Reproducible Reservoir Computing with Thermally Driven Superparamagnets: Controlling Temperature Sensitivity
Authors: Zhengfei Chen, Alex Welbourne, Matthew O. A. Ellis, Dan A. Allwood, Eleni Vasilaki, Thomas J. Hayward
Organizations: School of Chemical, Materials and Biological Engineering, University of Sheffield, UK · Department of Computer Science, University of Sheffield, UK
Abstract
Unconventional computing systems must demonstrate robust performance under real-world environmental conditions to enable practical deployments. We have recently proposed superparamagnetic nanodot ensembles driven by strain-induced magnetoelectric coupling as exciting candidates for use as ultra-low energy consumption reservoir computing substrates. However, because their dynamics are governed by thermal activation effects, these systems are intrinsically sensitive to ambient temperature fluctuations, leading to degraded task performance when operated outside the temperature range used during training. In this paper we simulate how temperature variations affect the magnetization dynamics of such superparamagnetic ensembles, and quantify how this affects task performance. We then show how heterogeneous nanodot patterns that incorporate different sizes of nanodots with different characteristic timescales for thermal activation mitigate this problem. Benchmark results on the NARMA-10 task show that introducing optimized heterogeneity stabilizes performance of the reservoirs across a wide range of ambient temperatures (5-35°C), with little loss of ultimate performance. We also characterize the trade-off between performance and temperature stability and show that it can be tuned via reservoir hyperparameters. Our study demonstrates a key step in making these novel devices suitable for real-world deployment.
Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations. Although reservoir performance is often characterized through memory, nonlinearity, and their tradeoff, such aggregate measures do not reveal how task-relevant information is organized within the state space. Here, we introduce an eigen-spectral decomposition framework linking the degree-wise information processing capacity to the corresponding state space modes. As a result, we are able to quantify the degree-wise representation energy, and show that in some cases, substantial amounts of information processing capacity may reside in low-energy modes that are vulnerable to experimental noise. These results suggest that useful reservoir computation depends not only on dimensionality expansion, but also on the geometric organization of task-relevant information, with direct implications on physical reservoir computers.
Parametrically driven oscillators provide a natural platform for neuromorphic computation, where nonlinear mode coupling and intrinsic dynamics enable both memory and high-dimensional transformation. Here, we investigate a two-mode system exhibiting 2:1 parametric resonance and demonstrate its operation as a reservoir computer across distinct dynamical regimes, including sub-threshold, parametric resonance, and frequency-comb states. By encoding input signals into the drive amplitude and sampling the resulting temporal and spectral responses, we perform one step-ahead prediction of benchmark chaotic systems, including Mackey-Glass, Rossler, and Lorenz dynamics. We find that optimal computational performance is achieved within the parametric resonance regime, where nonlinear interactions are activated while temporal coherence is preserved. In contrast, although frequency-comb states introduce increased spectral dimensionality, their performance is not consistently good across their existence band and also degrades in the chaotic comb regime due to loss of phase coherence. Mapping prediction error over parameter space reveals a direct correspondence between computational capability and the underlying bifurcation structure, with low-error regions aligned with the parametric resonance boundary. We further show that the input modulation, the detuning from the frequency matching condition, damping ratio, and input data rate systematically control the accessible dynamical regimes and thereby the computational performance. These results establish parametric resonance as a robust operating regime for oscillator-based reservoir computing and provide design principles for tuning physical systems toward optimal neuromorphic functionality.
This work addresses a hardware constraint in reservoir computing: the limited size of the readout layer imposed by systems with a physical readout. We investigate a strategy to accommodate this constraint based on random projection, which compresses high-dimensional reservoir states into a lower-dimensional subspace while preserving key properties of the source space and information- processing capabilities. To evaluate this approach, we compare a small, standalone time delay reservoir against a larger configuration whose output is projected down to match the same restricted readout dimension. Using task-independent metrics, we demonstrate that the distribution of information-processing capacities may differ between the two configurations, even at identical readout sizes. Furthermore, we perform a comprehensive hyperparameter scan to assess how both systems behave under varying physical regimes. Finally, we benchmark this approach on the standard NARMA10 task, showing that the random projection framework can yield superior performance compared to a standalone constrained reservoir, within specific compression range. These results provide a scalable pathway to bypass physical readout bottlenecks in hardware-based reservoir computing.