A Genetic Algorithm For Deducing Ordinary Differential Equations

In scientific research and production,researchers often use ordinary differential equations?ODE?as mathematical modeling tools.For example,ordinary differential equations can be used to model a series of problems such as cell regulatory systems,transmission and control of infectious diseases,kinetic problems of particles,changes in weather,population growth,and HIV infection kinetics^[1].Ordinary differential equations is often used to describe the laws of dynamic systems.It can predict the future state of the system based on time variables^[2]and have been widely used in many fields.Therefore,the study of the method to derive ordinary differential equations has a great significance and value for scientific research.There are many types of ordinary differential equations,and they are affected by many factors.Therefore,it is very difficult to figure out ordinary differential equation models.The key issue is that the model's parameter space and model structure space are very complex.Therefore,how to use dynamic modeling of ordinary differential equations is transformed into how to find the parameter space and model structure space suitable for ordinary differential equations.In order to solve many problems encountered in the process of finding ordinary differential equation models,this paper propose to use genetic algorithm to derive the parameter space and structure space of the ordinary differential equation model.We design a reasonable encoded mode,so that each ordinary differential equation can be represented as a chromosome.And in this way,practical problems are transformed as chromosome and gene.This paper first selected the HIV virus model for experiments.This model was chosen because the model already exists,and the experimental results obtained by comparing the experimental data with the data generated by the real HIV virus model can better represent the real effect of the algorithm.Then three groups of other models were tested.The three groups are artificial models,namely three-variable model,four-variable model and five-variable model.These three sets of models are more complex than the real ones and are more convincing for validating the proposed method.For each of the above models,ten identical experiments were performed in this paper,and the specific effects of the proposed method were described by showing the experimental results.In addition,for each model of the experiment,five experimental results were selected to display.By comparing the five results in each model,we can know that the better the fitness is,the better the experimental results and the experimentally generated models are,and the better the time-processing data matches the known data.By analyzing and summarizing the experimental results of the above four groups of models,we can see that it is a very effective method to use the genetic algorithm to simultaneously derive the structure and parameters of the ordinary differential equation model.