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Machine learning force fields (MLFFs) are a promising approach to balance the accuracy of quantum mechanics with the efficiency of classical potentials, yet selecting an optimal model amid increasingly diverse architectures that delivers…

Machine Learning · Computer Science 2025-12-09 Bangchen Yin , Yue Yin , Yuda W. Tang , Hai Xiao

We investigate in details the inertial dynamics of a uniform magnetization in the ferromagnetic resonance (FMR) context. Analytical predictions and numerical simulations of the complete equations within the Inertial Landau-Lifshitz-Gilbert…

Materials Science · Physics 2014-12-12 E. Olive , Y. Lansac , M. Meyer , M. Hayoun , J. -E. Wegrowe

This report documents the development of a versatile model for longitudinal gradient bending magnets (LGB's) and its implementation in particle tracking simulations. The model presented below may be used to represent an arbitrary magnetic…

Accelerator Physics · Physics 2015-10-27 Noah Bittermann

Parametric surrogate models of electric machines are widely used for efficient design optimization and operational monitoring. Addressing geometry variations, spline-based computer-aided design representations play a pivotal role. In this…

Computational Engineering, Finance, and Science · Computer Science 2026-01-12 Merle Backmeyer , Michael Wiesheu , Sebastian Schöps

We present a general approach to the derivation of the effective anisotropy field which determines the dynamical behaviour of magnetic spins according to the Landau-Lifshitz-Gilbert equation. The approach is based on the gradient in…

The Landau-Lifshitz-Gilbert (LLG) equation is a widely used model for fast magnetization dynamics in ferromagnetic materials. Recently, the inertial LLG equation, which contains an inertial term, has been proposed to capture the ultra-fast…

Numerical Analysis · Mathematics 2022-09-13 Jingrun Chen , Panchi Li , Cheng Wang

Designing suitable reward functions for numerous interacting intelligent agents is challenging in real-world applications. Inverse reinforcement learning (IRL) in mean field games (MFGs) offers a practical framework to infer reward…

Machine Learning · Computer Science 2025-09-05 Yang Chen , Xiao Lin , Bo Yan , Libo Zhang , Jiamou Liu , Neset Özkan Tan , Michael Witbrock

Recent theoretical and experimental advances show that the inertia of magnetization emerges at sub-picoseconds and contributes to the ultrafast magnetization dynamics which cannot be captured intrinsically by the LLG equation. Therefore, as…

Numerical Analysis · Mathematics 2021-08-09 Panchi Li , Lei Yang , Jin Lan , Rui Du , Jingrun Chen

Machine learning (ML) entered the field of computational micromagnetics only recently. The main objective of these new approaches is the automatization of solutions of parameter-dependent problems in micromagnetism such as fast response…

Computational Physics · Physics 2021-07-15 Sebastian Schaffer , Norbert J. Mauser , Thomas Schrefl , Dieter Suess , Lukas Exl

The dynamics of a magnetic moment or spin are of high interest to applications in technology. Dissipation in these systems is therefore of importance for improvement of efficiency of devices, such as the ones proposed in spintronics. A…

Mesoscale and Nanoscale Physics · Physics 2023-08-29 Robin C. Verstraten , Tim Ludwig , Rembert A. Duine , Cristiane Morais Smith

We add the magnetic degrees of freedom to the widely used Gaussian Approximation Potential of machine learning (ML) and present a model that describes the potential energy surface of a crystal based on the atomic coordinates as well as…

Materials Science · Physics 2026-04-13 Yuqiang Gao , Menno Bokdam , Paul J. Kelly

The stochastic Landau--Lifshitz--Gilbert (LLG) equation describes the behaviour of the magnetization under the influence of the effective field consisting of random fluctuations. We first reformulate the equation into an equation the…

Numerical Analysis · Mathematics 2015-02-05 Beniamin Goldys , Kim-Ngan Le , Thanh Tran

The Landau-Lifshitz-Gilbert (LLG) equation has emerged as a fundamental and indispensable framework within the realm of magnetism. However, solving the LLG equation, encompassing full nonlinearity amidst intricate complexities, presents…

Pattern Formation and Solitons · Physics 2023-08-17 Xin-Wei Jin , Zhan-Ying Yang , Zhimin Liao , Guangyin Jing , Wen-Li Yang

We explore the limitations and validity of semi-classically formulated spin equations of motion. Using a single-molecule magnet as a test model, we employ three qualitatively different approximation schemes. From a microscopic model, we…

Mesoscale and Nanoscale Physics · Physics 2017-12-13 Henning Hammar , Jonas Fransson

The effective spin Hamiltonian method is widely adopted to simulate and understand the behavior of magnetism. However, the magnetic interactions of some systems, such as itinerant magnets, are too complex to be described by any explicit…

Materials Science · Physics 2022-05-20 Hongyu Yu , Changsong Xu , Feng Lou , L. Bellaiche , Zhenpeng Hu , Xingao Gong , Hongjun Xiang

Global machine learning force fields (MLFFs), that have the capacity to capture collective many-atom interactions in molecular systems, currently only scale up to a few dozen atoms due a considerable growth of the model complexity with…

Precise modeling of the magnetization dynamics of nanoparticles with finite size effects at fast varying temperatures is a computationally challenging task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse grained model…

Materials Science · Physics 2019-08-07 Christoph Vogler , Claas Abert , Florian Bruckner , Dieter Suess

The Landau-Lifshitz-Gilbert (LLG) equation is widely used to describe magnetization dynamics. We develop a unified framework of the microscopic LLG equation based on the nonequilibrium Green's function formalism. We present a unified…

Mesoscale and Nanoscale Physics · Physics 2023-10-16 Fuming Xu , Gaoyang Li , Jian Chen , Zhizhou Yu , Lei Zhang , Baigeng Wang , Jian Wang

We present a machine learning (ML) force-field framework for simulating the non-equilibrium dynamics of charge-density-wave (CDW) order driven by the Peierls instability. Since the Peierls distortion arises from the coupling between lattice…

Statistical Mechanics · Physics 2025-10-24 Ho Jang , Yang Yang , Gia-Wei Chern

Simulations of magnetization dynamics in a multiscale environment enable rapid evaluation of the Landau-Lifshitz-Gilbert equation in a mesoscopic sample with nanoscopic accuracy in areas where such accuracy is required. We have developed a…

Computational Physics · Physics 2016-11-28 Andrea De Lucia , Benjamin Krüger , Oleg A. Tretiakov , Mathias Kläui