Julius Berner

Analysis of the generalization error: Empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations

Arnulf Jentzen, Philipp Grohs, Julius Berner, 2018, SIAM J. Math. Data Sci..

Towards a regularity theory for ReLU networks – chain rule and global error estimates

Arnulf Jentzen, Philipp Grohs, Julius Berner, 2019, 2019 13th International conference on Sampling Theory and Applications (SampTA).

How degenerate is the parametrization of neural networks with the ReLU activation function?

Philipp Grohs, Julius Berner, Dennis Elbrächter, 2019, NeurIPS.

Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning pdf

Philipp Grohs, Julius Berner, Markus Dablander, 2020, NeurIPS.

The Modern Mathematics of Deep Learning pdf

Gitta Kutyniok, Philipp Petersen, Philipp Grohs, 2021, ArXiv.