Modelling Reservoir Computing with the Discrete Nonlinear Schr\"odinger Equation

TL;DR

This paper introduces a general framework for reservoir computing using the discrete nonlinear Schrödinger equation, enabling information processing in arbitrary physical systems driven out of equilibrium, demonstrated through pattern recognition tasks.

Contribution

It formulates a novel reservoir computing approach based on DNLS, applicable to any physical system, with a thermodynamical interpretation of encoding and processing.

Findings

Numerical demonstration of pattern recognition using nonlinear oscillator networks.

Reservoir encoding via thermodynamical forces and currents.

Framework is independent of specific physical reservoir implementations.

Abstract

We formulate, using the discrete nonlinear Schroedinger equation (DNLS), a general approach to encode and process information based on reservoir computing. Reservoir computing is a promising avenue for realizing neuromorphic computing devices. In such computing systems, training is performed only at the output level, by adjusting the output from the reservoir with respect to a target signal. In our formulation, the reservoir can be an arbitrary physical system, driven out of thermal equilibrium by an external driving. The DNLS is a general oscillator model with broad application in physics and we argue that our approach is completely general and does not depend on the physical realisation of the reservoir. The driving, which encodes the object to be recognised, acts as a thermodynamical force, one for each node in the reservoir. Currents associated to these thermodynamical forces in turn encode the output signal from the reservoir. As an example, we consider numerically the problem of supervised learning for pattern recognition, using as reservoir a network of nonlinear oscillators.