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Over the last few years deep artificial neural networks (DNNs) have very successfully been used in numerical simulations for a wide variety of computational problems including computer vision, image classification, speech recognition, natural language processing, as well as computational advertisement.
Deep Learning
Goodfellow, I., Bengio, Y., and Courville, A · 2016
Earlier work this paper cites.
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Deep reinforcement learning for partial differential equation control
Farahmand, A.-m., Nabi, S., and Nikovski, D. N · 2017
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Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM
Henry-Labordere, P · 2017
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Long, Z., Lu, Y., Ma, X., and Dong, B · 2017
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Optimal approximation of piecewise smooth functions using deep ReLU neural networks
Petersen, P., and Voigtlaender, F · 2017
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Error bounds for approximations with deep ReLU networks
Yarotsky, D · 2017
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DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing
Elbrächter, D., Grohs, P., Jentzen, A., and Schwab, C · 2018
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Grohs, P., Hornung, F., Jentzen, A., and von Wurstemberger, P · 2018
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Han, J., Jentzen, A., and E, W · 2018
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Han, J., and Long, J · 2018
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Jentzen, A., Salimova, D., and Welti, T · 2018
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Magill, M., Qureshi, F., and de Haan, H · 2018
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Petersen, P., Raslan, M., and Voigtlaender, F · 2018
Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High dimensional BSDEs
Fujii, M., Takahashi, A., and Takahashi, M · 2019
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Machine Learning for Pricing American Options in High Dimension
Goudenege, L., Molent, A., and Zanette, A · 2019
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Deep Neural Network Approximation Theory
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Huré, C., Pham, H., and Warin, X · 2019
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Sirignano, J., and Spiliopoulos, K · 2018
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Deep splitting method for parabolic PDEs
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Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations
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