NeuralMag: an open-source nodal finite-difference code for inverse micromagnetics

Introduction

Micromagnetic simulations are a fundamental tool in the study of magnetization dynamics and play a crucial role in understanding and designing magnetic materials and devices. These simulations model the behavior of magnetic and magnonic systems at the nanoscale, providing insight into phenomena such as domain wall motion, magnetization reversal, and spin wave propagation. The field relies on various computational methods, with finite-difference and finite-element schemes being widely used. Notable examples of established finite-difference codes include OOMMF¹ and fidimag² for CPU-based simulations and mumax3³, BORIS⁴, and magnum.np⁵ for GPU-accelerated simulations. Finite-element-based methods, such as those implemented in NMag⁶, Tetramag⁷, FastMag⁸, FinMag⁹, and magnum.fe¹⁰, provide greater flexibility in handling complex geometries but can be computationally more expensive. More recently, the finite-element solver TetraX¹¹ has gained popularity in the magnonics community due to its efficient eigenmode solver in infinite geometries.

In addition to standard micromagnetic simulations, inverse problems have attracted considerable attention in recent years. These problems involve determining the optimal parameters, such as material properties, external fields, or device geometries, that lead to a desired magnetic configuration or device functionality. A significant body of work has focused on inverse modeling of the demagnetization field, a static inverse problem. This has been particularly useful in the context of magnetic 3D printing, where topology optimization techniques are employed to design optimal material layouts, and the inverse modeling is used to infer the magnetization configuration of printed samples^{12, 13–14}.

More recently, research in the emerging field of inverse magnonics has gained momentum, focusing on optimizing the functionality of magnonic devices. Magnonics uses spin waves (magnons) for information processing, and designing efficient magnonic devices poses complex nonlinear optimization challenges. Inverse-design approaches have been increasingly applied to magnonics, allowing researchers to automate the design of devices by specifying a desired functionality and using computational algorithms to find the optimal configuration^{15, 16, 17–18}.

In this paper, we present a novel discretization strategy for micromagnetic simulations, adjoint-state algorithms for efficiently solving time-dependent inverse problems, and the software design of NeuralMag, which integrates these advancements into a flexible and high-performance computational framework.

Results

Micromagnetics

The micromagnetic model provides a semi-classical continuum description...