Lukas Exl

My research lies at the intersection of Applied Mathematics, Computational Physics, and Scientific Machine Learning, , with a strong emphasis on numerical methods and the mathematical modeling of complex physical systems. I am particularly passionate about developing and analyzing algorithms for PDE‐based simulations, reduced‐order modeling, and data‐driven approaches that capture multiscale phenomena. My core research focuses on the following areas of numerical methods and physical system modeling:

• Computational Micromagnetism & Magnetic Materials for Green Energy - Numerical (multiscale) modeling and (machine-learning-based) simulation of magnetic material properties and magnetization processes (Landau-Lifschitz-Gilbert equations), including simulation-based optimization of rare-earth reduced permanent magnets for sustainable energy technologies.
• Mathematically-Grounded Machine Learning - Development and analysis of machine learning methods with a focus on numerical mathematics aspects and complexity in scientific applications.
• Machine Learning for Physical Systems - Data-driven methods including neural architectures such as Extreme Learning Machines (ELMs), Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs), incorporate physical laws and enable accelerated, constraint-aware learning of complex physical processes through (data-driven) reduced order models.
• Numerical Low-Rank Tensor Methods - Efficient solvers for high-dimensional problems using tensor decompositions and advanced integration schemes.
• Trustworthy and Explainable AI (TAI/XAI) - Development of reliable, interpretable AI models grounded in physical laws and scientific transparency.

https://homepage.univie.ac.at/lukas.exl/

• FWF Principal Investigator Project (EUR 484k, 2024-2028) "Data-driven Reduced Order Approaches for Micromagnetism (Data-ROAM)" at WPI Vienna

• FWF Principal Investigator Project (EUR 254k, 2022-2027) "Design of Nanocomposite Magnets by Machine Learning (DeNaMML)" at MMM c/o Univ. Wien

• FWF Principal Investigator Project (EUR 402k, 2018-2024) "Reduced Order Approaches for Micromagnetics (ROAM)" at WPI Vienna

(cv sketch)

Higher Education

• 2024 Habilitation (venia docendi) in the field of Computational Science (Privatdozent), University of Vienna, Austria; Referees: Prof. Carstensen (Humboldt Universität zu Berlin), Dr.  Chubykalo-Fesenko (Materials Science Institute of Madrid, CSIC) and Prof. Després (Sorbonne Université).
• 2010 - 2014 PhD in computational physics (Dr.techn., w/ distinction), supervisor/examiner: Thomas Schrefl / Claudio Serpico, Vienna University of Technology, Austria
• 2004 - 2010 Diploma in technical mathematics (Dipl.-Ing., w/ distinction) concentration in mathematics in science, Vienna University of Technology, Austria

Appointments & Positions

• since 2024: Research Director - Head of Math. AI/ML Research Division at Wolfgang Pauli Institute (WPI) Vienna
• since 2020: Senior Scientist (1⁄2 permanent) at University of Vienna
• since 2016: (External) Lecturer in computational science and numerical mathematics at University of Vienna
• 2018 - 2024: Group leader (Machine learning & Model reduction) at Wolfgang Pauli Institute (WPI) Vienna
• 2014 - 2018: Postdoc positions within SFBs in groups of N. Mauser, D. Suess and D. Praetorius at University of Vienna and Vienna University of Technology