153 citations · 294 across the 8 of their papers we have counts for
8 papers
Physics-informed diffusion models in spectral space
Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito +1
We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions o…
Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory
Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger
This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including…
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…