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The inverse design approach in magnonics exploits the wave nature of spin waves and machine learning techniques to develop logical devices with functionalities that exceed the capabilities of analytical methods. While promising for analog, Boolean, and neuromorphic computing, current implementations of inverse micromagnetics face significant memory limitations that hinder the design of complex systems. In this work, we present a level-set parameterization method for topology optimization, combined with an adjoint-state approach for memory-efficient simulation of magnetization dynamics [1]. The framework is implemented in NeuralMag [2], a GPU-accelerated micromagnetic solver featuring a nodal finite-difference scheme and automatic differentiation tools provided by the JAX backend. The level-set method provides a natural way of handling topological changes such as boundary merging, the formation of new shapes, or the disappearance of existing ones, which typically challenge conventional shape optimization approaches. Its combination with the adjoint-state method for solving the Landau-Lifshitz-Gilbert equation enables efficient gradient computation without overwhelming computational resources, thus overcoming the hardware constraints of existing inverse-design algorithms in magnonics.
To validate the method, we designed a 300 nm-wide yttrium iron garnet demultiplexer achieving frequency-selective spin-wave separation, where the gradient-based optimization required fewer simulations compared to the previously used direct binary search method [3]. These results highlight the algorithm's efficiency in exploring local minima across various initial configurations, establishing its utility as a versatile tool for the inverse design of magnonic logic devices. As a next step, we have also achieved the utilization of nonlinear spin-wave behavior within our level-set framework, reproducing the example of a nonlinear switch introduced by Wang et al. [3]. This advancement opens new possibilities for developing complex magnonic logic gates, including half-adders and multi-frequency nonlinear devices, further broadening the applicability of the proposed method for next-generation spintronic technologies.
[1] A. A. Voronov et al., npj Spintronics 3, 19 (2025).
[2] C. Abert et al., npj Computational Materials 11, 1 (2025).
[3] Q. Wang, A. V. Chumak, and P. Pirro, Nat. Commun. 12, 2636 (2021).