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Neural networks can be used as surrogates for PDE models.
A hybrid neural network-first principles approach to process modeling
D. C. Psichogios and L. H. Ungar · 1992
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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 the difficulty of training deep feedforward neural networks
X. Glorot and Y. Bengio · 2010
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Adam: A method for stochastic optimization
D. P. Kingma and J. Ba · 2015
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Automatic differentiation in machine learning: a survey
A. G. Baydin, B. A. Pearlmutter, A. A. Radul, and J. M. Siskind · 2018
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A. T. Mohan and D. V. Gaitonde · 2018
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Gradient-based optimization with B-splines on sparse grids for solving forward-dynamics simulations of three-dimensional, continuum-mechanical musculoskeletal system models
J. Valentin, M. Sprenger, D. Pflüger, and O. Röhrle · 2018
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Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario
M. Köppel, F. Franzelin, I. Kröker, S. Oladyshkin, G. Santin, D. Wittwar, A. Barth, B. Haasdonk, W. Nowak, D. Pflüger, and C. Rohde · 2019
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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. Karniadakis · 2019
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A reduced basis method for the wave equation
S. Glas, A. T. Patera, and K. Urban · 2020
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Solving parametric PDE problems with artificial neural networks
Y. Khoo, J. Lu, and L. Ying · 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
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Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems
A. M. Tartakovsky, C. O. Marrero, P. Perdikaris, G. D. Tartakovsky, and D. Barajas-Solano · 2020
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Understanding and mitigating gradient pathologies in physics-informed neural networks
S. Wang, Y. Teng, and P. Perdikaris · 2020
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Fourier neural operator for parametric partial differential equations
Z. Li, N. B. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. M. Stuart, and A. Anandkumar · 2021
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Optimally weighted loss functions for solving PDEs with neural networks
R. van der Meer, C. Oosterlee, and A. Borovykh · 2021
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CFDNet: A deep learning-based accelerator for fluid simulations
O. Obiols-Sales, A. Vishnu, N. Malaya, and A. Chandramowliswharan · 2020
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When and why pinns fail to train: A neural tangent kernel perspective
S. Wang, X. Yu, and P. Perdikaris · 2021
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