Dipl.-Ing. Dr.techn. Lukas EXL, Priv.-Doz.
Math AI/ML
Wolfgang Pauli Institute (WPI)

Department of Mathematics
University of Vienna

Oskar-Morgenstern-Platz 1
A-1090 Wien, Austria

office: Room 08.127
e-mail: lukas.exl@univie.ac.at
phone: +43-1-4277-50426
web: https://homepage.univie.ac.at/lukas.exl/
ORCID iD iconorcid.org/0000-0002-5343-6938
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WPI






Uni Wien




MMM Uni Wien



FWF

I am currently Research Director at the Wolfgang Pauli Institute (WPI) and Head of the Mathematical AI/ML Research Division at WPI, after serving as a group leader there since 2018. In parallel, I hold a part-time permanent position as Senior Scientist at the Department of Mathematics at the University of Vienna. My teaching includes Machine Learning, Computational Science, and Applied and Numerical Mathematics in various bachelor's and master's programmes. I obtained my habilitation (venia docendi) in Computational Science at the University of Vienna with a thesis on Machine Learning and Numerical Methods for Computational Magnetism; it was the first habilitation in this area to bridge disciplines and faculties.

Research

My research is in Applied Mathematics, with a focus on Scientific Machine Learning and Computational PDEs. I develop numerical and data-driven methods for the simulation, approximation, and optimization of complex physical systems, combining mathematical structure with modern machine learning. Particular interests include nonlocal and nonlinear PDEs, reduced-order modeling, low-rank approximation, and physics-informed learning. Computational micromagnetism and magnetic-material design form a principal application domain of my research.

  • Computational PDEs & Numerical Methods - Development of efficient numerical methods for nonlinear, nonlocal, and multiscale PDEs, including magnetostatics, energy minimization, and dynamical systems arising in computational physics.
  • Scientific Machine Learning - Development and analysis of mathematically and physically structured machine-learning methods, including PINNs, Neural Operators, ELMs, and structure-preserving latent models, with emphasis on reliability, interpretability, physical consistency, and scientific transparency.
  • Reduced-Order & Low-Rank Methods - Efficient approximation of high-dimensional and parametric problems using reduced-order models, latent representations, kernel methods, and low-rank tensor techniques.
  • Computational Micromagnetism & Magnetic Materials - Multiscale simulation of magnetization processes governed by the Landau-Lifshitz-Gilbert equation, efficient computation of magnetostatic interactions, and simulation-driven design of rare-earth-reduced permanent magnets for sustainable-energy technologies.
I welcome collaborations on problems at the interface of applied mathematics, scientific machine learning, and computational physics. Please, do not hesitate to contact me via lukas.exl@univie.ac.at.

Grants & Awards

Academic Positions & Qualifications

since 2024 Research Director and Head of Mathematical AI/ML, Wolfgang Pauli Institute, Vienna
2024 Habilitation in Computational Science, University of Vienna
since 2020 Senior Scientist, Department of Mathematics, University of Vienna
2018–2024 Group Leader, Wolfgang Pauli Institute, Vienna
2014–2018 Postdoctoral Researcher, University of Vienna / TU Wien
2014 PhD, TU Wien

Theses Supervision

  • Nina Trojer, "Analysis and Application of the super-potential method for the screened Poisson equation", Master's thesis, Computational Science, Faculty of Physics, University of Vienna.
  • Moritz Pfurtscheller, "Higher-Order Physics-Informed Neural Networks (HO-PINNs) for Solving Partial Differential Equations", Master's thesis, Computational Science, Faculty of Physics, University of Vienna.

    • Finished:

  • Mahdi Mohaddes (2026), "Spectral-temporal graph neural networks for demand forecasting on bipartite supply-customer graphs", Master's thesis, Applied Mathematics, Faculty of Mathematics, University of Vienna.
  • Sebastian Schmuckermayr (2026), "The minimization of Brown's energy bounds for the magnetostatic energy with the Finite Element Method", Master's thesis, Applied Mathematics, Faculty of Mathematics, University of Vienna.
  • Caroline Maitz (2025), "Dynamical ELM for the solution of time-dependent (partial) differential equations", Master's thesis, Computational Science, Faculty of Physics, University of Vienna.
  • Claas Fillies (2025), "Shape optimization of tunneling magnetoresistance sensor design via automated micromagnetic simulations", Master's thesis (in co-operation w/ DUK), Computational Science, Faculty of Physics, University of Vienna.
  • Verena Alton (2025), "Application and analysis of generative AI algorithms for probabilistic energy forcasts", Master's thesis (in co-operation w/ AIT), Computational Science, Faculty of Physics, University of Vienna.
  • Felix Lasthofer (2025), "Predicting properties of granular microstructures with graph neural networks", Master's thesis (in co-operation w/ DUK), Computational Science, Faculty of Physics, University of Vienna.
  • Thomas Kroiss (2025), "Physics-Informed Extreme Learning Machines for efficient Poisson equation solutions", Master's thesis, Computational Science, Faculty of Physics, University of Vienna.
  • Emina Demirovic (2025), "Algorithmic investigation of trustworthy AI", Master's thesis, Computational Science, Faculty of Physics, University of Vienna. (co-supervision w/ NJ Mauser)
  • Ivan Novikau (2025), "Magnetic and rheological properties of magnetic nanogels", PhD thesis, Faculty of Physics, University of Vienna. (co-supervision w/ S Kantorovich)
  • Sebastian Schaffer (2024), "Physics Informed Machine Learning in the Field of Micromagnetism", PhD thesis, Faculty of Mathematics, University of Vienna. (co-supervision w/ NJ Mauser)
  • Clemens Wager (2024), "Exploring performance of active learning for optimization", Master's thesis (in co-operation w/ DUK), Computational Science, Faculty of Physics, University of Vienna. (co-supervision w/ NJ Mauser)
  • Anatol Ehrlich (2024), "Reaction guided modeling", Master's thesis, Computational Science, Faculty of Physics, University of Vienna. (co-supervision w/ C. Flamm)
  • Alexander Kornell (2021), "Description of collective magnetization processes with machine learning models", Master's thesis (in co-operation w/ DUK), Computational Science, Faculty of Physics, University of Vienna. (co-supervision w/ NJ Mauser)
  • Sebastian Schaffer (2021), "Machine learning methods for the prediction of micromagnetic magnetization dynamics", Master's thesis, Computational Science, Faculty of Physics, University of Vienna. (co-supervision w/ NJ Mauser)

News

  • An Energy-Based Conservative-Dissipative Latent Neural Evolution Operator for Magnetization Dynamics
    - Preprint Sep 2026 [preprint] (cite as: S. Schaffer et al. (2026) arXiv preprint arxiv:2609.04530.)
    - Code Sep 2026 [zenodo] (cite as: S. Schaffer and L. Exl (2026) ebm_llg [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.22281255.)
  • We participate in the 16th International Conference on Barkhausen Noise and Micromagnetic Testing (ICBM16) at TU Dortmund University, Germany, on Sep 21 - 24, 2026.
    Keynote Talk: L. Exl: ''Numerical Methods and Machine Learning for Micromagnetism and Permanent Magnet Design.''
  • Together with Claas Abert (U.Wien), I am organizing the session "Micromagnetics, Modeling, and Scientific Machine Learning" at the 11th International Conference on Superconductivity and Magnetism in Ölüdeniz-Fethiye (Mugla), Turkey, on Apr 19 - 26, 2026.
  • Higher order stray field computation on tensor product domains
    - Published online in J. Comput. Phys. Jan 2026 [open access]
    - Preprint May 2025 [preprint] (cite as: L. Exl et al. (2025) arXiv preprint arxiv:2505.19180.)
    - Code Nov 2025 [zenodo] (cite as: L. Exl and S. Schaffer (2025) Higher order stray field computation on tensor product domains [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.17722988.)
  • Physics-informed low-rank neural operators with application to parametric elliptic PDEs
    - Preprint Sep 2025 [preprint] (cite as: S. Schaffer and L. Exl (2025) arXiv preprint arxiv:2509.07687.)
  • Physics aware machine learning for micromagnetic energy minimization: recent algorithmic developments
    - Preprint Sep 2024 [preprint] (cite as: S. Schaffer et al. (2024) arXiv preprint arxiv:2409.12877.)
    - Published online in Comput. Phys. Commun. Jun 2025 [open access]
  • Near-field-free super-potential FFT method for the three-dimensional free-space Poisson equation
    - Preprint Jun 2025 [preprint] (cite as: L. Exl et al. (2025) arXiv preprint arxiv:2506.04489.)
  • We participate in the 10th International Conference on Superconductivity and Magnetism in Ölüdeniz-Fethiye (Mugla), Turkey, on April 26 - May 3, 2025
    Invited Talk: L. Exl: ''Physics aware extreme learning for computational micromagnetism.''
  • PhD defense of Sebastian SCHAFFER
    Friday, 17. Jan 2025, 15:00-17:00, MMM-WPI-SemRoom, 8th floor, Oskar-Morgenstern-Platz 1, 1090 Wien [announcement]
    We start at 13:40 (same place) with a talk by Prof. D'Aquino (Univ. Napoli Federico II)
  • Explainable Machine Learning and Feature Engineering applied to Nanoindentation Data
    - Preprint Jan 2025 w/ C.O.W. Trost, S. Zak, S. Schaffer, L. Walch, J. Zitz, T. Kluensner, H. Leitner, M.J. Cordill.
    - Published online in Materials and Design Mar 2025 [open access]
  • We participate in the IEEE Conference on Advances in Magnetics (IEEE-AIM2025) in Bressanone (Bolzano), Italy, on February 9-12, 2025
    Talk: S. Schaffer: ''Constraint Free Physics-Informed Machine Learning for Micromagnetic Energy Minimization.''
  • I have been awarded a new Principal Investigator Project (€ 484k) by the Austrian Science Fund (FWF): "Data-driven Reduced Order Approaches for Micromagnetism (Data-ROAM)".
    Many thanks to my team, the WPI and the Austrian Science Fund (FWF)!
    I am delighted to be recognized for my work in data & computational sciences and for the opportunity to expand my team. Also, I am looking forward to the collaboration with project partners at Danube University Krems and at the Technical University of Denmark Department of Energy Conversion and Storage.
  • Constraint Free Physics-Informed Machine Learning for Micromagnetic Energy Minimization
    - Published online in Comput. Phys. Commun. Apr 2024 [open access]
  • Image-based prediction and optimization of hysteresis properties of nanocrystalline permanent magnets using deep learning
    - Published online in JMMM Mar 2024 [open access]
  • MagPI was developed during Sebastian Schaffer's PhD project within Dr. Lukas Exl's research group at WPI and MMM. It represents a starting point for a broader modular PINN framework for computational micromagnetism (and beyond).
  • We participate in the 13th HMM conference at TU Wien, Vienna 5-7 June 2023
    Talk: L. Exl ''Computational micromagnetics with physics-informed neural networks.''
  • Physics-informed machine learning and stray field computation with application to micromagnetic energy minimization
    - Published online in JMMM Apr 2023 [open access]
    - Preprint Feb 2023 (accepted in JMMM Apr 2023) [preprint] (cite as: S. Schaffer et al. (2023) arXiv preprint arxiv.org/abs/2301.13508.)
  • We participate in the Vienna Deep Learning Meetup at UBB University of Vienna 29 March 2023
    Invited Talk: L. Exl, S. Schaffer ''Physics-Informed Neural Networks.''
  • We participate in the 2023 AIM IEEE Advances in Magnetics conference in Moena (IT) from 15-18 Jan 2023
    Invited Talk in Session "Artificial Intelligence, machine learning and Soft-Computing": L. Exl, ''Machine learning methods in computational micromagnetism.''
  • The joint DUK/MMM project Design of Nanocomposite Magnets by Machine Learning with PI H. Oezelt (DUK) and national research partner L. Exl (Univ. Vienna research platform MMM) was acceped by the FWF (EUR 591k, May 2022).
  • Description of collective magnetization processes with machine learning models
    - Preprint May 2022 [preprint] (cite as: A. Kornell et al. (2022) arXiv preprint arxiv.org/abs/2205.03708.)
  • Exploring the hysteresis properties of nanocrystalline permanent magnets using deep learning
    - Preprint Mar 2022 [preprint] (cite as: A. Kovacs et al. (2022) arXiv preprint arxiv.org/abs/2203.16676.)
  • Bridging Fidelities to Predict Nanoindentation Tip Radii Using Interpretable Deep Learning Models
    - Published online in Springer JOM Apr 2022 [open access]
  • Magnetostatics and micromagnetics with physics informed neural networks
    - Published online in JMMM Jan 2022 [JMMM]
    - Preprint Jun 2021 [preprint] (cite as: A. Kovacs et al. (2021) arXiv preprint arxiv:2106.03362.)
  • Conditional physics informed neural networks
    - Published online in CNSNS Sep 2021 [CNSNS]
    - Preprint Apr 2021 [preprint] (cite as: A. Kovacs et al. (2021) arXiv preprint arxiv:2104.02741.)
  • Prediction of magnetization dynamics in a reduced dimensional feature space setting utilizing a low-rank kernel method
    - Published online in J. Comput. Phys. Jul 2021 [J. Comput. Phys.]
    - Preprint Aug 2020 [accepted manuscript] (cite as: L. Exl et al. (2020) arXiv preprint arXiv:2008.05986.)
  • Machine learning methods for the prediction of micromagnetic magnetization dynamics
    - Published online in IEEE Trans. Magn. Jul 2021 [IEEE Trans. Magn.]
    - Preprint Mar 2021 [accepted manuscript] (cite as: S. Schaffer et al. (2021) arXiv preprint arXiv:2103.09079.)
  • Micromagnetism (book chapter)
    - Published online in Handbook of Magnetism and Magnetic Materials. Springer, Cham. Apr 2021 [book chapter] (cite as: Exl L., Suess D., Schrefl T. (2021) Micromagnetism. In: Coey M., Parkin S. (eds) Handbook of Magnetism and Magnetic Materials. Springer, Cham. https://doi.org/10.1007/978-3-030-63101-7_7-1.)
  • !!! POSTPONED TO 2022 !!!
    The conference CMAM 2022 takes place in Vienna, Aug 29 - Sep 2, 2022    .
    We organize
    - The minisymposium MS09 Machine learning and computational micromagnetism.
    - Submission of one-page abstracts possible until Feb 1, 2022, see [abstract submission]
  • Learning time-stepping by nonlinear dimensionality reduction to predict magnetization dynamics
    - Published online in CNSNS Jan 2020 [CNSNS]
    - Preprint and accepted manuscript Jan 2020 [accepted manuscript] (cite as: L. Exl et al. (2019) arXiv preprint arXiv:1904.04215.)
  • Learning magnetization dynamics
    - Published online in JMMM Jul 2019 [JMMM]
    - Preprint Mar 2019 [preprint] (cite as: A. Kovacs et al. (2019) arXiv preprint arXiv:1903.09499.)
  • Optimal control of the self-bound dipolar droplet formation process
    - Published online in CPC Jun 2019 [CPC]
    - Preprint and accepted manuscript May 2019 [accepted manuscript] (cite as: J.-F. Mennemann et al. (2019) arXiv preprint arXiv:1905.12546.)
  • Exploring Many-Body Physics with Bose-Einstein Condensates
    - Published in High Performance Computing in Science and Engineering'18. Springer, Cham, 2019. 89-110. [Springer]
  • Magnetic microstructure machine learning analysis
    - Published online in JPhys Materials 2019 [open access]
  • Computational micromagnetics with Commics
    - Preprint Dec 2018 [preprint] (cite as: C.-M. Pfeiler et al. (2018) arXiv preprint arXiv:1812.05931.)
    - Published in CPC Mar 2020 [CPC]
  • A magnetostatic energy formula arising from the L²-orthogonal decomposition of the stray field
    - Published in JMAA Nov 2018 [JMAA] [accepted manuscript]
  • Preconditioned nonlinear conjugate gradient (P-NCG) method for micromagnetic energy minimization
    - Published online in CPC Sep 2018 [CPC]
    - Preprint 11. Jan 2018 [preprint] (cite as: L. Exl et al. (2018) arXiv preprint arXiv:1801.03690.)
  • Many-body physics in two-component Bose-Einstein condensates in a cavity: fragmented superradiance and polarization
    - Published in NEW J PHYS Apr 2018 [open access]
  • Topical review on Micromagnetics for Permanent Magnets
    - Published in J PHYS D APPL PHYS Mar 2018 [open access]
  • Searching the weakest link: Demagnetizing fields and magnetization reversal in permanent magnets
    - Published in SCRIPTA MATER Dec 2017 [SCRIPTA MATER]
  • An optimization approach for dynamical Tucker tensor approximation
    - Preprint 28. Sep 2017 [preprint] (cite as: L. Exl (2017) arXiv preprint arXiv:1709.09966.)
    - Published online in RINAM 2019 [open access]
  • A solver for the Poisson equation in whole (3d) space via tensor product Gaussian-sum approximation
    - Published in CPC Dec 2017 [CPC] [preprint]
    - Version 26. Apr 2017 [download program]
  • On the limits of coercivity in permanent magnets
    - Published online in APL Aug 2017 [APL] [preprint]
  • Highly Parallel Demagnetization Field Calculation Using the Fast Multipole Method on Tetrahedral Meshes with Continuous Sources
    - Published in JMMM Nov 2017 [JMMM] [preprint]
  • An extrapolation-based explicit integrator for the Landau-Lifschitz-Gilbert (LLG) equation with variable order and step size selection
    - Published in JCOMP Oct 2017 [JCOMP] [preprint]
  • Nonlinear conjugate gradient methods in micromagnetics
    - Published in AIP Apr 2017 [AIP]

– ◊ –

Misc

  • Algorithmic description of Non-uniform fast Fourier transform (NUFFT)
    - Version 11. Dec 2015 [pdf]
    (cite as: L. Exl (2015). Problem descriptions: Non-uniform fast Fourier transform. University of Vienna, Institut f. Mathematik.)
    • Problem description in order to initiate joint project with research group Scientific Computing (Faculty of Computer Science UniVie)
    For application in micromagnetics see:
    L.Exl and T.Schrefl, "Non-uniform FFT for the finite element computation of the micromagnetic scalar potential." J.Comput.Phys. 270 (2014): 490-505. [arXiv] [JCOMP]
  • Gaussian-sum approximation of log(r) kernel (in [Intel] Fortran)
    - Version 7. Oct 2014 [zip]
    • See also:
    L.Exl, N.J.Mauser, Y.Zhang, "Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation", J.Comput.Phys. 327 (2016): 629-642. [arXiv] [JCOMP]
  • Splitting methods for time-dependent Schrödinger equation
    - Version 24. Jun 2013 [pdf]
    • Time splitting methods; Strang splitting plus proof of second order convergence for bounded potential and bounded iterated commutators; Split-step Fourier scheme

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