Two approaches of Neural Network system - Chemotaxis PDE and Tranfer Learning

Abstract

We consider the mathematical model of chemotaxis introduced by Patlak, Keller, and Segel. Aggregation and progression waves are present everywhere in the population dynamics of chemotactic cells. Aggregation originates from the chemotaxis of mobile cells, where cells are attracted to migrate to higher concentrations of the chemical signal region produced by themselves. The neural net can be used to find the approximate solution of the PDE. We proved that the error, the difference between the actual value and the predicted value, is bound to a constant multiple of the loss we are learning. Also, the Neural Net approximation can be easily applied to the inverse problem. It was confirmed that even when the coefficient of the PDE equation was unknown, prediction with high accuracy was achieved. Artificial intelligence (AI) technology has been spreading to the depths of industries, and research on the development of flexible AI technology that replaces the existing domain experts is spurring. Manufacturing industries, such as the semiconductor, steel, and chemical industries, require thedevelopment of AI that responds to the rapidly changing environment. Manufacturing data generated from dozens to hundreds of sensors are high-dimensional numerical float data, which are different fromthe existing image and text data, and generating data for re-training is time-intensive. Therefore,data collection is difficult. In addition, most tasks in manufacturing require a regression model to find the numerical control or predicted values. To solve this manufacturing problem, we developedatransformed supervised domain adaptation (TSDA) based on domain adaptation. TSDA has developed a technology using a transformation map to apply domain adaptation, mainly for classification problemsapplied to images and text, to a regression model based on numerical data. The performance was verified based on actual steel industry data and two general datasets.