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; Philippe von Wurstemberger (CoRR, 2018)

Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations. - Sebastian Becker; Ramon Braunwarth; Martin Hutzenthaler; Arnulf Jentzen; Philippe von Wurstemberger (CoRR, 2020)

High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations. - Pierfrancesco Beneventano; Patrick Cheridito; Arnulf Jentzen; Philippe von Wurstemberger (CoRR, 2020)

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 (J. Complex., 2020)

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; Philippe von Wurstemberger (CoRR, 2022)

Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations. - Arnulf Jentzen; Adrian Riekert; Philippe von Wurstemberger (CoRR, 2023)

Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory. - Arnulf Jentzen; Benno Kuckuck; Philippe von Wurstemberger (CoRR, 2023)

An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning. - Lukas Gonon; Arnulf Jentzen; Benno Kuckuck; Siyu Liang; Adrian Riekert; Philippe von Wurstemberger (CoRR, 2024)

An overview of diffusion models for generative artificial intelligence. - Davide Gallon; Arnulf Jentzen; Philippe von Wurstemberger (CoRR, 2024)