Photonic next-generation reservoir computer based on distributed feedback in optical fiber

TL;DR

This work addresses the memory and latency limitations of cavity-based photonic reservoir computing by proposing a fiber-optic NG-RC that uses Rayleigh backscattering to perform nonlinear projections of time-delayed inputs. Memory is explicitly controllable through the memory length $K$ and a fixed memory mask, with a quadratic readout enabling rich feature representations without a physical cavity. The approach achieves state-of-the-art cross-prediction performance on chaotic time-series (Rössler, Lorenz) and high-dimensional spatiotemporal data (Kuramoto-Sivashinsky), while offering favorable latency and potential energy advantages over digital implementations, especially at high dimensionality and nonlinearity. This photonic platform thus provides a scalable, low-latency alternative for real-time dynamical-system analysis and high-dimensional time-series forecasting, with clear paths to further speedups and energy reductions via higher encoding rates and analog readout.

Abstract

Reservoir computing (RC) is a machine learning paradigm that excels at dynamical systems analysis. Photonic RCs, which perform implicit computation through optical interactions, have attracted increasing attention due to their potential for low latency predictions. However, most existing photonic RCs rely on a nonlinear physical cavity to implement system memory, limiting control over the memory structure and requiring long warm-up times to eliminate transients. In this work, we resolve these issues by demonstrating a photonic next-generation reservoir computer (NG-RC) using a fiber optic platform. Our photonic NG-RC eliminates the need for a cavity by generating feature vectors directly from nonlinear combinations of the input data with varying delays. Our approach uses Rayleigh backscattering to produce output feature vectors by an unconventional nonlinearity resulting from coherent, interferometric mixing followed by a quadratic readout. Performing linear optimization on these feature vectors, our photonic NG-RC demonstrates state-of-the-art performance for the observer (cross-prediction) task applied to the Rössler, Lorenz, and Kuramoto-Sivashinsky systems. In contrast to digital NG-RC implementations, this scheme is easily scalable to high-dimensional systems while maintaining low latency and low power consumption.

Figures (9)

• Figure 1: An overview of the photonic NG-RC system, detailing (a) the problem definition, (b) the construction of input feature vectors, (c) the experimental fiber-optic setup, and (d) the final prediction step in digital electronics.
• Figure 2: Experimental data for the Rössler observer. a) the phase modulator input voltage that encodes the input vector $\mathbf{v}_{\text{in},n}$ at $n=800$ ($t_{\text{R\"ossler}} = 100$). b) the voltage output proportional to the RBS irradiance that is downsampled to form the output vector $\mathbf{v}_{\text{out},n}$ at $n=800$. c) a plot of the first 1000 retrieved speckle patterns, with the dotted blue line marking the location of the pattern shown in part b.
• Figure 3: Output of the Photonic NG-RC observer (red dashed) with $K=30$ and a random mask compared to ground truth (blue solid) for $N=3000$ samples of the Rössler system. The grey shaded region marks the training set of $N_{\text{train}}=1000$ points following a $K-1 = 29$-step warm-up time. The errors for the data shown are $\text{NRMSE}_y=1.23 \times 10^{-2}$, $\text{NRMSE}_z=1.89 \times 10^{-2}$.
• Figure 4: a) NRMSE versus memory length $K$/duration $t_{\text{R\"ossler},K}$ and mask type for the Rössler observer. b) NRMSE for the Rössler system versus number of training points ($N_\text{train}$) using a memory with $K=30$ and a random mask.
• Figure 5: Output of the Photonic NG-RC observer (red dashed) with $K=30$ and a random mask compared to ground truth (blue solid) for $N=3000$ samples of the Lorenz system. The grey shaded region marks the training set of $N_{\text{train}}=1000$ points following a $K-1 = 29$-step warm-up time. The errors for the data shown are $\text{NRMSE}_y= 2.04 \times 10^{-2}$, $\text{NRMSE}_z= 2.77 \times 10^{-2}$.