Reservoir computing with dynamical systems in Rust

A programm to integrate dynamical systems written in Rust.

At the moment it is capable of calculating the Lang-Kobayashi- and Mackey-Glass-system.

This Program is mainly for learning Rust. Right now it can only integrate the Lang-Kobayashi- and Mackey-Glass system and then write out the dynamical variables. There's a simple plot.py script to see the timeseries.

implemented features

• timeseries simplification via RDP¹ to greatly reduce file sizes
• runge-kutta-4 integration method for delay-differential equations
• dynamical systems: Lang-Kobayashi, Mackey-Glass, Stuart-Landau, Hindmarsh-Rose, Lorenz, FitzHugh-Nagumo
• multi-delay network topologies.

traits

• dynamical systems
• dynamical systems with feedback

todos

• add more dynamical systems

  • Rössler
  • Van der Pol oscillator
  • Kuramoto-oscillator

• reservoir computing benchmarks

  • NARMA
  • Legendre-functions
  • prediction of dynamical-systems

• saving parametric plots

  • save n-dimensional curves
  • use derive possible variable-indices from system-variables

• network

  • make network generic in regards to the type of weights WeightT
  • make network's delays an Option
  • network with "no" weights (all weights = 1)
  • normalize weights by node's total output

• curve simplification

• optimize the perpendicular distance from a point to a line in n dimensions.

traits

- implement generalized `FeedbackType`-trait to allow each system define a specific type of feedback.
- implement generalized `Weight`-trait to make network generic (`Network<T: WeightT>`)
right now only two types of delayed-Feedback are possible : `Complex<f64>` and `f64`
but systems might want `[f64; 3]` as Feedback-type and something similar to a matrix as weight.
That way each system can have each feedback-input be a weighted sum of the state's variables.
- systems with noise
- systems with external driving force (needed for reservoir computing)

Footnotes

1. Ramer-Douglas-Peucker algorithm ↩