A benchmark set of 2-state nonlinear ordinary differential equations adapted from Strogatz's book "Nonlinear Dynamics and Chaos"
Note: these datasets are now available as part of the Penn Machine Learning Benchmark (PMLB).
This repository contains 2-state dynamic models adapted from Steven Strogatz’s book “Chaos and Nonlinear Dynamics”. They represent idealized dynamical systems from many fields of study.
Each system can exhibit chaotic and/or nonlinear behavior. For the purposes of modeling, these systems are simulated using initial conditions within stable basins of attraction.
The systems are simulated using simulink and matlab.
The data files from simulation are provided for benchmarking purposes for system identification / machine learning. The goal should be not only to produce an accurate dynamic model, but to produce a model that captures/matches the underlying processes used to generate the data.
It has been used as a benchmark dataset in the following publications:
La Cava, W., Orzechowski, P., Burlacu, B., de Franca, F., Virgolin, M., Jin, Y., Kommenda, M., & Moore, J. (2021). Contemporary Symbolic Regression Methods and their Relative Performance. Proceedings of the Neural Information Processing Systems Track on Datasets and Benchmarks, 1. neurips.cc
La Cava, W., Danai, K., Spector, L., (2016). “Inference of Compact Nonlinear Dynamic Models by Epigenetic Local Search.” Engineering Applications of Artificial Intelligence. doi:10.1016/j.engappai.2016.07.004
Schmidt, M.D. (2011) Machine Science: Automated Modeling of Deterministic and Stochastic Dynamical Systems. PhD Thesis.
The original problems are from: