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10/24/2022
An efficient Monte Carlo scheme for Zakai equations
In this paper we develop a numerical method for efficiently approximatin...
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06/15/2021
Fluctuations of water quality time series in rivers follow superstatistics
Superstatistics is a general method from nonequilibrium statistical phys...
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03/03/2021
Full history recursive multilevel Picard approximations for ordinary differential equations with expectations
We consider ordinary differential equations (ODEs) which involve expecta...
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12/22/2020
An overview on deep learning-based approximation methods for partial differential equations
It is one of the most challenging problems in applied mathematics to app...
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12/02/2020
Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems
In this article we introduce and study a deep learning based approximati...
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09/29/2020
Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations
The approximative calculation of iterated nested expectations is a recur...
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03/01/2020
Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations
Recently, so-called full-history recursive multilevel Picard (MLP) appro...
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07/15/2019
Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approx
One of the most challenging problems in applied mathematics is the appro...
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07/08/2019
Deep splitting method for parabolic PDEs
In this paper we introduce a numerical method for parabolic PDEs that co...
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06/01/2018
Solving stochastic differential equations and Kolmogorov equations by means of deep learning
Stochastic differential equations (SDEs) and the Kolmogorov partial diff...
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09/18/2017