TensorFlow Chaotic Prediction and Blow Up

Predicting the dynamics of complex systems exhibiting high-dimensional spatiotemporal chaos is a challenging machine learning problem with important applications in: physics, biology, medicine, economics, meteorology etc. Another problem of interest, is the inverse problem of inferring the connectivity network of such a system from input-output measurements. Such an example is the case of inferring the connectivity of genetic regulatory networks from the measurements of gene expression data. Here we explore the feasibility of these problems using a complex system corresponding to a non-linear network model we previously discussed in [1]. This is a continuous model of non-linear random networks (NLRN), which exhibits a phase transition from ordered to chaotic dynamics as a function of the average network connectivity (in-degree). In the chaotic regime, these networks show strong sensitivity to initial conditions, quickly forgetting their past states, making them harder to predict and to infer their connectivity. In our approach we use the TensorFlow library [2], which is the state of the art for deep neural networks training and prediction. Our numerical results show that the dynamics of the considered system can be successfully predicted for short times.