Neural Dynamics

by Christopher A. Shaw (Author)

The book represents the first attempt to systematically deal with the use of deep neural networks to forecast chaotic time series. Differently from most of the current literature, it implements a multi-step approach, i.e., the forecast of an entire interval of future values. This is relevant for many applications, such as model predictive control, that requires predicting the values for the whole receding horizon. Going progressively from deterministic models with different degrees of complexity and chaoticity to noisy systems and then to real-world cases, the book compares the performances of various neural network architectures (feed-forward and recurrent). It also introduces an innovative and powerful approach for training recurrent structures specific for sequence-to-sequence tasks. The book also presents one of the first attempts in the context of environmental time series forecasting of applying transfer-learning techniques such as domain adaptation.

This book treats essentials from neurophysiology (Hodgkin–Huxley equations, synaptic transmission, prototype networks of neurons) and related mathematical concepts (dimensionality reductions, equilibria, bifurcations, limit cycles and phase plane analysis). This is subsequently applied in a clinical context, focusing on EEG generation, ischaemia, epilepsy and neurostimulation.

This book originated from a forefront R&D project pursued at Siemens Corporate Technology over the past several years. As a name for this project, we chose "Information Dynamics", which stands for information processing in complex dynamical systems. In the project, we wanted to grasp the flow of information in such systems in a quantitative manner, on the one hand by making use of an existing arsenal of methods and techniques from areas such as information theory, mathematical statistics, neural networks, nonlinear dynamics, probability theory, and statistical physics, and on the other hand by deriving new methods and techniques if required.