Neuromorphic computing hardware has gained significant interest due to the inefficiency of digital systems (CPUs, GPUs) for analog tasks and the limitations of traditional MOS-transistor-based devices for neuromorphic applications. A key challenge is creating highly interconnected systems of artificial neurons. Wave-based computing offers a solution, as interference patterns in a wave-propagating substrate can realize all-to-all interconnections. Hughes et al. proposed a theoretical framework for implementing a recurrent neural network (RNN) using a nonlinear wave equation, but left unanswered questions regarding performance and physical realization of the nonlinearity. This paper explores the use of spin waves, which exhibit both high interconnectivity and nonlinearities suitable for neuromorphic computing, offering a potential solution to the challenges posed by previous approaches.

The authors review existing work on neuromorphic computing hardware and wave-based computing. They highlight the limitations of digital systems for analog tasks and the challenges of creating highly interconnected systems of artificial neurons. They discuss the work of Hughes et al., which proposed a theoretical framework for implementing an RNN using a nonlinear wave equation, but noted limitations in its numerical simulations and lack of detail on physical implementation. The authors contrast this with the potential benefits of spin waves, which combine high interconnectivity with inherent nonlinearities, making them suitable for neuromorphic computing applications.

The researchers utilized a custom-built micromagnetic solver, named Spintorch, based on the PyTorch machine learning framework. Spintorch inverse-designs the magnetic-field distribution to steer spin waves and achieve desired functions. The system is modeled using a magnetic thin film with a spatially non-uniform magnetic field. The solver discretizes the region into 25 nm × 25 nm × 25 nm volumes and solves the Landau-Lifshitz-Gilbert (LLG) equations to calculate magnetic moment precession. The solver accounts for the demagnetizing field, which is the source of nonlinearity. The algorithm uses a gradient-based optimization to find the optimal magnetic-field distribution (represented by the up/down configuration of nanomagnets). For simulations with higher degrees of freedom, the authors used external magnetic-field values as training parameters directly, without simulating magnets. The authors validate their solver against the mumax3 solver and describe the magnetic material properties used, including YIG for low-damping spin-wave propagation and nanomagnets with perpendicular magnetic anisotropy (PMA) for field control.

The study demonstrated the successful design of a nanoscale spin-wave scatterer capable of performing various functions, including frequency separation (spectrum analyzer) and vowel recognition. In the small-amplitude (linear) regime, Spintorch effectively designed a spectrum analyzer separating 3, 3.5, and 4 GHz components. The authors then explored vowel recognition using a dataset from the Wavetorch package. Comparing linear and nonlinear regimes (varying excitation fields), they observed significantly improved accuracy in the nonlinear regime, particularly on the test dataset. A confusion matrix analysis confirmed superior performance in the nonlinear regime, showing that the nonlinear system acted as a true neural network capable of nonlinear classification and generalization beyond the training data. A simple example highlighting the limitations of linear interference in comparison to the capabilities of the nonlinear system further supported their findings. The energy efficiency of the spin-wave scatterer was estimated to be significantly lower than that of CPUs and GPUs, showing potential for energy-efficient neuromorphic computation.

The results demonstrate the feasibility of using spin waves for neuromorphic computing, showcasing the advantages of nonlinear spin-wave interference over linear methods. The improved performance in vowel recognition highlights the potential of the system to act as an RNN, going beyond linear signal processing. The low energy consumption of the spin-wave scatterer suggests significant advantages over traditional electronic implementations. While limitations exist in scaling up the system due to computational constraints, the study's findings offer a promising pathway towards developing compact and energy-efficient neuromorphic computing devices.

This research presents a significant advance in magnonic computing. The authors successfully demonstrated a nanoscale spin-wave scatterer capable of performing complex neuromorphic functions, surpassing linear methods through the exploitation of nonlinearities. The low energy consumption highlights the potential for energy-efficient computing. Future research should focus on scaling up the system and exploring the full capabilities of nonlinear spin-wave interference for more complex computations.

The study's scalability is currently limited by the computational resources required for the micromagnetic simulations. Larger systems and datasets could not be explored due to GPU memory constraints. The authors also mention that the net power efficiency is influenced by the magneto-electric transducer, which was not optimized in this study.