ABSTRACT
Inspired by our understanding of the biological neurons, the construction of artificial neural networks has always been motivated by the desire to better understand and emulate the brain. On the other hand, many years of research efforts have developed these networks to effective computational tools in different application fields.
In this chapter, some concepts and procedures concerning neural networks and ordinary differential equations are presented. In particular, based on a multi-layer perceptron, a stochastic gradient scheme and a backpropagation procedure are discussed and applied to solve a Cauchy problem and a parameter identification problem.
