Towards pattern generation and chaotic series prediction with photonic reservoir computers

Abstract

Reservoir Computing is a bio-inspired computing paradigm for processing time dependent signals that is particularly well suited for analog implementations. Our team has demonstrated several photonic reservoir computers with performance comparable to digital algorithms on a series of benchmark tasks such as channel equalisation and speech recognition. Recently, we showed that our opto-electronic reservoir computer could be trained online with a simple gradient descent algorithm programmed on an FPGA chip. This setup makes it in principle possible to feed the output signal back into the reservoir, and thus highly enrich the dynamics of the system. This will allow to tackle complex prediction tasks in hardware, such as pattern generation and chaotic and financial series prediction, which have so far only been studied in digital implementations. Here we report simulation results of our opto-electronic setup with an FPGA chip and output feedback applied to pattern generation and MackeyGlass chaotic series prediction. The simulations take into account the major aspects of our experimental setup. We find that pattern generation can be easily implemented on the current setup with very good results. The Mackey-Glass series prediction task is more complex and requires a large reservoir and more elaborate training algorithm. With these adjustments promising result are obtained, and we now know what improvements are needed to match previously reported numerical results. These simulation results will serve as basis of comparison for experiments we will carry out in the coming months.

Brain-Inspired Photonic Signal Processor for Generating Periodic Patterns and Emulating Chaotic Systems

“…The main constraint comes from the ADC and DAC, limited to 14 and 16 bits, respectively. Numerical simulations, reported in [18], show that such precision is sufficient for all tasks studied in this work. It was also shown in [18] that the precision of the readout weights w i has a significant impact on the performance of the system.…”

“…Random pattern generation is a natural step forward from the frequency generation task to a more complex problem -instead of a regularly-shaped continuous function, the system is trained to generate an arbitrarilyshaped discontinuous function (that remains periodic, though). Specifically, a pattern is a short sequence of L randomly chosen real numbers (here within the interval [−0.5, 0.5]) that is repeated periodically to form an infinite time series [18]. Similarly to the physical frequency in section III A, the physical period of the pattern is given by τ pattern = L · T .…”

“…This additional feedback significantly enriches the internal dynamics of the system, enabling it to generate time series autonomously, that is without receiving any input signal. With this modification, reservoir computing can be used for long-term prediction of chaotic series [1,5,[17][18][19]. In fact, this approach holds, to the best of our knowledge, the record for such chaotic time series prediction [1,5].…”

Forecasting chaotic systems with very low connectivity reservoir computers

“…(1) coupled with the chosen input (Eqs. (6) to (8)) via the hybrid Runge-Kutta 5(4) 18 method from t = 0 to 300 with a fixed time step ∆t = 0.01, and divide this interval into three ranges:…”

Embodiment of Learning in Electro-Optical Signal Processors

“…Implementing the full training algorithm on the FPGA would drastically increase the speed of the experiment. FPGA's have already been demonstrated to be useful for controlling and training electro-optical signal processors [32,33].…”