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We present a novel algorithmic approach and an error analysis leveraging Quasi-Monte Carlo points for training deep neural network (DNN) surrogates of Data-to-Observable (DtO) maps in engineering design.
Low-discrepancy point sets obtained by digital constructions over finite fields
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Robert N. Gantner and Christoph Schwab · 2016
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Ian Goodfellow, Yoshua Bengio, and Aaron Courville · 2016
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Jan S. Hesthaven, Gianluigi Rozza, and Benjamin Stamm · 2016
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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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F. Regazzoni, L. Dedè, and A. Quarteroni · 2019
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Ruben Aylwin, Carlos Jerez-Hanckes, Christoph Schwab, and Jakob Zech · 2020
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J. Dick, M. Longo, and Ch. Schwab · 2020
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