The Austrian Science Fund (FWF) project Reduced Order Approaches for Micromagnetics (ROAM) started end of 2018 at the Wolfgang Pauli Institute (WPI), where I have the project lead.

We focus on the development of mathematical models and numerical methods utilizing model order reduction (MOR) mainly for partial differential equations (PDE) like the LLG equation as the central PDE in micromagnetism as well as numerical energy minimization.

Data-driven approaches and models are integral for ROAM:

  • Machine learning and nonlinear model order reduction (nl-MOR) for magnetic materials such as permanent magnets.
  • Data-driven models of micromagnetic magnetization dynamics (feature space integration via nl-MOR, (un)supervised learning, (low-rank) kernel methods, regularized neural networks and autoencoders).
  • Numerical tensor techniques as MOR approach for economical solution of PDEs on tensorial grids.
  • We follow the philosophy of utilizing data-driven research in connection with underlying PDE models for the physics to solve the real problem in the application. Furthermore, we make use of certain synergy effects to enhance numerical methods in computational quantum dynamics for e.g. Bose-Einstein condensates modelled via nonlinear Schrödinger(-Poisson) equation as well as optimal control for e.g. the dipolar droplet formation process.

We run the accompanying Vienna Scientific Cluster (VSC) project 71140 on the clusters VSC-3 and VSC-4 to support ROAM for computational tasks and simulations.

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Work / Activities funded by ROAM:

  • 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.''
  • We extended our associated project 71140 on VSC-3 and VSC-4 for another period ending spring 2024.
  • Research visit in group of Rasmus Bjørk at TU Denmark, Aug 23 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]
  • We extended our associated project 71140 on VSC-3 and VSC-4 for another period ending spring 2023.
  • 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.)
  • Sebastian Schaffer successfully finished his master studies on machine learning in micromagnetism and its numerical aspects within the ROAM project in Aug 2021. He will now start his PhD studies within the University of Vienna research platform MMM co-financed by ROAM.
  • 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.)
  • The master student Sophie Reisinger joined the ROAM project in April 2021 working on machine learning and its numerical aspects in computational micromagnetism.
  • We participate in the INTERMAG 2021 virtual conference from 26 - 30 April 2021
    Session GC: New Approaches in Computational Magnetism
    Talk (GC-06): L. Exl, ''Machine learning methods for the prediction of micromagnetic magnetization dynamics.'', [contribution] [presentation slides]
  • We extended our associated project 71140 on VSC-3 and VSC-4 for another period ending spring 2022.
  • The master student Sebastian Schaffer joined the ROAM project in March 2020 working in machine learning and its numerical aspects, specifically on prediction of micromagnetic dynamics (LLG) via nonlinear model reduction with kernel methods.
  • We extended our associated project 71140 on VSC-3 and VSC-4 for another period ending spring 2021.
  • 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.)
  • Research on machine learning for permanent magnets will be presented at MMM 2019 conference in Las Vegas (USA). Participating talk (CA-03): ''Classification and optimization of a magnet’s microstructure.''
  • A working group on ''Micromagnetics of permanent magnets'' took place at WPI on 14th Oct 2019. Participating talk: ''Machine Learning and Dimensionality Reduction for Computational Micromagnetism.''
  • 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]
  • We participate in the 15th ViCoM Workshop in Vienna (AUT)
    Talk: L. Exl, ''Machine Learning for computational Micromagnetism.'', [presentation slides]
  • We participate in the 2019 JOINT MMM-INTERMAG conference in Washington D.C. (USA)
    Talk: (FG-05) L. Exl, ''Magnetic microstructure machine learning analysis.''
  • 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]
  • An optimization approach for dynamical Tucker tensor approximation
    - Published online in RINAM 2019 [open access]
  • We participate in the 2018 MANA conference in Vienna (AUT)
  • A magnetostatic energy formula arising from the L²-orthogonal decomposition of the stray field
    - Published in JMAA Nov 2018 [JMAA] [accepted manuscript]
  • 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]