Combining Multiple Inputs to a Delay-line Reservoir Computer: Control of a Forced Van der Pol Oscillator System

The Reservoir Computing (RC) paradigm is a supervised machine learning approach that makes use of the inherent processing capacity of dynamical systems. Using the system's transient response to an external input, delayed chaotic systems offer rich dynamics for information processing, and have therefore been recognised as ideal systems for reservoir computing. A distinctive feature of delay-line reservoirs is their single-input/single-output structure, which makes them efficient for physical implementation. However, this also presents a significant limitation to multi-input tasks, as the sequence of information in the time-multiplexed input stream is not obvious. Here, we propose enhancing the input masking process used in delay-feedback RCs to mix multiple inputs in the time domain. We investigate two approaches: ‘interleaved’ and ‘sequential’, of injecting multi-input signals into a delay-line reservoir without modifying its topology. Further, we propose a novel task for RC, which inherently requires multiple inputs, to evaluate our approach: the control of a forced Van der Pol oscillator system. We use the trained reservoir as a controller to regulate the nonlinear dynamics of the Van der Pol system by constraining its trajectory to a circle. We find that, with careful choice of model parameters and offset masking scheme, the ‘sequential’ method outperforms the ‘interleaved’ method on this task.