Reservoir Computing: Observation and Prediction of ChaosTAT I A N A D AV I D S O N B A J A N D A S ( U N I V E R S I T Y O F C H I C AG O )

J O S E P H D H A RT 1 , 2 , J A I D E E P PAT H A K 1 , 2 , E D WA R D OT T 1 , 2 , 3 , T H O M A S M U R P H Y 1 , 3 , R A J A R S H I R OY 1 , 2 , 3

1U M D P H Y S I C S , 2 I R E A P U M D, 3E C E U M D

Overview§Many systems exhibit chaos however they’ve remained difficult to model up till now.§One thing Reservoir Computing can do is give us new ability to understand these systems.

Central Ideas

§What is chaos? Small changes can lead to vast differences in a system over time. Think butterfly effect.§What is reservoir computing? An extension of artificial neural networks where only the output weights are changed.§What are we trying to figure out? The observation task and the prediction task, done on two systems: one reservoir computer implemented digitally on a laptop and one on a tabletop experiment.

Chaotic Attractors

Rossler Attractor

Chaotic attractor of RabinovichFabrikant systemChaotic attractor of Sprott H.

system

The Lorenz system

The Lorenz system is described by three differential equations

The Lorenz Attractor

Reservoir Computer Schematic

Methods.

Tabletop Setup Implemented Digitally

Results – Observation Task

Results – Prediction Task