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Deep neural networks have been shown to provide accurate function approximations in high dimensions.
Note on exchange phenomena in the thomas atom
P. A. M. Dirac · 1930
Earlier work this paper cites.
Wave Mechanics, Advanced General Theor
J. Frenkel · 1934
Earlier work this paper cites.
A family of embedded Runge-Kutta formulae
J. Dormand and P. Prince · 1980
Earlier work this paper cites.
Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation
T. R. Taha and M. I. Ablowitz · 1984
Earlier work this paper cites.
Neural-network-based approximations for solving partial differential equations
M. W. M. G. Dissanayake and N. Phan-Thien · 1994
Earlier work this paper cites.
Perspectives in Flow Control and Optimization
M. D. Gunzburger · 2002
Earlier work this paper cites.
Theory and practice of finite elements
A. Ern and J.-L. Guermond · 2004
Earlier work this paper cites.
Dynamical low‐rank approximation
O. Koch and C. Lubich · 2007
Earlier work this paper cites.
Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations
G. Rozza, D. Huynh, and A. Patera · 2007
Earlier work this paper cites.
From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis
C. Lubich · 2008
Earlier work this paper cites.
Random features for large-scale kernel machines
A. Rahimi and B. Recht · 2008
Earlier work this paper cites.
Dynamically orthogonal field equations for continuous stochastic dynamical systems
T. P. Sapsis and P. F. Lermusiaux · 2009
Earlier work this paper cites.
A survey of projection-based model reduction methods for parametric dynamical systems
P. Benner, S. Gugercin, and K. Willcox · 2015
Earlier work this paper cites.
Error analysis of the dynamically orthogonal approximation of time dependent random pdes
E. Musharbash, F. Nobile, and T. Zhou · 2015
Earlier work this paper cites.
Online adaptive model reduction for nonlinear systems via low-rank updates
B. Peherstorfer and K. Willcox · 2015
Earlier work this paper cites.
Reduced basis techniques for nonlinear conservation laws
T. Taddei, S. Perotto, and A. Quarteroni · 2015
Earlier work this paper cites.
Dynamical model reduction method for solving parameter-dependent dynamical systems
M. Billaud-Friess and A. Nouy · 2017
Earlier work this paper cites.
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
W. E, J. Han, and A. Jentzen · 2017
Cited alongside, same era.
A unified deep artificial neural network approach to partial differential equations in complex geometries
J. Berg and K. Nyström · 2018
Cited alongside, same era.
Solving high-dimensional partial differential equations using deep learning
J. Han, A. Jentzen, and W. E · 2018
Cited alongside, same era.
Solving for high-dimensional committor functions using artificial neural networks
Y. Khoo, J. Lu, and L. Ying · 2018
Cited alongside, same era.
The shifted proper orthogonal decomposition: a mode decomposition for multiple transport phenomena
J. Reiss, P. Schulze, J. Sesterhenn, and V. Mehrmann · 2018
Cited alongside, same era.
Model reduction for transport-dominated problems via online adaptive bases and adaptive sampling
B. Peherstorfer · 2020
Later among the works it cites.
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E. Qian, B. Kramer, B. Peherstorfer, and K. Willcox · 2020
Later among the works it cites.
Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism
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Later among the works it cites.
Model reduction and neural networks for parametric PDEs
K. Bhattacharya, B. Hosseini, N. B. Kovachki, and A. M. Stuart · 2021
Later among the works it cites.
Evolutional deep neural network
Y. Du and T. A. Zaki · 2021
Later among the works it cites.
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