Després B. Neural Networks and Numerical Analysis

De Gruyter, 2022. — 174 p. — (De Gruyter Series in Applied and Numerical Mathematics 06). — 978-3-11-078318-6.Artificial Intelligence, Deep Learning, Machine Learning - whatever you’re doing if you don’t understand it - learn it. Because otherwise, you’re going to be a dinosaur within 3 years. This book uses numerical analysis as the main tool to investigate methods in Machine Learning and AI. The effciency of neural network representation on for polynomial functions is studied in detail, together with an original description of the Latin hypercube method. In addition, unique features include the use of Tensorflow for implementation on the session and the application n to the construction of new optimized numerical schemes.Traditionally, the bread and butter in applied mathematics is the modeling of real phenomena with partial differential equations and the numerical analysis of the corresponding discretized equations. An observation is that applied sciences and industry turn more and more in the direction of using Neural Networks, Machine Learning, and Deep Learning. This is clear at the inspection of the exponentially growing number of publications on the coupling of Machine Learning and Neural Networks with computational fluid dynamics, modeling of turbulence, and many other problems.Objective functions, neural networks, and linear algebra.
Approximation properties.
A functional equation.
Datasets.
Stochastic gradient methods.
Examples and research in the field.