  The striking fractal geometry of strange attractors underscores the
generative nature of chaos: like probability distributions, chaotic systems can
be repeatedly measured to produce arbitrarily-detailed information about the
underlying attractor. Chaotic systems thus pose a unique challenge to modern
statistical learning techniques, while retaining quantifiable mathematical
properties that make them controllable and interpretable as benchmarks. Here,
we present a growing database currently comprising 131 known chaotic dynamical
systems 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 of
arbitrary length and granularity. Our dataset is annotated with known
mathematical properties of each system, and we perform feature analysis to
broadly categorize the diverse dynamics present across the collection. Chaotic
systems inherently challenge forecasting models, and across extensive
benchmarks we correlate forecasting performance with the degree of chaos
present. We also exploit the unique generative properties of our dataset in
several proof-of-concept experiments: surrogate transfer learning to improve
time series classification, importance sampling to accelerate model training,
and benchmarking symbolic regression algorithms.
