Event: MLDS, Machine Learning and Dynamical Systems Seminar Date: Thu. October 30, 2025 at 17:00H (local time) Organizer: The Alan Turing Institute Inaugural Lecture: Machine Learning, Control Theory, and PDEs: Foundations and Advances from Variational Pathologies to Diffusion Models for Generative AI Speaker: Prof. Enrique Zuazua, FAU – Friedrich-Alexander-Universität Erlangen-Nürnberg […]
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Date: Mon. November 10, 2025 Event: FAU MoD Lecture Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) FAU MoD Lecture: AI Components in PDE Solvers Speaker: Prof. Dr. Nils Thürey Affiliation: TUM, Technical University of Munich Abstract. In this lecture, I will talk […]
Join us on Saturday October 25, 2025 at the #NdW25! Our FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship will be at the “Lange Nacht der Wissenschaften” (Long Night of Sciences) in Erlangen, Fürth and Nürnberg with: Exhibition Sentimentanalyse mit Transformern in Aktion […]
Event: #NdW25, Long Night Sciences 2025 • Martin Gugat, Professor Akad. Director at FAU DCN-AvH. • Christopher Sorg, PhD student at FAU DCN-AvH. Poster 1: The Turnpike Phenomenon in Gas Networks (Das Turnpike-Phänomen in Gasnetzen) View this poster Poster 2: (Two examples) The Turnpike Phenomenon in Gas Networks View this […]
Date: Mon. October 27, 2025 Event: FAU MoD Lecture Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) FAU MoD Lecture: Finding the optimal model complexity of whole-brain models and digital twins Speaker: Prof. Dr. Xenia Kobeleva Affiliation: Department of Neurostimulation, Ruhr-Universität Bochum (Germany) […]
Date: Mon. October 13, 2025 Event: FAU MoD Lecture Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) FAU MoD Lecture: Disruption in science and engineering happens at scale Speaker: Prof. Dr. Johannes Brandstetter Affiliation: Johannes Kepler University Abstract. In the era of LLM […]
Join us on Saturday October 25, 2025 at the #NdW25! Our FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship will be at the “Lange Nacht der Wissenschaften” (Long Night of Sciences) in Erlangen, Fürth and Nürnberg with: Exhibition Das Turnpike-Phänomen in Gasnetzen. Theoretische […]
Next Thursday September 25, 2025 our team member Martín Hernández will present his PhD Thesis on: “From Optimal Control to Random and Neural Network Approximation” Supervisor: Prof. Enrique Zuazua, FAU – Friedrich Alexander-Universität Erlangen-Nürnberg (Germany) Abstract. This talk presents contributions grounded in control and computation. First, we focus on long-time […]
On Wednesday September 24, 2025 Prof. Enrique Zuazua will give a lecture on Inverse design for parabolic and hyperbolic problems at the Hyperbolic Problems in Nürnberg workshop organized by our research fellow Dr. Nicola de Nitti and Prof. Emil Wiedermann (FAU) on September 24-26, 2025 in Nürnberg, Germany. Hyperbolic conservation […]
Next Fall on September 15 – 19, 2025 there is the 9th. international conference on “Advanced COmputational Methods in ENgineering and Applied Mathematics” (ACOMEN2025) in Ghent, Belgium. The conference aims to provide an international forum to present and discuss the latest developments in computational and applied mathematics in various emerging […]
Date: Tue. September 23, 2025 Event: FAU MoD Lecture Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) Session 01: 11:30H HYCO: Hybrid-Cooperative Learning for PDEs Speaker: Dr. Lorenzo Liverani Affiliation: FAU MoD, Research Center for Mathematics of Data | FAU DCN-AvH at Friedrich-Alexander-Universität […]
Event: JLU Short-course Date: Mon.-Wed. July 21-23, 2025 Title: PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning Speaker: Prof. Enrique Zuazua. FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) Videos/recordings Find this course at our YouTube channel @faumod: https://www.youtube.com/@faumod Watch the complete course at our @Youtube playlist • Session 1/3: https://youtu.be/Vet36bGpleM • […]
Multi-physics problems, involving coupled phenomena such as fluid mechanics, thermodynamics, and chemistry, are common in science and engineering. These problems often involve distinct governing equations (e.g., Navier–Stokes, elasticity, diffusion) and specialized solvers, making monolithic solutions computationally prohibitive. Domain decomposition (DD) offers an effective strategy by partitioning the domain into […]
On August 26-29, 2025 our researcher FAU DCN-AvH, Director Akad. Prof. Martin Gugat and Prof. Jan Sokolowski organized the “The Exponential Turnpike Property for Neural Differential Equations”, a special session on Recent Developments in Optimal Design of Control Systems & the Turnpike Property at the MMAR 2025 – 29th International […]
Date: Fri. August 15, 2025 at 09:00H (local time) Event: CIRM Workshop “Mathematical and Computational Foundations of Digital Twins” Talk: HYCO: A Hybrid-Cooperative Strategy for Data-Driven PDE Model Learning Speaker: Prof. Enrique Zuazua, FAU – Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) Abstract. In this talk, we introduce a novel Hybrid-Collapse (HYCO) strategy for […]
On August 11-15, 2025 there is the “Mathematical and Computational Foundations of Digital Twins” Workshop at CIRM, France. This workshop will bring together experts from academia, industry, and research agencies to explore how advancements in real-time synchronization between digital twins and their physical counterparts, along with developments in areas such […]
Evaluating client contribution in Federated learning In the recent years federated learning has emerged as a powerful paradigm for training machine learning models across decentralized data sources, enabling collaborative intelligence without compromising data privacy. In this post, which follows a great introduction by Ziqi Wang on the topic of […]
A relaxed splitting method for solving variational inclusion and fixed point problems 1 Introduction Variational inclusion and fixed point problems are fundamental in many areas of applied mathematics, including optimization, inverse problems, equilibrium theory, image processing, and machine learning. These problems can be formulated as finding a common solution […]
Date: Fri.- Sun. July 25 – 27, 2025 Event: Workshop on Recent Trends in Applied Mathematics and Machine Learning 2025 Title: Recent Trends in Applied Mathematics and Machine Learning 2025 This July, Jilin University will host the Workshop on Recent Trends in Applied Mathematics and Machine Learning 2025, organized in […]
Event: ICBS 2025, International Congress of Basic Science 2025 Poster: Approximation Theory and applications of semi-autonomous Neural ODEs Award: Outstanding Poster Award • Ziqian Li, FAU DCN-AvH. Friedrich-Alexander-Universität Erlangen–Nürnberg • Lorenzo Liverani, FAU DCN-AvH/FAU MoD. Friedrich-Alexander-Universität Erlangen–Nürnberg • Enrique Zuazua, FAU DCN-AvH/FAU MoD. Friedrich-Alexander-Universität Erlangen–Nürnberg • Kang Liu, Université Bourgogne […]
Date: Mon. July 7, 2025 Event: FAU MoD Lecture Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) FAU MoD Lecture: Exemplary applications of machine learning and optimization in quantum chemistry Speaker: Prof. Dr. Andreas Görling Affiliation: FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg Abstract. Two exemplary applications […]
Introduction The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these systems can yield critical insights for developing strategies in ecological management and biodiversity conservation. In this post, we […]
Event: ICBS2025, International Congress of Basic Science 2025 Date: Tue. July 15, 2025 at 15:30 (local time) Talk: PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning Speaker: Prof. Enrique Zuazua, FAU – Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) Slides VIDEO Watch this talk @YouTube: https://youtu.be/WWHOMEKvXmU Abstract. Partial Differential Equations (PDEs) form […]
Date: June 30 to July 4, 2025 Event: IEECI-IGSC 2025: International Graduate School on Control 2025 Module Control and Machine Learning (M18 DUBROVNIK) Speakers: • Prof. Enrique Zuazua. FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg • Prof. Martin Lazar. University of Dubrovnik Outline • Historical preliminaries • Control of linear finite-dimensional systems • The […]
Mathematical modeling and numerical simulations for Gas Dynamics (on Networks) Gas transport networks are essential in the real world, e.g, energy supply, industrial applications, and emergency services. In our model, we focus on the gas flow of pipeline networks that are described by the Euler equations, which are given by […]
Date: Mon.-Tue. June 23 – 24, 2025 Event: FAU MoD Lecture & Workshop Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) FAU MoD Lecture: Mon. June 23, 2025 at 16:00H AI for maths and maths for AI Speaker: Dr. François Charton Affiliation: Meta […]
On Tuesday June 24, 2025 Prof. Enrique Zuazua will give a talk as keynote speaker on PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning at the LSMS 2025 conference, 12th. Annual Meeting of the “Lebanese Society for the Mathematical Sciences” held at the American University of Beirut on […]
Date: Tue. June 3, 2025 Event: FAU MoD Lecture Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) FAU MoD Lecture: Optimization-based control for large-scale and complex systems: When and why does it work? Speaker: Prof. Dr. Lars Grüne Affiliation: Universität Bayreuth (Germany) Abstract. […]
HYCO: The hybrid-collapse strategy for time-independent PDEs This post explores core ideas on a novel hybrid modelling procedure, within the framework of time-independent partial differential equations, drawn from ongoing research in collaboration with Lorenzo Liverani and Enrique Zuazua. GitHub Repository The code to reproduce the experiments can be found at […]
On Wednesday May 28, 2025 our researchers at FAU DCN-AvH, Director Akad. Prof. Martin Gugat and postdoctoral researcher Dr. Michael Schuster participated at the vocatium Fürth 2025 workshop organized by the IfT Institute for Talent Development in Fürth, Germany. There Prof. Gugat and Dr. Schuster did provide information about careers […]
Hybrid parabolic-hyperbolic effect for heat equations with memory 1 Introduction PDEs with memory involve the past values of solutions. In the modeling, one physical quantity induces time-delayed actions on others, and and a large number of such actions form memory (as a time integral). Such models with memory are […]
From June 16 – 20, 2025, our FAU MoD, Research Center for Mathematics of Data at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg is co-hosting with the Universidade Federal Fluminense the “Trends in Mathematical Sciences and Data Sciences” workshop with the support of the FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics […]
Boundary and Interior Control in a Diffusive Lotka-volterra Model 1 Introduction 1.1 Problem formulation and main results In this post, we consider a general diffusive Lotka-Volterra Model (LVM) for two competing species. The system, with boundary controls and an interior multiplicative control, is described by where are positive parameters, […]
Date: Fri. – Thu. May 2 – 8, 2025 Event: FAU MoD Course Organizer: FAU MoD, Research Center for Mathematics of Data at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg FAU MoD Course: Towards a Mathematical Foundation of Deep Learning: From Phenomena to Theory Speaker: Prof. Dr. Yaoyu Zhang Affiliation: Institute of Natural Sciences […]
Date: Wed. May 7, 2025 Event: FAU MoD Lecture Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) FAU MoD Lecture: Mathematics of neural stem cells: Linking data and processes Speaker: Prof. Dr. Ana Martin-Villalba Affiliation: Molecular Neurobiology. DKFZ, German Cancer Research Center (Deutsches […]
Optimal control of Fokker-Planck and transport equations using renormalized solutions 1 Introduction The fundamental general optimal control problem we consider is the following: This is a bilinear optimal control problem for a Fokker-Planck equation (1.1) with time-dependent control . In the objective function to be minimized, with are weighting […]
Date: Fri. May 2, 2025 Event: FAU MoD Lecture Series (double session) May 2025 Organized by: FAU MoD, the Research Center for Mathematics of Data at Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) Session 01: 10:00H FAU MoD Lecture: Random Batch Methods for classical and quantum molecular dynamics Speaker: Prof. Dr. Shi Jin Affiliation: […]
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, […]
Mathematics & Philosophy: On the philosophical foundations of mathematics and its role as a structural science When we talk about mathematics today, many people think primarily of numbers, formulas, and calculations. Yet anyone who delves more deeply into the field soon discovers that mathematics is far more than a mere […]
On Wednesday April 9, 2025 Prof. Enrique Zuazua will give a talk as keynote speaker on Modelling, Machine Learning and Control at the HB Conference on Evolution Equations and Control Theory organized in honor of Prof. Hammadi Bouslous by Team of Analysis and Control of Systems and Interactions (TACSI), the […]
On Friday April 4, 2025 Prof. Enrique Zuazua will give a ICMAT Seminar on Machine Learning on Control and Machine Learning organized at ICMAT, Instituto de Ciencias Matemáticas in Madrid, Spain. Abstract. Systems control, or cybernetics—a term first coined by Ampère and later popularized by Norbert Wiener—refers to the science […]
On Tuesday April 1, 2025 Prof. Enrique Zuazua will give a Langtangen Seminar on Control and Machine Learning organized (online) by Marie E. Rognes and Thomas M. Surowiec. Named in honour of Professor Hans Petter Langtangen, the Langtangen Seminar on Scientific Computing series by Simula, is a new online seminar […]
The hidden challenge in heat equation control: Slow decay of gramian eigenvalues 20.03.2025. Rethinking Heat Equation Controllability: The Hidden Limitations of Slow Eigenvalue Decay “New research challenges long-held assumptions about the controllability of heat systems. Professors Lazar and Zuazua reveal that Gramian eigenvalues decay at a slower, polynomial rate rather […]
Federated Learning for Systems Identification Federated learning (FL) operates in a decentralized manner, as shown Figure 1, allowing multiple clients (or devices) to collaboratively train a model while ensuring the privacy of local data. This method is particularly relevant for systems identification, where clients have access to limited and environmentspecific […]
3−wave turbulence kinetics: Numerical approach for energy cascading This post provides an overview of the results presented in the paper “Numerical schemes for a fully nonlinear coagulation-fragmentation model coming from wave kinetic theory” by Arijit Das and Minh-Binh Tran [1]. 1. Introduction The theory of wave turbulence has been […]
Next Monday March 10, 2025: FAU DCN-AvH Mini-Workshop on Analysis, Numerics, Control and Machine Learning Organized by: FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany) Session 01. Title: Model order reduction for parametric dynamical systems Speaker: Giulia Sambataro […]
On Tuesday March 4, 2024 our postdoctoral researchers Michael Schuster will talk at the SIGOPT 2025 International Conference on Optimization in Siegen, Germany. Slides Abstract. In the operation of pipeline networks, compressors play a crucial role in ensuring the network’s functionality for various scenarios. In this contribution we address the […]
On Wednesday February 26, 2025 Prof. Enrique Zuazua will give a Frontiers of Mathematics lecture on Control and Machine Learning organized at The University of Hong Kong (HKU). Abstract. Systems control, or cybernetics—a term first coined by Ampère and later popularized by Norbert Wiener—refers to the science of control and […]
How to steer a fleet of agents by controlling only a few: a mean-field approach 1 Introduction The challenge of controlling large systems of interacting agents has garnered significant attention in recent years. Applications of such problems include crowd evacuations, achieving consensus within a large group, and traffic flow […]
Clustering in discrete-time self-attention Since the article Attention Is All You Need [1] published in 2017, many Deep Learning models adopt the architecture of Transformers, especially for Natural Language Processing and sequence modeling. These Transformers are essentially composed of layers, alternating between self-attention layers and feed forward layers, with normalization […]