We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.

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Summary Neuronal plasticity helps animals learn from their environment. However, it is challenging to link specific changes in defined neurons to altered behavior. Here we focus on circadian rhythms in the structure of the principal s-LNv clock neurons in Drosophila. By quantifying neuronal architecture, we observed that s-LNv structural plasticity changes the amount of axonal material in addition to cycles of fasciculation and defasciculation. We found that this is controlled by rhythmic Rho1 activity that retracts s-LNv axonal termini by increasing myosin phosphorylation and simultaneously changes the balance of pre-synaptic and dendritic markers. This plasticity is required to change clock network hierarchy and allow seasonal adaptation. Rhythms in Rho1 activity are controlled by clock-regulated transcription of Puratrophin-1-like (Pura), a Rho1 GEF. Since spinocerebellar ataxia is associated with mutations in human Puratrophin-1, our data support the idea that defective actin-related plasticity underlies this ataxia.