Machine Learning and PDEs Workshop

Last update: 15.05.2025

On April 28 – 30, 2025, our FAU MoD, Research Center for Mathematics of Data is hosting the “Machine Learning and PDEs” workshop (MLPDES25) supported by the FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics, the AFOSR, Air Force Office of Scientific Research, PoliBa, Politecnico di Bari and the Alexander von Humboldt Stiftung/Foundation organized from April 28 to 30, 2025 at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg in Erlangen – Bavaria (Germany).

This international workshop brings together researchers from across Europe and the United States to explore the growing connection between Machine Learning (ML) and Partial Differential Equations (PDEs)—two core fields in modern mathematics that are now developing a dynamic, mutually beneficial relationship. ML methods are increasingly used to simulate and solve complex PDEs, such as those found in bio-mathematics and fluid dynamics. Meanwhile, techniques from PDE and control theory are helping us better understand and improve ML models.

#MLPDES25 @YouTube: Watch the spot (short) | Video teaser

With participants from diverse backgrounds, this event aims to establish a collaborative platform for experts to network, share insights, and drive progress in this exciting field. We’ll dive into recent theoretical advancements and applications, while also discussing ongoing challenges in areas such as:
• Control and PDE methods for universal approximation and data classification
• Mean field analysis of neural networks
• ML applications in traffic flow modeling and autonomous driving
• ML and numerical simulation in bio-mechanics and micro-fluidics

Join us as we bridge these fields, focusing on both foundational research and practical applications.

Poster of the #MLPDES25

LECTURES • Mon. April 28, 2025

• Enrique Zuazua (FAU) Friedrich-Alexander-Universität Erlangen-Nürnberg and Giuseppe Maria Coclite. Politecnico di Bari
Opening ceremony
See pdf

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• Paola Antonietti. Politecnico di Milano
Lecture: Machine learning enhanced polytopal finite element methods for neurodegenerative disorder modeling
Recording (FAU only): https://www.fau.tv/clip/id/57418

• Daniel Tenbrinck. FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg
Lecture: Eigenvalue problems on graphs and hypergraphs
See slides

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• Camilla Nobili. University of Surrey
Lecture: Quantification of enhanced dissipation and mixing for time-dependent shear flows

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• Paola Goatin. Inria, Sophia-Antipolis
Lecture: Modern calibration strategies for macroscopic traffic flow models
See slides

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• Michele Palladino. Università degli Studi dell’Aquila
Lecture: Handling uncertainty in optimal control
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• Alexander Keimer. Universität Rostock
Lecture: Optimal control of nonlocal conservation laws and the singular limit
See slides

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• Fariba Fahroo and Felix J. Knutson, Air Force Office of Scientific Research
Lecture: International grant opportunities and research interests of the Air Force Office of Scientific Research

• Lorenzo Liverani. FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg
Lecture: Projects and opportunities at the Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship

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LECTURES • Tue. April 29, 2025

• Gabriel Peyré. CNRS, ENS-PSL
Lecture: Transformers are universal in-context learners
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• Gianluca Orlando. Politecnico di Bari
Lecture: Replicator dynamics as the large-population limit of a multi-strategy discrete Moran process
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• Alessandro Coclite. Politecnico di Bari
Lecture: Replicator dynamics on a network

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• Borjan Geshkovski. Inria, Sorbonne Université
Lecture: Many-particle systems perspective on Transformers
Recording (restricted access): https://www.fau.tv/clip/id/57455

• Domènec Ruiz-Balet. Université Paris Dauphine
Lecture: Some remarks on matching measures with Machine Learning architectures

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• Alessio Porretta. Università di Roma Tor Vergata
Lecture: Diffusion effects in optimal transport and mean-field planning models
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• Yaoyu Zhang. Shanghai Jiao Tong University
Lecture: The condensation phenomenon of Deep Neural Networks
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• Günter Leugering. FAU MoD, Friedrich-Alexander-Universität Erlangen-Nürnberg
Lecture: The Speinshart Scientific Center for AI and Supertech

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LECTURES • Wed. April 30, 2025

• Juncheng Wei. Chinese University of Hong Kong
Lecture: On Brezis’s first open problem: a complete solution

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• Francesco Regazzoni. Politecnico di Milano
Lecture: Discovering the hidden low-dimensional dynamics of time-dependent PDEs with latent dynamics networks
See slides

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• Daniela Tonon. Università di Padova
Lecture: Hamilton-Jacobi equations on infinite dimensional spaces
Recording (FAU only): https://www.fau.tv/clip/id/57540

• Shi Jin. SJTU, Shanghai Jiao Tong University
Lecture: Allen-Cahn message passing in graph neural networks and fast Sinkhorn for Wasserstein-1 metric

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• Anne Koelewijn. FAU MoD / BioMAC. Friedrich-Alexander-Universität Erlangen-Nürnberg
Lecture: SSPINNpose: Self-supervised learning of biomechanical variables without ground truth
See slides

• Wei Zhu. Georgia Institute of Technology
Lecture: Structure-Preserving Machine Learning and Data-Driven structure discovery
See slides

• Giovanni Fantuzzi. FAU MoD/DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg
Lecture: Exact sequence classification with hardmax transformers

AUDIENCE

This is a hybrid event (On-site/online) open to: Public, Students, Postdocs, Professors, Faculty, Alumni and the scientific community all around the world.

PROGRAM

#MLPDE25 Program details
#MLPDE25 Schedule

REGISTRATION

Registration is closed.

Certificates: Thank you for your participation! Your certificate will be sent to the email address specified on your registration by 15.05.2025. (Non-academic credits)

WHEN

Mon. – Wed. April 28 – 30, 2025 • 09:30H – 17:00H
This event at your local time

WHERE

On-site / Online

[On-site] FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg
Senatssaal (Senate Hall) im Kollegienhaus
Universitätsstraße 15, 91054
Erlangen – Bavaria, Germany
How to get to Erlangen?

[Online] Live-streaming
https://www.fau.tv/fau-mod-livestream-2025

Scientific Committee

• Giuseppe Maria Coclite. Politecnico di Bari
• Enrique Zuazua. FAU MoD/DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg

Organizing Committee

• Darlis Bracho Tudares. FAU MoD/DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg
• Nicola De Nitti. Università di Pisa
• Lorenzo Liverani. FAU DCN-AvH, Friedrich-Alexander-Universität Erlangen-Nürnberg