Functional Networks Trained by Optimization

Artificial neural networks (ANNs) gained much attention due to its capacity to mimic neural cells of living organisms which have intelligence. ANNs and some of its variations, have been applied in text and image recognition, among other applications, and are the basic building blocks of artificial intelligence (AI). A known problem, however, is the impossibility to extract the knowledge achieved by training. To solve this problem, a new neural network is hereby presented, called functional network (FN). This functional network differs from the ANNs basically by the fact that the sigmoid function can be substituted by any mathematical expression, that each functional neuron has multiple inputs and multiple function outputs, and that the trained information can be extracted in the form of a mathematical expression, denominated generative mathematical expression (GME).Although a moderate size FN may give a very large number of possible combinations, requiring very expensive computation efforts on training, recent developments in computation such as quantum computers indicate it increasingly becomes a viable alternative for large patterns and complex models. Thus, the GME of pattern representations can be extracted from a FN in order to simplify AI and numerical modeling tasks in general, such as finite element models (FEM) of structures, or computer fluid dynamic (CFD) models, decreasing overall computation costs.