Mathematical modeling and simulation of biophysics systems using neural network

Abstract

Many of the real-life problems including dynamical structures can be modeled in the shape of differential equations. A number of analytic and numerical methods are being proposed for the solution of these differential equations but for some instances, we may come across a few limitations attached to them. However, theoretically strong and computationally favorable tools such as artificial neural networks can be utilized to approximate the solutions of these differential equations. In this work, we developed mathematical models for some biophysics systems on the basis of their dynamical behavior and opted a neural network having single hidden layer of 50 neurons and Broyden-Fletcher-Goldfarb-Shanno algorithm as an optimizer to simulate the results for population of micro-organisms. The graphical representations of the results obtained both from the neural network and analytic methods are compared for different parameters and we got almost the same results.