Dynamical Diversity for Reservoir Computing in Reconfigurable Nanomechanics
Authors: Humayun Ahmed, Inês S. Garcia, Filipa C. Mota, Muhammad Asim, Ghaith Mahook, Suleyman Celik, Yunus Selcuk, Filipe S. Alves, +2 more
Organizations: International Iberian Nanotechnology Laboratory (INL), Braga, 4715-330, Portugal. · Department of Mechanical Engineering, Bilkent University, 06800 Ankara, Turkey · UNAM - Institute of Materials Science and Nanotechnology, Bilkent University, 06800 Ankara, Turkey · Nanotechnology Research and Application Centre (SUNUM), Sabanci University, Tuzla, Istanbul, 34956, Turkey · Department of Electrical Engineering, Koc University, 34450 Istanbul, Turkey
Physical reservoir computing uses nonlinear dynamics and a trained linear readout to process information. Nanoelectromechanical (NEMS) resonators combine geometric Duffing nonlinearity with fading memory, but most electromechanical implementations use a single resonance mode. Here, we demonstrate reservoir computing with two interacting modes of a single NEMS resonator measured through one readout port. We introduce dynamical diversity through complementary modal drive settings: the same input sequence is replayed under different allocations of drive amplitude between the modes, and the responses are concatenated into a single feature matrix. This multiplexing expands the representation available to the readout without additional devices or training of internal parameters. On NARMA-2, it reduces variance-normalized test error more than 28-fold relative to single-mode operation and more than threefold relative to the best individual two-mode setting. Linear memory-capacity measurements show that accessible recall spans only a few symbols at the tested symbol duration. Its rapid decline with delay, consistent with mechanical dissipation, accompanies rising NARMA error and the eventual loss of multiplexing gains at higher orders. We also use electrical feedthrough as an internal reference for assessing the computational contribution of the NEMS response. Separate linear readouts are trained on feedthrough features and features derived from the measured NEMS response, using the same recordings and matched drive settings and processing. On challenging nonlinear mapping tasks, the multiplexed NEMS features yield substantially lower errors than the feedthrough features. These results demonstrate how dynamical diversity through variations in modal drive amplitudes expands the computational capability of a single multimode NEMS resonator.
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.
Mahadev Sunil Kumar, Adarsh Ganesan
Amrita School of Computing, Amrita Vishwa Vidyapeetham, Kollam, India 690525 · Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science, Pilani – Dubai Campus, Dubai, United Arab Emirates 345055
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.
Mohab Abdalla, Damien Rontani
CentraleSupélec, Université de Lorraine, LMOPS EA-4423 Laboratory, 57070 Metz, France
Nonlinear thermodynamic computers based on Langevin dynamics exploit thermal fluctuations as a physical substrate for computation. Recent work has shown that quartic-confined fluctuating degrees of freedom can act as thermodynamic neurons capable of nonlinear function approximation at finite observation times. Here we extend this paradigm from mean-only readout to moment-resolved readout. Instead of representing each driven reservoir solely by its first moment, we construct a response vector from the elementwise raw polynomial moments E[x], E[x⊙2], and E[x⊙4]. These observables combine displacement and central-shape contributions and are naturally aligned with the linear, quadratic, and quartic terms of the local driven dynamics. We further introduce a heterogeneous multi-reservoir architecture in which three reservoirs with distinct initialization and training histories form a joint 2304-dimensional response representation. Under the fixed MNIST 60000/10000 reproduction protocol, feature-level fusion achieves the best observed accuracy of 9695/10000=96.95%, compared with 9682/10000=96.82% for the strongest single-reservoir model and 9684/10000=96.84% for equal-weight logit averaging. An exact paired McNemar test does not establish a statistically significant improvement over the strongest single reservoir, but the ablation and wrong-set overlap results provide suggestive evidence of complementary classification errors. These results motivate higher-order polynomial-moment readout and reservoir heterogeneity as candidate design principles for finite-time Langevin computing.
JiZheng Duan, MingYang Zhao, YanWei Chen +1
Institute of Modern Physics, Chinese Academy of Sciences