Predicting the future with magnons

TL;DR

This work addresses forecasting chaotic time series by leveraging a magnon-scattering reservoir (MSR) that maps a one-dimensional input into a high-dimensional spectral state through intrinsic nonlinear magnon interactions in a vortex-state Ni81Fe19 disk. The Mackey-Glass sequence serves as the benchmarking signal, and the MSR uses time-resolved Brillouin light scattering to capture a rich, multimodal spectral response that is linearly read out to predict future values. Key findings include accurate predictions up to 300 steps ahead, performance enhancement by combining multiple device geometries, and an optimal spectral binning that balances dimensionality with learning complexity. The results establish magnonics as a promising, CMOS-compatible platform for physical reservoir computing with potential impact on real-time edge forecasting and unconventional computing architectures.

Abstract

Forecasting complex, chaotic signals is a central challenge across science and technology, with implications ranging from secure communications to climate modeling. Here we demonstrate that magnons - the collective spin excitations in magnetically ordered materials - can serve as an efficient physical reservoir for predicting such dynamics. Using a magnetic microdisk in the vortex state as a magnon-scattering reservoir, we show that intrinsic nonlinear interactions transform a simple microwave input into a high-dimensional spectral output suitable for reservoir computing, in particular, for time series predictions. Trained on the Mackey-Glass benchmark, which generates a cyclic yet aperiodic time series widely used to test machine-learning models, the system achieves accurate and reliable predictions that rival state-of-the-art physical reservoirs. We further identify key design principles: spectral resolution governs the trade-off between dimensionality and accuracy, while combining multiple device geometries systematically improves performance. These results establish magnonics as a promising platform for unconventional computing, offering a path toward scalable and CMOS-compatible hardware for real-time prediction tasks.

Figures (9)

• Figure 1: Principle of chaotic time-series prediction based on a magnon-scattering reservoir: a one-dimensional temporal input is encoded in a microwave current and applied to a magnon-scattering reservoir in form of a Ni$_{81}$Fe$_{19}$ microdisk in the vortex state. Nonlinear interactions between various magnon modes transform the one-dimensional input into a multi-dimensional spectral output trained to forecast the future trajectory of the chaotic signal.
• Figure 2: (a) Scanning electron microscopy image of the magnon-scattering reservoir (MSR) in form of a 5 µm-wide and 50 nm-thick disk embedded in the $\Omega$-shaped microwave antenna. Red dots indicate the measurement positions used for spatial averaging of the BLS signal. (b) Schematic of a three-magnon splitting process: a directly excited mode ($2,0$) at frequency $f_\text{initial}$ decays into two secondary modes ($2,\pm 4$) and ($0,\mp 4$) with frequencies $f_{+}$ and $f_{-}$, conserving both energy and momentum. (c) BLS spectra measured on the device in (b) at an excitation power of 23 dBm, i.e. above the threshold for nonlinear three-magnon splitting. Each column corresponds to a spectrum recorded at a fixed excitation frequency $f_\text{RF}$, with intensity color coded on a logarithmic scale. The strongest nonlinear response is observed for excitation frequencies between 5.5 and 8.8 GHz.
• Figure 3: (a) The Mackey-Glass time series is mapped onto a microwave current using continuous-phase frequency-shift keying. (b) Each microwave frequency is held for a certain time window of $\delta t = 0.6$ ns and injected into the $\Omega$-shaped antenna surrounding the MSR. (c) The time-resolved BLS spectrum reveals both direct responses and nonlinear magnon–magnon scattering, expanding the input into a richer spectral space. (d) Zoomed in section of the data from panel d. White dots indicate the input frequencies from the arbitrary waveform generator. The measured magnon intensities persist well beyond the direct input window, providing fading memory. (e) The integrated spectral intensities form state vectors that serve as inputs for a linear readout used to generate predictions for a given horizon $t^\prime$. (f) Definition of intensity vector and weight vector.
• Figure 4: (a) Training data for the MSR when predicting $t^\prime = 16$ steps into the future, as indicated by the shaded area. (b) Testing results for the MSR for increasing prediction horizon $t^\prime = 16$, 100, and 300 steps, as indicated by shaded areas. (c) Normalized root mean squared error (NRMSE) as a function of prediction horizon $t^\prime$, comparing training (dotted) and testing (solid). Viable forecasts are achieved even up to 300 steps, demonstrating long-range prediction performance. (d) Training data of the reference prediction task without MSR when predicting $t^\prime = 16$ steps into the future. (e) Testing results without the MSR for increasing prediction horizon $t^\prime = 16$, 100, and 300 steps. (f) NRMSE as a function of prediction horizon $t^\prime$, comparing training (dotted) and testing (solid) for the reference task. Note that in panels (a), (b), (d), and (e) the displayed errors correspond to the deviation of the training and testing outputs from the target MG data and are therefore larger than the NRMSE shown in the lower panels.
• Figure 5: (a) BLS spectra extracted with different frequency bin sizes. (b) Average NRMSE as a function of bin size, showing an optimal performance at twice the natural BLS spectral resolution. Excessive binning reduces spectral richness and degrades forecasting accuracy.