The purpose of this Doctoral Thesis is to propose a viable alternative to the approximation of models and processes in science and, particularly, for complex applications in bioengineering, in which it is impossible or very difficult to find a direct relationship between inputs and outputs using simple mathematical models or statistical approaches.

Similarly, it is interesting to achieve a compaction of the data needed by a model to get a prediction or classification in minimum time and with the lowest implementation cost. A model can be greatly simplified by reducing the number of inputs or applying mathematical calculations to transform them into new variables. In many regression problems (function approximation), classification and general optimization, new methodologies based on artificial intelligence are employed. Artificial intelligence is a branch of computer science that seeks to automate the computational ability of a system to respond to the stimuli it receives and propose appropriate and rational solutions. This occurs through a learning process guided by the presentation of certain samples or “examples” and their corresponding outputs to the model, and it learns to propose the corresponding outputs to new stimuli that it has not previously seen. This is called supervised learning. It may also be the case that this model groups together inputs with similar characteristics to produce a classification of input samples without an output pattern. This learning model is called unsupervised learning.

The most representative application of artificial intelligence for function approximation and classification are artificial neural networks. These models have clearly shown their advantages in the field of statistical modeling and prediction over other classical methods.

We do not want to leave aside the importance of preprocessing variables to optimize the response of a prediction system based on neural networks. The adaptation of the input variables is as important as the proper design
of the predictive system. Therefore, special attention has been devoted to analyze the selection of input variables of a system and its transformation (scaling, projection, etc.) to optimize its response. In particular, we have made use of a more and more popular criterion to decide which variables are really important for a prediction. This test criterion is called Delta Test, and is a nonparametric estimator based on the approximation of the variance of the noise at the output of a function. The combination of input variables that achieves the minimization of this criterion will provide an optimal predictive performance of the neural network under study. This method will be evaluated on real data sets to verify their practical use.

The present work aims to carry out the implementation of neural networks and data preprocessing to try to approach a series of complex problems in bioengineering, all of them by supervised learning. For example, we will try to apply neural networks the prediction of the presence of toxins (mycotoxins) that are considered carcinogenic and are associated to fungi that can grow in certain foods due
to different environmental factors associated to climate change. This was done by the cultivation of certain mycotoxin-producing fungi (in particular fungi that are producers of deoxynivalenol and ochratoxin A) in a laboratory over a number of days and under strict environmental conditions. Diverse factors or inputs are used to try to predict the amount of mycotoxin, such as the storage time, incubation temperature, water activity, the diameter of the inocule or the presence of fungicides.

Another application of neural networks that will be presented in this Thesis is related to the medical image reconstruction on a detector for positron emission tomography, correcting intrinsic errors due to the nature of the optical and physical phenomena experienced by photons on their way to the detector. The neural networks designed and trained for this purpose can be easily implemented in hardware, freeing the computer from an important computational load, and allow the automatic online correction of impact position of photons in a real time PET system.