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Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a great degree.
Neural-network-based approximations for solving partial-differential equations
M. W. M. G. Dissanayake and N. Phan-Thien · 1994
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A multiresolution strategy for reduction of elliptic PDEs and eigenvalue problems
G. Beylkin and N. Coult · 1998
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A parareal in time procedure for the control of partial differential equations
Y. Maday and G. Turinici · 2002
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Finite difference methods for two-dimensional fractional dispersion equation
M. M. Meerschaert, H.-P. Scheffler, and C. Tadjeran · 2006
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CUDA by example: an introduction to general-purpose GPU programming
J. Sanders and E. Kandrot · 2010
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Adaptive subgradient methods for online learning and stochastic optimization
J. Duchi, E. Hazan, and Y. Singer · 2011
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Adam: A method for stochastic optimization
D. P. Kingma and J. Ba · 2014
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On the computational efficiency of training neural networks
R. Livni, S. Shalev-Shwartz, and O. Shamir · 2014
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Localized lattice Boltzmann equation model for simulating miscible viscous displacement in porous media
X. Meng and Z. Guo · 2016
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Doing the impossible: Why neural networks can be trained at all
N. O. Hodas and P. Stinis · 2018
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Exascale deep learning for climate analytics
T. Kurth, S. Treichler, J. Romero, M. Mudigonda, N. Luehr, E. Phillips, A. Mahesh, M. Matheson, J. Deslippe, M. Fatica, Prabhat, and M. Houston · 2018
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Optimization methods for large-scale machine learning
L. Bottou, F. Curtis, and J. Nocedal · 2018
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Physics-informed generative adversarial networks for stochastic differential equations
L. Yang, D. Zhang, and G. E. Karniadakis · 2018
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D. Zhang, L. Lu, L. Guo, and G. E. Karniadakis · 2018
Fast deep neural network training on distributed systems and cloud TPUs
Y. You, Z. Zhang, C. Hsieh, J. Demmel, and K. Keutzer · 2019
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Solving irregular and data-enriched differential equations using deep neural networks
C. Michoski, M. Milosavljevic, T. Oliver, and D. Hatch · 2019
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Physics-informed echo state networks for chaotic systems forecasting
N. A. K. Doan, W. Polifke, and L. Magri · 2019
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Physical symmetries embedded in neural networks
M. Mattheakis, P. Protopapas, D Sondak, M. Di Giovanni, and E. Kaxiras · 2019
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D. Zhang, L. Guo, and G. E. Karniadakis · 2019
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fPINNs: Fractional physics-informed neural networks
G. Pang, L. Lu, and G. E. Karniadakis · 2018
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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. E. Karniadakis · 2019
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Analyzing machine learning workloads using a detailed GPU simulator
J. Lew, D. A. Shah, S. Pati, S. Cattell, M. Zhang, A. Sandhupatla, C. Ng, N. Goli, M. D. Sinclair, T. G. Rogers, and T. M. Aamodt · 2019
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Adversarial uncertainty quantification in physics-informed neural networks
Y. Yang and P. Perdikaris · 2019
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Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics
A. Blumers, Z. Li, and G. E. Karniadakis · 2019
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