He X., Xu S. Process Neural Networks. Theory and Applications

Zhejiang University Press / Springer, 2009. — 253 p.The original idea for this book came from a conference on applications of agricultural expert systems, which may not seem obvious. During the conference, the ceaseless reports and repetitious content made me think that the problems the attendees discussed so intensely, no matter which kind of crop planting was involved, could be thought of as the same problem, i.e. a "functional problem" from the viewpoint of a mathematical expert. To achieve some planting indexes, e.g. output or quality, whatever the crop grown, different means of control performed by the farmers, e.g. reasonable fertilization, control of illumination, temperature, humidity, concentration of CO₂, etc., all can be seen as diversified time-varying control processes starting from sowing and ending at harvest. They could just as easily be seen as the inputs for the whole crop growth process. The yield or the quality index of the plant can then be considered as a functional dependent on these time-varying processes. Then the pursuit of high quantity and high quality becomes an issue of solving an extremum of the functional.
At that time, my research interest focused on computational intelligence mainly including fuzzy computing, neural computing, and evolutionary computing, so I thought of neural networks immediately. I asked myself why not study neural networks whose inputs and outputs could both be a time-varying processes and why not study some kinds of more general neural networks whose inputs and outputs could be multi-variable functions and even points in some functional space. Traditional neural networks are only used to describe the instantaneous mapping relationship between input values and output values. However, these new neural networks can describe the accumulation or aggregation effect of the outputs on the inputs on the time axis. This new ability is very useful for solving many problems including high-tech applications in agriculture and for elaborate description of the behavior of a biological neuron. The problems that the traditional neural networks solved are function approximation and function optimization, and the problems we need to solve now are functional approximation and functional optimization, which are more complicated. However, as a mathematician my intuition told me that there existed the possibility of resolving these problems with certain definite constraints and that there might be the prospect of broader applications in the future. In research during the following years, I was attracted by these issues. In addition to numerous engineering tasks (e.g. I had assumed responsibility in China for manned airship engineering), almost all the rest of my time was spent on this study. I presented the concept of the "Process Neural Network (PNN)", which would be elaborated in this book. In recent years, we have done some further work on the theories, algorithms, and applications of process neural networks, and we have solved some basic theory issues, including the existence of solutions under certain conditions, continuity of the process neural network models, several approximation theorems (which are the theoretical foundations on which process neural network models can be applied to various practical problems), and we have investigated PNN's computational capability. We have also put forward some useful learning algorithms for process neural networks, and achieved some preliminary applications including process control of chemical reactions, oil recovery, dynamic fault inspection, and communication alert and prediction. It is so gratifying to obtain these results in just a few years. However, the research is arduous and there is a long way to go. Besides summarizing the aforementioned preliminary achievements, this monograph will highlight some issues that need to be solved.Artificial Neural Networks
Process Neurons
Feedforward Process Neural Networks
Learning Algorithms for Process Neural Networks
Feedback Process Neural Networks
Multi-aggregation Process Neural Networks
Design and Construction of Process Neural Networks
Application of Process Neural Networks