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Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints.
Multiplier and gradient methods,
M. R. Hestenes, · 1969
Earlier work this paper cites.
A. Pinkus, n-Widths in Approximation Theory, Springer, Berlin, Heidelberg, 1985
1985
Earlier work this paper cites.
R. J. LeVeque, Numerical methods for conservation laws, volume 214, Springer, 1992
1992
Earlier work this paper cites.
On n-widths for elliptic problems,
J. M. Melenk, · 2000
Earlier work this paper cites.
On the optimality of the proper orthogonal decomposition and balanced truncation,
S. M. Djouadi, · 2008
Earlier work this paper cites.
n-Widths, sup–infs, and optimality ratios for the k-version of the isogeometric finite element method,
J. A. Evans, Y. Bazilevs, I. Babuška, T. J. Hughes, · 2009
Earlier work this paper cites.
On the connection between balanced proper orthogonal decomposition, balanced truncation, and metric complexity theory for infinite dimensional systems,
S. M. Djouadi, · 2010
Earlier work this paper cites.
Adam: A method for stochastic optimization,
D. P. Kingma, J. Ba, · 2014
Earlier work this paper cites.
A. Quarteroni, A. Manzoni, F. Negri, Reduced Basis Methods for Partial Differential Equations, volume 92 of UNITEXT
2016
Earlier work this paper cites.
Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows,
R. Mojgani, M. Balajewicz, · 2017
Earlier work this paper cites.
A localization strategy for data assimilation; Application to state estimation and parameter estimation,
T. Taddei, A. T. Patera, · 2018
Earlier work this paper cites.
Dimensional splitting of hyperbolic partial differential equations using the Radon transform,
D. Rim, · 2018
Earlier work this paper cites.
Physics–informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,
M. Raissi, P. Perdikaris, G. Karniadakis, · 2019
Earlier work this paper cites.
Kolmogorov n-widths for linear dynamical systems,
B. Unger, S. Gugercin, · 2019
Earlier work this paper cites.
Memory embedded non-intrusive reduced order modeling of non-ergodic flows,
S. E. Ahmed, S. M. Rahman, O. San, A. Rasheed, I. M. Navon, · 2019
Earlier work this paper cites.
M. Nonino, F. Ballarin, G. Rozza, Y. Maday, · 2019
Earlier work this paper cites.
Limitations of physics informed machine learning for nonlinear two-phase transport in porous media,
O. Fuks, H. A. Tchelepi, · 2020
Earlier work this paper cites.
Physics–informed neural networks for high-speed flows,
Z. Mao, A. D. Jagtap, G. E. Karniadakis, · 2020
Earlier work this paper cites.
R. Mojgani, Reduced order modeling of convection-dominated flows, dimensionality reduction and stabilization, Ph.D. thesis, University of Illinois at Urbana-Champaign, Urbana, IL, USA, 2020
2020
Earlier work this paper cites.
Model reduction for transport-dominated problems via online adaptive bases and adaptive sampling,
B. Peherstorfer, · 2020
Earlier work this paper cites.
Manifold approximations via transported subspaces: Model reduction for transport-dominated problems,
D. Rim, B. Peherstorfer, K. T. Mandli, · 2020
Cited alongside, same era.
A registration method for model order reduction: Data compression and geometry reduction,
T. Taddei, · 2020
Cited alongside, same era.
Breaking the Kolmogorov barrier in model reduction of fluid flows,
S. E. Ahmed, O. San, · 2020
Cited alongside, same era.
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders,
K. Lee, K. T. Carlberg, · 2020
Cited alongside, same era.
Lagrangian dynamic mode decomposition for construction of reduced-order models of advection-dominated phenomena,
H. Lu, D. M. Tartakovsky, · 2020
Cited alongside, same era.
M. A. Mirhoseini, M. J. Zahr, · 2021
Later among the works it cites.
Low-rank registration based manifolds for convection-dominated PDEs,
R. Mojgani, M. Balajewicz, · 2021
Later among the works it cites.
Model reduction of traveling-wave problems via radon cumulative distribution transform,
J. Ren, W. R. Wolf, X. Mao, · 2021
Later among the works it cites.
A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks,
S. Dong, N. Ni, · 2021
Later among the works it cites.
Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs,
T. Taddei, L. Zhang, · 2021
Later among the works it cites.
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When and why PINNs fail to train: A neural tangent kernel perspective,
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