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Julius Berner
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Mathematical Capabilities of ChatGPT
S Frieder, L Pinchetti, RR Griffiths, T Salvatori, T Lukasiewicz, ...
Advances in Neural Information Processing Systems 36, 2024
398*2024
The Modern Mathematics of Deep Learning
J Berner, P Grohs, G Kutyniok, P Petersen
Mathematical Aspects of Deep Learning, 1-111, 2022
200*2022
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of …
J Berner, P Grohs, A Jentzen
SIAM Journal on Mathematics of Data Science 2 (3), 631-657, 2020
1992020
Group testing for SARS-CoV-2 allows for up to 10-fold efficiency increase across realistic scenarios and testing strategies
CM Verdun, T Fuchs, P Harar, D Elbrächter, DS Fischer, J Berner, ...
Frontiers in Public Health 9, 583377, 2021
652021
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning
J Berner, M Dablander, P Grohs
Advances in Neural Information Processing Systems 33, 2020
492020
How degenerate is the parametrization of neural networks with the ReLU activation function?
J Berner, D Elbrächter, P Grohs
Advances in Neural Information Processing Systems, 7790-7801, 2019
38*2019
An optimal control perspective on diffusion-based generative modeling
J Berner, L Richter, K Ullrich
Transactions on Machine Learning Research, 2024
312024
Improved sampling via learned diffusions
L Richter, J Berner
International Conference on Learning Representations, 2024
182024
Towards a regularity theory for ReLU networks–chain rule and global error estimates
J Berner, D Elbrächter, P Grohs, A Jentzen
2019 13th International conference on Sampling Theory and Applications …, 2019
152019
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning
L Richter, J Berner
International Conference on Machine Learning, 18649-18666, 2022
142022
Learning ReLU networks to high uniform accuracy is intractable
J Berner, P Grohs, F Voigtlaender
International Conference on Learning Representations, 2023
82023
Physics-Informed Neural Operators with Exact Differentiation on Arbitrary Geometries
C White, J Berner, J Kossaifi, M Elleithy, D Pitt, D Leibovici, Z Li, ...
The Symbiosis of Deep Learning and Differential Equations III, 2023
52023
DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training
Z Hao, C Su, S Liu, J Berner, C Ying, H Su, A Anandkumar, J Song, J Zhu
arXiv preprint arXiv:2403.03542, 2024
32024
Neural Operators with Localized Integral and Differential Kernels
M Liu-Schiaffini, J Berner, B Bonev, T Kurth, K Azizzadenesheli, ...
arXiv preprint arXiv:2402.16845, 2024
32024
Large Language Models for Mathematicians
S Frieder, J Berner, P Petersen, T Lukasiewicz
International Mathematical News 254, 2023
32023
Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs
MA Rahman, RJ George, M Elleithy, D Leibovici, Z Li, B Bonev, C White, ...
arXiv preprint arXiv:2403.12553, 2024
22024
Solving Poisson Equations using Neural Walk-on-Spheres
HC Nam, J Berner, A Anandkumar
Forty-first International Conference on Machine Learning, 2024
2024
Mathematical Analysis of Deep Learning with Applications to Kolmogorov Equations
J Berner
University of Vienna, 2023
2023
Die moderne Mathematik des tiefen Lernens
J Berner, P Grohs, G Kutyniok, P Petersen
Mitteilungen der Deutschen Mathematiker-Vereinigung 29 (4), 191-197, 2021
2021
Solving stochastic differential equations and Kolmogorov equations by means of deep learning and Multilevel Monte Carlo simulation
J Berner
University of Vienna, 2018
2018
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