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02/07/2023
Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations
In this article we propose a new deep learning approach to solve paramet...
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02/06/2022
Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing
In financial engineering, prices of financial products are computed appr...
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12/08/2020
High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations
In this paper we develop a new machinery to study the capacity of artifi...
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05/20/2020
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations
One of the most challenging issues in applied mathematics is to develop ...
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09/07/2018
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
Artificial neural networks (ANNs) have very successfully been used in nu...
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03/22/2018
