Deep Learning In Multistep Prediction Of Chaotic Dynamics From Deterministic Models To Realworld Systems First Matteo Sangiorgio by Matteo Sangiorgio 9783030944810, 3030944816 instant download after payment.

In the present data-rich era, we know that time series of many variables can hardly
be interpreted as regular movements plus some stochastic noise. For half a century,
we have also known that even apparently simple sets of nonlinear equations can
produce extremely complex movements that remain within a limited portion of the
variables space without being periodic. Such movements have been named “chaotic”
(“deterministic chaos” when the equations include no stochasticity).
Immediately after they were discovered, Lorenz and other researchers were troubled
by the problem of predictability. How far into the future can we reliably forecast
the output of such systems? For many years, the answer to such a question remained
limited to very few steps. Today, however, powerful computer tools are available
and have been successfully used to accomplish complex tasks. Can we extend our
predictive ability using such tools? How far? Can we predict not just a single value,
but also an entire sequence of outputs?
This book tries to answer these questions by using deep artificial neural networks
as the forecasting tools and analyzing the performances of different architectures of
such networks. In particular,we compare the classical feed-forward (FF) architecture
with the more recent long short-term memory (LSTM) structure. For the latter, we
explore the possibility of using or not the traditional training approach known as
“teacher forcing”.