Deep attractors: Where deep learning meets chaos

In nonlinear dynamics, when the state space is thought to be multidimensional but all we have for data is just a univariate time series, one may attempt to reconstruct the true space via delay coordinate embeddings. However, it is not clear a priori how to choose dimensionality and time lag of the reconstruction space. In this post, we show how to use an autoencoder architecture to circumvent the problem: Given just a scalar series of observations, the autoencoder directly learns to represent attractors of chaotic systems in adequate dimensionality.

Feb 11, 2025 - 11:35

Deep attractors: Where deep learning meets chaos

In nonlinear dynamics, when the state space is thought to be multidimensional but all we have for data is just a univariate time series, one may attempt to reconstruct the true space via delay coordinate embeddings. However, it is not clear a priori how to choose dimensionality and time lag of the reconstruction space. In this post, we show how to use an autoencoder architecture to circumvent the problem: Given just a scalar series of observations, the autoencoder directly learns to represent attractors of chaotic systems in adequate dimensionality.