Publications and Preprints

2024 M. Liu-Schiaffini, J. Berner, B. Bonev, T. Kurth, K. Azizzadenesheli, A. Anandkumar Neural Operators with Localized Integral and Differential Kernels.

ICML 2024

Oral presentation at ICLR 2024 Workshop on AI4Differential Equations In Science
2024 H. C. Nam, J. Berner, A. Anandkumar Solving Poisson Equations using Neural Walk-on-Spheres.

ICML 2024

ICLR 2024 Workshop on AI4Differential Equations In Science
2024 Z. Hao, C. Su, S. Liu, J. Berner, C. Ying, H. Su, A. Anandkumar, J. Song, J. Zhu DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training. ICML 2024
2023 L. Richter, J. Berner, G.-H. Liu Improved sampling via learned diffusions.

ICLR 2024

ICML 2023 Workshop on New Frontiers in Learning, Control, and Dynamical Systems
2023 S. Frieder, L. Pinchetti, R. Griffiths, T. Salvatori, T. Lukasiewicz, P. Petersen, A. Chevalier, J. Berner Mathematical Capabilities of ChatGPT.

NeurIPS 2023 Datasets and Benchmarks Track

Interview on Ars Technica

Featured in a study for the German parliament

Note on LLMs for Mathematicians (IMN 2023)
2022 J. Berner, L. Richter, and K. Ullrich An optimal control perspective on diffusion-based generative modeling.

Transactions on Machine Learning Research

Oral presentation at NeurIPS 2022 workshop on score-based methods
2022 J. Berner, P. Grohs, and F. Voigtlaender Learning ReLU networks to high uniform accuracy is intractable.

ICLR 2023

Featured in "What’s Happening in the Mathematical Sciences" (AMS)
2022 L. Richter, J. Berner Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning.

Proceedings of ICML 2022

Featured on deeppde.org
2021 J. Berner, P. Grohs, G. Kutyniok, and P. Petersen The Modern Mathematics of Deep Learning.

Mathematical Aspects of Deep Learning (Cambridge University Press)

Magazine of the German Mathematical Society (shortened, in German)
2020 J. Berner, M. Dablander, and P. Grohs Numerically Solving Parametric Families of High-Dimensional Kolmogorov Partial Differential Equations via Deep Learning.

Proceedings of NeurIPS 2020

Oxford Mathematics case study

Featured on deeppde.org
2020 C. M. Verdun, T. Fuchs, P. Harar, D. Elbrächter, D. S. Fischer, J. Berner, P. Grohs, F. J. Theis, and F. Krahmer Group testing for SARS-CoV-2 allows for up to 10-fold efficiency increase across realistic scenarios and testing strategies.

Frontiers in Public Health

Featured in SIAM News article
2019 J. Berner, D. Elbrächter, and P. Grohs How degenerate is the parametrization of neural networks with the ReLU activation function? Proceedings of NeurIPS 2019
2019 J. Berner, D. Elbrächter, P. Grohs, and A. Jentzen Towards a regularity theory for ReLU networks–chain rule and global error estimates. Proceedings of SampTA 2019
2018 J. Berner, P. Grohs, and A. 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 Journal on Mathematics of Data Science

Featured in "What’s Happening in the Mathematical Sciences" (AMS)

Scientific Activities

05/2023 Poster Presentation ICLR 2024 Vienna Exhibition and Congress Center
04-05/2024 Research Visit Machine Learning Group (Klaus-Robert Müller) TU Berlin
04/2024 Invited Speaker AI Bootcamp - Physics Informed Learning and Computation Caltech
03/2024 Award Recipient

Excellence grant and ring of honor for Promotio sub auspiciis Praesidentis rei publicae

News: Presidential Chancellery, Faculty of Mathematics, University of Vienna, Newspaper

 Presidential Chancellery of Austria
02/2024 Oral Presentation SIAM UQ24 Savoia Excelsior Palace Trieste
02/2024 Speaker Math Machine Learning seminar MPI MIS + UCLA Virtual-only (MPI and UCLA)
01-03/2024 Teaching Assitant Foundations of Machine Learning Caltech
12/2023 Comittee Member Member of the AI graduate admissions committee Caltech
12/2023 Poster Presentation NeurIPS 2023 New Orleans Convention Center
10/2023 Invited Panelist ARIT 2023 Millennium Biltmore Hotel
09/2023 Fellowship Recipient Wally Baer and Jeri Weiss Postdoctoral Fellowship in IST Caltech
06/2023 PhD Defense Committee: Christoph Reisinger (University of Oxford), Siddhartha Mishra (ETH Zurich), Philipp Grohs (University of Vienna, Supervisor) University of Vienna
05/2023 Poster Presentation ICLR 2023 Kigali Convention Centre
2023 Reviewer Reviews for ICLR '24, NeurIPS '23, ICML '23, Nature Mach. Intell., AISTATS '24, SN PDEA, SIMODS, ACHA, Journal of Complexity, ICML '23 Workshop Frontiers4LCD, NeurIPS '23 Datasets and Benchmarks Track
03/2023 Speaker Learning on Graphs and Geometry (LoGG) reading group Virtual-only (MIT and Valence Discovery)
2022 Reviewer Reviews for ICLR, NeurIPS, ICML (outstanding reviewer), JUQ, SISC
12/2022 Oral Presentation

NeurIPS 2022 workshop on score-based methods

(G-Research travel grant [blog, video])

 New Orleans Convention Center
11/2022 Speaker PhD Colloquium Vienna School of Mathematics
10/2022 Speaker Research Group Meeting (Anima Anandkumar) Caltech
09/2022 Participant Summer School Vienna School of Mathematics
09/2022 Speaker Research Group Meeting (Christoph Lampert) ISTA
07/2022 Paper Presentation ICML 2022 Baltimore Convention Center
09-12/2022 Intern Remote extension of the internship at Fair Labs Magnit @ Meta
05-08/2022 Intern AI Research (generative modeling in the context of neural compression) with Karen Ullrich and Matthew Muckley Meta (Fair Labs)
04/2022 Participant ICLR 2022 Virtual-only Conference
03/2022 Invited Participant LMS Invited Lectures on the Mathematics of Deep Learning Isaac Newton Institute
2021 Reviewer Reviews for NeurIPS, ICLR (highlighted reviewer), ACHA, SISC
08/2021 Invited Guest The Mathematics of Deep Learning ACIT Science Podcast
08/2021 Participant Mathematics of Machine Learning Center for Interdisciplinary Research, Bielefeld University
07-12/2021 Invited Participant Mathematics of deep learning Isaac Newton Institute for Mathematical Sciences
2019-2020 Reviewer Reviews for AAP, ISIT, SampTA
12/2020 Poster Presentation NeurIPS 2020 Virtual-only Conference
09/2020 Participant Summer School Vienna School of Mathematics
05-10/2020 Intern AI Research (semi-supervised & active learning for autonomous driving) with Elmar Haussmann and Christoph Angerer NVIDIA
03/2020 Speaker VSM Student Retreat Vienna School of Mathematics
02/2020 Invited Tutor Machine Learning in Physics: VDSP-ESI Winter School 2020 Erwin Schrödinger International Institute for Mathematics and Physics
12/2019 Poster Presentation NeurIPS 2019 Vancouver Convention Center
11/2019 Participant WeAreDevelopers Congress 2019 Hofburg Vienna
11/2019 Speaker Oberwolfach Graduate Seminar: Mathematics of Deep Learning Mathematical Research and Conference Center in Będlewo
10/2019 Speaker Mathematical and Computational Aspects of Machine Learning Centro di Ricerca Matematica Ennio De Giorgi at Scuola Normale Superiore
09/2019 Participant Summer School Vienna School of Mathematics
09/2019 Invited Participant and Speaker Innovative Approaches to the Numerical Approximation of PDEs Oberwolfach Research Institute for Mathematics
07/2019 Speaker SampTA 2019 Université de Bordeaux
06/2019 Speaker RTG Summer Lectures University of Chicago
06/2019 Speaker Research Group Meeting (Joan Bruna and Afonso Bandeira) NYU Center for Data Science
03/2019 Participant Winter School on Quantum Computation VDS Mathematics
02/2019 Speaker GAMM Annual Meeting 2019 TU Vienna
Since 02/2019 Co-Organizer Deep Learning Seminar University of Vienna, OFAI, ARI

Theses

2023 Mathematical Analysis of Deep Learning with Applications to Kolmogorov Equations. PhD Thesis University of Vienna
2018 Solving stochastic differential equations and Kolmogorov equations by means of deep learning and Multilevel Monte Carlo simulation. Master's Thesis University of Vienna
2016 Diskrete Kosinustransformation in der Bildverarbeitung (in German). Bachelor's Thesis University of Vienna
"Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different." - Goethe