Reduced Order Approaches for Micromagnetics

Computational micromagnetics is a discipline which describes and calculates magnetic phenomenons on nano- to micrometer scales using both classical and quantum physics. It emerged from applications like magnetic recording and magnetic material design and is nowadays a booster for the design of rare earth reduced high-performance magnets for green energy applications for electric/hybrid vehicles and electric wind and hydro-power generation. Among many others, further applications are random access memory, magnetic sensors and nanomagnetic materials and devices. However, the computer simulations which are used for the design of these applications encounter computational limits since the interplay of phenomenons of rather large length scales (classical electromagnetism) and very small (quantum physics) need both to be taken into account. This exceeds the available computational resources very easily. The project Reduced Order Approaches for Micromagnetics aims at providing applied physicists, theorists and engineers with novel and feasible mathematical tools for their materials and design simulations. The approaches concentrate on ways to reduce the complexity by underlying simplified (numerical) models, such as tensor product approaches, which reduce the dimensionality but still catch the essence. A main objective is the development of computer simulation methods which track the time-dependent change of magnetic states in materials of several microns in size, a task which is definitely not possible for conventional methods nowadays. The project is an example for enhancement of a discipline of computational science by innovative theoretical models and practical numerical methods and is directly linked and useful for applications in engineering.

The primary objective of this project was to advance the development, analysis, and implementation of highly efficient numerical methodologies for micromagnetic simulations. These simulations play a crucial role in various applications, including the design of magnetic materials and the creation of high-performance magnets tailored for green energy applications such as electric/hybrid vehicles, as well as wind and hydro-power generation. Given the computational challenges posed by the complex interplay between large-scale classical electromagnetism and small-scale quantum physics phenomena, we focused on exploring reduced order methods. These methods, which encompass low-rank tensor calculus and data-driven machine learning techniques, offer promising avenues for mitigating computational constraints. Specifically, we devised novel methodologies like the embedded Stoner-Wolfarth model to analyze large-scale grain structures, facilitating micromagnetic machine learning studies on coercive field behaviors of permanent magnets at unprecedented length scales. Notably, our research unveiled the efficacy of edge-hardening through Dy-diffusion, enabling a reduction in rare-earth content while simultaneously enhancing the energy density product. Our pioneering work represented some of the earliest forays into applying machine learning to computational micromagnetics. A significant portion of our efforts was directed towards developing effective data-driven reduced order approaches for magnetic field calculations in magnetostatics, given their inherently computationally intensive nature. Of particular note are the innovative physics-informed machine learning techniques we pioneered, particularly for modeling long-range stray field interactions using unsupervised learning methodologies. Through penalty-free frameworks and efficient higher order training schemes, we paved the way for constraint-free micromagnetic total energy minimization. Furthermore, our investigations demonstrated the feasibility of learning magnetization dynamics in magnetic thin films through non-linear model order reduction techniques, leveraging storage- and computationally efficient low-rank kernel methods alongside neural network auto-encoder models. The outcomes of our project were disseminated through numerous peer-reviewed international journal publications and presentations at various international scientific conferences. Additionally, we initiated the development of a modular physics-informed machine learning framework to facilitate further advancements in this field. This project also supported the financing of several working groups, thematic programs at WPI, two master's theses, and one PhD thesis. Furthermore, it contributed to the habilitation of the principal investigator.