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ORCIDJulius Berner
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Journal Articles
- 2024
[j2]Julius Berner, Lorenz Richter, Karen Ullrich:
An optimal control perspective on diffusion-based generative modeling. Trans. Mach. Learn. Res. 2024 (2024)- 2020
- [j1]Julius Berner
, Philipp Grohs, Arnulf Jentzen:
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. SIAM J. Math. Data Sci. 2(3): 631-657 (2020)
Conference and Workshop Papers
- 2024
- [c10]Simon Frieder, Mirek Olsák, Julius Berner, Thomas Lukasiewicz:
The IMO Small Challenge: Not-Too-Hard Olympiad Math Datasets for LLMs. Tiny Papers @ ICLR 2024 - [c9]Lorenz Richter, Julius Berner:
Improved sampling via learned diffusions. ICLR 2024 - [c8]Zhongkai Hao, Chang Su, Songming Liu, Julius Berner, Chengyang Ying, Hang Su, Anima Anandkumar, Jian Song, Jun Zhu:
DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training. ICML 2024 - [c7]Miguel Liu-Schiaffini, Julius Berner, Boris Bonev, Thorsten Kurth, Kamyar Azizzadenesheli, Anima Anandkumar:
Neural Operators with Localized Integral and Differential Kernels. ICML 2024 - [c6]Hong Chul Nam, Julius Berner, Anima Anandkumar:
Solving Poisson Equations using Neural Walk-on-Spheres. ICML 2024 - 2023
- [c5]Julius Berner, Philipp Grohs, Felix Voigtländer:
Learning ReLU networks to high uniform accuracy is intractable. ICLR 2023 - [c4]Simon Frieder, Luca Pinchetti, Alexis Chevalier, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Petersen, Julius Berner:
Mathematical Capabilities of ChatGPT. NeurIPS 2023 - 2022
- [c3]Lorenz Richter, Julius Berner:
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning. ICML 2022: 18649-18666 - 2020
- [c2]Julius Berner, Markus Dablander, Philipp Grohs:
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning. NeurIPS 2020 - 2019
- [c1]Dennis Elbrächter, Julius Berner, Philipp Grohs:
How degenerate is the parametrization of neural networks with the ReLU activation function? NeurIPS 2019: 7788-7799
Informal and Other Publications
- 2024
- [i20]Miguel Liu-Schiaffini, Julius Berner, Boris Bonev, Thorsten Kurth, Kamyar Azizzadenesheli, Anima Anandkumar:
Neural Operators with Localized Integral and Differential Kernels. CoRR abs/2402.16845 (2024) - [i19]Zhongkai Hao, Chang Su, Songming Liu, Julius Berner, Chengyang Ying, Hang Su, Anima Anandkumar, Jian Song, Jun Zhu:
DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training. CoRR abs/2403.03542 (2024) - [i18]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:
Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs. CoRR abs/2403.12553 (2024) - [i17]Hong Chul Nam, Julius Berner, Anima Anandkumar:
Solving Poisson Equations using Neural Walk-on-Spheres. CoRR abs/2406.03494 (2024) - [i16]Bingliang Zhang, Wenda Chu, Julius Berner, Chenlin Meng, Anima Anandkumar, Yang Song:
Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing. CoRR abs/2407.01521 (2024) - [i15]Hrishikesh Viswanath, Yue Chang, Julius Berner, Peter Yichen Chen, Aniket Bera:
Reduced-Order Neural Operators: Learning Lagrangian Dynamics on Highly Sparse Graphs. CoRR abs/2407.03925 (2024) - [i14]Jingtong Sun, Julius Berner, Lorenz Richter, Marius Zeinhofer, Johannes Müller, Kamyar Azizzadenesheli, Anima Anandkumar:
Dynamical Measure Transport and Neural PDE Solvers for Sampling. CoRR abs/2407.07873 (2024) - [i13]Chuwei Wang, Julius Berner, Zongyi Li, Di Zhou, Jiayun Wang, Jane Bae, Anima Anandkumar:
Beyond Closure Models: Learning Chaotic-Systems via Physics-Informed Neural Operators. CoRR abs/2408.05177 (2024) - [i12]Freya Shah, Taylor L. Patti, Julius Berner, Bahareh Tolooshams, Jean Kossaifi, Anima Anandkumar:
Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems. CoRR abs/2409.03302 (2024) - 2023
- [i11]Simon Frieder, Luca Pinchetti, Ryan-Rhys Griffiths, Tommaso Salvatori, Thomas Lukasiewicz, Philipp Christian Petersen, Alexis Chevalier, Julius Berner:
Mathematical Capabilities of ChatGPT. CoRR abs/2301.13867 (2023) - [i10]Lorenz Richter, Julius Berner, Guan-Horng Liu:
Improved sampling via learned diffusions. CoRR abs/2307.01198 (2023) - [i9]Simon Frieder, Julius Berner, Philipp Petersen, Thomas Lukasiewicz:
Large Language Models for Mathematicians. CoRR abs/2312.04556 (2023) - 2022
- [i8]Julius Berner, Philipp Grohs, Felix Voigtländer:
Training ReLU networks to high uniform accuracy is intractable. CoRR abs/2205.13531 (2022) - [i7]Lorenz Richter, Julius Berner:
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning. CoRR abs/2206.10588 (2022) - [i6]Julius Berner, Lorenz Richter, Karen Ullrich:
An optimal control perspective on diffusion-based generative modeling. CoRR abs/2211.01364 (2022) - 2021
- [i5]Julius Berner, Philipp Grohs, Gitta Kutyniok, Philipp Petersen:
The Modern Mathematics of Deep Learning. CoRR abs/2105.04026 (2021) - 2020
- [i4]Julius Berner, Markus Dablander, Philipp Grohs:
Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning. CoRR abs/2011.04602 (2020) - 2019
- [i3]Julius Berner, Dennis Elbrächter, Philipp Grohs, Arnulf Jentzen:
Towards a regularity theory for ReLU networks - chain rule and global error estimates. CoRR abs/1905.04992 (2019) - [i2]Julius Berner, Dennis Elbrächter, Philipp Grohs:
How degenerate is the parametrization of neural networks with the ReLU activation function? CoRR abs/1905.09803 (2019) - 2018
- [i1]Julius Berner, Philipp Grohs, Arnulf Jentzen:
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. CoRR abs/1809.03062 (2018)
Coauthor Index
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