153 citations · 294 across the 8 of their papers we have counts for
6 papers · 1 filter
Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing
Sebastian Becker, Arnulf Jentzen, Marvin S. Müller +1
In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many fina…
High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations
Pierfrancesco Beneventano, Patrick Cheridito, Arnulf Jentzen +1
In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of di…
Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations
Sebastian Becker, Ramon Braunwarth, Martin Hutzenthaler +2
One of the most challenging issues in applied mathematics is to develop and analyze algorithms which are able to approximately compute solutions of high-dimensional nonlinear parti…
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations
Philipp Grohs, Fabian Hornung, Arnulf Jentzen +1
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recogniti…
Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates
Arnulf Jentzen, Philippe von Wurstemberger
The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of…
Strong error analysis for stochastic gradient descent optimization algorithms
Arnulf Jentzen, Benno Kuckuck, Ariel Neufeld +1
Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications. In this article we perform a rigorous strong error analy…