I am Senior Scientist (permanent) and team lead at University of Vienna, as well as Lecturer for Machine Learning, Computational Sciences and Applied Mathematics at the Departments of Mathematics, Physics, Earth Science (Meteorology-Geophysics- Astronomy) and at Basic Experimental Physics Training and University Didactics. I am assigned to the works council of the scientific staff at University of Vienna as an elected member.
At Wolfgang Pauli Institute (WPI) I hold the position of a Senior Research Fellow & Principal Investigator, where I lead the research division Machine Learning & Model Order Reduction.

My research concerns numerical methods and modelling related to applications, including topics like

  • Computational micromagnetism
  • Machine learning methods and models for magnetization processes
  • Trustworthy / explainable AI
  • Machine learning and data analysis of magnetic materials for the green energy transition
  • Higher-order stochastic training methods
  • Physics-informed neural networks (PINNs), data-driven solution of PDEs and numerical (low-rank) tensor calculus
  • Data-driven nonlinear model order and dimensionality reduction
  • Nonlocal potential and field calculation
  • Numerical optimization
My national and international network is always open for collaborative work and projects.
Please, do not hesitate to contact me via lukas.exl@univie.ac.at.

FWF Project site "Reduced Order Approaches for Micromagnetics (ROAM)"

FWF Project site "Design of Nanocomposite Magnets by Machine Learning (DeNaMML)"

Vienna Scientific Cluster (VSC) Project 71140

Vienna Scientific Cluster (VSC) Project 71952

Modular PINN framework MagPI for computational micromagnetism (and beyond)

University of Vienna research platform "MMM Mathematics-Magnetism-Materials"

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  • Emina Demirovic started her master thesis on ''Algorithmic investigation of trustworthy machine learning models'' with focus on transparency, stability and robustness within my research group in the project DeNaMML at platform MMM, where we develop robust ML models and efficient higher-order stochastic training algorithms, among others, to drive the green energy transition .
  • 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]



  • 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