentzen · 2017
Cited alongside, same era.
Solving high-dimensional partial differential equations using deep learning
J. Han, A. Jentzen, and E. Weinan · 2018
Cited alongside, same era.
Pde-net: Learning pdes from data
Z. Long, Y. Lu, X. Ma, and B. Dong · 2018
Cited alongside, same era.
Dgm: A deep learning algorithm for solving partial differential equations
J. Sirignano and K. Spiliopoulos · 2018
Cited alongside, same era.
Hessian-based analysis of large batch training and robustness to adversaries
Z. Yao, A. Gholami, Q. Lei, K. Keutzer, and M. W. Mahoney · 2018
Cited alongside, same era.
Hamiltonian neural networks
S. Greydanus, M. Dzamba, and J. Yosinski · 2019
Modeling the dynamics of pde systems with physics-constrained deep auto-regressive networks
N. Geneva and N. Zabaras · 2020
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Stiff-pinn: Physics-informed neural network for stiff chemical kinetics
W. Ji, W. Qiu, Z. Shi, S. Pan, and S. Deng · 2020
Later among the works it cites.
Universal differential equations for scientific machine learning
C. Rackauckas, Y. Ma, J. Martensen, C. Warner, K. Zubov, R. Supekar, D. Skinner, A. Ramadhan, and A. Edelman · 2020
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
M. Raissi, A. Yazdani, and G. E. Karniadakis · 2020
Later among the works it cites.
Physics-informed neural networks for cardiac activation mapping
F. Sahli Costabal, Y. Yang, P. Perdikaris, D. E. Hurtado, and E. Kuhl · 2020
Later among the works it cites.
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Cited alongside, same era.
A primal dual formulation for deep learning with constraints
Y. Nandwani, A. Pathak, P. Singla, et al · 2019
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.
Informed machine learning–a taxonomy and survey of integrating knowledge into learning systems
L. von Rueden, S. Mayer, K. Beckh, B. Georgiev, S. Giesselbach, R. Heese, B. Kirsch, J. Pfrommer, A. Pick, R. Ramamurthy, et al · 2019
Cited alongside, same era.
Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
Y. Zhu, N. Zabaras, P.-S. Koutsourelakis, and P. Perdikaris · 2019
Cited alongside, same era.
Machine learning for fluid mechanics
S. L. Brunton, B. R. Noack, and P. Koumoutsakos · 2020
Cited alongside, same era.
Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Y. Chen, L. Lu, G. E. Karniadakis, and L. Dal Negro · 2020
Cited alongside, same era.
Integrating physics-based modeling with machine learning: A survey
J. Willard, X. Jia, S. Xu, M. Steinbach, and V. Kumar · 2020
Later among the works it cites.
Physics constrained learning for data-driven inverse modeling from sparse observations
K. Xu and E. Darve · 2020
Later among the works it cites.
Pyhessian: Neural networks through the lens of the hessian
Z. Yao, A. Gholami, K. Keutzer, and M. W. Mahoney · 2020
Later among the works it cites.
Dc3: A learning method for optimization with hard constraints
P. L. Donti, D. Rolnick, and J. Z. Kolter · 2021
Closest in time.
Distributed learning machines for solving forward and inverse problems in partial differential equations
V. Dwivedi, N. Parashar, and B. Srinivasan · 2021
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Nvidia simnet™: An ai-accelerated multi-physics simulation framework
O. Hennigh, S. Narasimhan, M. A. Nabian, A. Subramaniam, K. Tangsali, Z. Fang, M. Rietmann, W. Byeon, and S. Choudhry · 2021
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Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations
X. Jin, S. Cai, H. Li, and G. E. Karniadakis · 2021
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Physics-informed machine learning
G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang · 2021
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https://github.com/a1k12/characterizing-pinns-failure-modes, 2021
C. possible failure modes in physics-informed neural networks · 2021
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