A mutual information measure for predicting the performance of physical reservoir computers

Abstract

Physical reservoir computing (PRC) performance is known to strongly depend on its nonlinear dynamics which complicates identifying appropriate metrics for design purposes. Here, we evaluate nonlinear structural dynamics using mutual information to understand the PRC’s ability to track a target signal. The information processing ability of a mechanical PRC is first elucidated by introducing a simple three node causal structure that fuses information between discrete sensors and the PRC’s dynamic states. The three node directed acyclic graph (DAG) is motivated by the Monty Hall problem, where the PRC serves as the new information similar to increasing odds of winning the car in the game show Let’s Make a Deal. This concept is applied to PRCs to understand how information is processed through a nonlinear structure to increase the odds of knowing the state of the environment. For practical aerodynamic state estimation applications, we take pressure measurements from experimental supersonic cavity flow as the input to the PRC. It is computationally shown that mutual information provides a good measure to design nonlinearities into a PRC.