Spin-wave Holography for Neuromorphic Computing

Various physical phenomena have been examined to develop hardware capable of performing neuromorphic computations more efficiently than conventional CMOS-based devices. A well-known approach is wave interference-based computing. Several studies have demonstrated the use of inverse-designed spin-wave scatterers to perform computational tasks [1-2]. However, in most cases the designed devices function as a black-box, providing limited insight into the underlying mechanisms of the operation. Here we provide a theoretical investigation to examine the function of a spin-wave based network. We compared the holographic phenomena of optical waves and linear spin-waves by modelling the optical behaviour using the Huygens–Fresnel principle and a finite-difference time-domain approximation of the wave equation, and simulating the micromagnetic behaviour with MuMax3 [3] and SpinTorch [1].We found that forward volume linear spin-wave holography  reproduces key features of optical interference. A 1D-reduced MNIST dataset is used to evaluate the ability of both systems to capture linear dependencies and perform correlation-based classification. Although these systems perform well as associative memory, the classification accuracy remains limited. To improve the classification performance, we introduce 1D machine learned holograms optimized by our micromagnetic simulator SpinTorch.  Although this approach improves training accuracy over 80% on a 50-sample training set, generalization remains an open issue. Our results highlight a fundamental limitation of inverse-designed magnonic systems: machine learning approaches based on LLG solvers are severely constrained by the high computational cost of micromagnetic simulations. In contrast, optical inverse-design methods can accommodate a significantly larger number of training samples, enabling more efficient and scalable optimization. Achieving comparable accuracy with spin-wave-based systems necessitates a significantly more efficient training approach. Promising alternatives include wave-equation-based solvers [4] or physical learning methods [5].