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The striking fractal geometry of strange attractors underscores thegenerative nature of chaos: like probability distributions, chaotic systems canbe repeatedly measured to produce arbitrarily-detailed information about theunderlying attractor. Chaotic systems thus pose a unique challenge to modernstatistical learning techniques, while retaining quantifiable mathematicalproperties that make them controllable and interpretable as benchmarks. Here,we present a growing database currently comprising 131 known chaotic dynamicalsystems spanning fields such as astrophysics, climatology, and biochemistry.Each system is paired with precomputed multivariate and univariate time series.Our dataset has comparable scale to existing static time series databases;however, our systems can be re-integrated to produce additional datasets ofarbitrary length and granularity. Our dataset is annotated with knownmathematical properties of each system, and we perform feature analysis tobroadly categorize the diverse dynamics present across the collection. Chaoticsystems inherently challenge forecasting models, and across extensivebenchmarks we correlate forecasting performance with the degree of chaospresent. We also exploit the unique generative properties of our dataset inseveral proof-of-concept experiments: surrogate transfer learning to improvetime series classification, importance sampling to accelerate model training,and benchmarking symbolic regression algorithms.

Chaos as an interpretable benchmark for forecasting and data-driven modelling