Julius Berner

According to our database, Julius Berner authored at least 15 papers between 2019 and 2024.

Collaborative distances:

• Dijkstra number of four.
• Erdős number of three.

2024

Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs.

Md Ashiqur Rahman, Robert Joseph George, Mogab Elleithy, Daniel V. Leibovici, Zongyi Li, Boris Bonev, Colin White, Julius Berner, Raymond A. Yeh, Jean Kossaifi, Kamyar Azizzadenesheli, Anima Anandkumar

CoRR, 2024

DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training.

Zhongkai Hao, Chang Su, Songming Liu, Julius Berner, Chengyang Ying, Hang Su, Anima Anandkumar, Jian Song, Jun Zhu

CoRR, 2024

Neural Operators with Localized Integral and Differential Kernels.

Miguel Liu-Schiaffini, Julius Berner, Boris Bonev, Thorsten Kurth, Kamyar Azizzadenesheli, Anima Anandkumar

CoRR, 2024

2023

Large Language Models for Mathematicians.

Simon Frieder, Julius Berner, Philipp Petersen, Thomas Lukasiewicz

CoRR, 2023

Improved sampling via learned diffusions.

Lorenz Richter, Julius Berner, Guan-Horng Liu

CoRR, 2023

Mathematical Capabilities of ChatGPT.

Simon Frieder, Luca Pinchetti, Alexis Chevalier, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Petersen, Julius Berner

Proceedings of the Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, 2023

Learning ReLU networks to high uniform accuracy is intractable.

Julius Berner, Philipp Grohs, Felix Voigtländer

Proceedings of the Eleventh International Conference on Learning Representations, 2023

2022

An optimal control perspective on diffusion-based generative modeling.

Julius Berner, Lorenz Richter, Karen Ullrich

CoRR, 2022

Training ReLU networks to high uniform accuracy is intractable.

Julius Berner, Philipp Grohs, Felix Voigtländer

CoRR, 2022

Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning.

Lorenz Richter, Julius Berner

Proceedings of the International Conference on Machine Learning, 2022

2021

The Modern Mathematics of Deep Learning.

Julius Berner, Philipp Grohs, Gitta Kutyniok, Philipp Petersen

CoRR, 2021

2020

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.

Julius Berner, Philipp Grohs, Arnulf Jentzen

SIAM J. Math. Data Sci., 2020

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

Julius Berner, Markus Dablander, Philipp Grohs

Proceedings of the Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, 2020

2019

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

Julius Berner, Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen

CoRR, 2019

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

Dennis Elbrächter, Julius Berner, Philipp Grohs

Proceedings of the Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, 2019