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We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations.
A. Al-Aradi, A. Correia, D. de Frietas Naiff, G. Jardim, and Y. Saporito · 1912
Earlier work this paper cites.
Non-Homogeneous Boundary Value Problems and Applications
J. L. Lions and E. Magenes · 1972
Earlier work this paper cites.
Non-Homogeneous Boundary Value Problems and Applications
J. L. Lions and E. Magenes · 1972
Earlier work this paper cites.
Approximation capabilities of multilayer feedforward networks
K. Hornik · 1991
Earlier work this paper cites.
A neural network model for estimating option prices
M. Malliaris and L. Salchenberger · 1993
Earlier work this paper cites.
A nonparametric approach to pricing and hedging derivative securities via learning networks
J. M. Hutchinson, A. W. Lo, and T. Poggio · 1994
Earlier work this paper cites.
The numerical solution of linear ordinary differential equations by feedforward neural networks
A. Meade and A. Fernandez · 1994
Earlier work this paper cites.
Neural networks for contingent claim pricing via the Galerkin method
E. Barucci, U. Cherubini, and L. Landi · 1997
Earlier work this paper cites.
Model reduction and neural networks for parametric PDEs
K. Bhattacharya, B. Hosseini, N. B. Kovachki, and A. M. Stuart · 2005
Earlier work this paper cites.
Weak error analysis for stochastic gradient descent optimization algorithms
A. Bercher, L. Gonon, A. Jentzen, and D. Salimova · 2007
Earlier work this paper cites.
Improved radial basis function methods for multi-dimensional option pricing
U. Pettersson, E. Larsson, G. Marcusson, and J. Persson · 2008
Earlier work this paper cites.
Quasi-Monte Carlo methods with applications in finance
P. L’Ecuyer · 2009
Earlier work this paper cites.
The deep learning Galerkin method for the general Stokes equations
J. Li, J. Yue, W. Zhang, and W. Duan · 2009
Earlier work this paper cites.
Two useful techniques for financial modelling problems
P. Doust · 2010
Earlier work this paper cites.
Analysis of Fourier transform valuation formulas and applications
E. Eberlein, K. Glau, and A. Papapantoleon · 2010
Earlier work this paper cites.
Understanding the difficulty of training deep feedforward neural networks
X. Glorot and Y. Bengio · 2010
Earlier work this paper cites.
Dimension-wise integration of high-dimensional functions with applications to finance
M. Griebel and M. Holtz · 2010
Earlier work this paper cites.
Fourier neural operator for parametric partial differential equations
Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandkumar · 2010
Cited alongside, same era.
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M. Holtz · 2011
Cited alongside, same era.
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N. Hilber, O. Reichmann, C. Schwab, and C. Winter · 2013
Cited alongside, same era.
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M. Abadi et al · 2015
Cited alongside, same era.
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M. B. Giles · 2015
Cited alongside, same era.
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Later among the works it cites.
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C. Beck, W. E, and A. Jentzen · 2019
Later among the works it cites.
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Q. Chan-Wai-Nam, J. Mikael, and X. Warin · 2019
Later among the works it cites.
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Later among the works it cites.
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T. O’Malley, E. Bursztein, J. Long, F. Chollet, H. Jin, L. Invernizzi, et al · 2019
Later among the works it cites.
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