An Algorithm For Deriving The Structure And Parameters Of Ordinary Differential Equations

Ordinary differential equations(ODE)models are quite useful in modeling dynamic processes in many scientific fields,such as physics,biomedical sciences and engineering.They are extremely useful in describing ecosystem(e.g.,population competition in biology),cell regulation system(e.g.,signaling pathways and gene regulatory networks),HIV dynamics and so on.In many cases,we can easily get the change of concentration or number of elements in a dynamic system,but it is not known how the interaction between elements is.Even experienced scientists can hardly build effective models.Therefore,the study of the derivation of the computational method for the ordinary differential model has important value and significance in many system identification problems.The difficulty in deriving the model problem of ordinary differential equations lies in the complexity of the search space.The search space includes the parameter space and the model structure space.In previous studies,the complexity of the model structure space was usually reduced by using specialized domain knowledge or constructing a complete ordinary differential equation model from partial ordinary differential equation models.However,both methods need to be based on comprehensive professional domain knowledge.Both methods are also limited in their versatility.This paper deduces the calculation method of the ordinary differential equation model,and proposes a Latin hypercube sampling particle swarm algorithm(LHS-PSO)based on swarm intelligence.This algorithm searches for the dynamic system to find a reasonable ordinary differential equation model based on the observed time-course data.Compared with previous methods,the LHS-PSO algorithm does not need to rely on related domain knowledge and partial ordinary differential equations as the basis to narrow the search space.The algorithm has strong commonality among different disciplines and provides a convenient method for experts and scholars in various fields to solve the problem of derivation of ordinary differential equations.In the experimental part of this paper,the effectiveness of the LHS-PSO algorithm is tested by a set of real ordinary differential equation models,the Human Immunodeficiency Virus(HIV)model and two sets of artificial models,the three-variable model and the four-variable model.In each set of experimental models,twenty experiments were performed and the box plots of the standard particle swarm optimization algorithm and the LHS-PSO algorithm were depicted based on the experimental results,also plots the experimental result data.In addition,in each chapter of the experimental section,five different results models with different fitness values were selected for demonstration.From the comparison of the five groups of result models,it can be seen that as the fitness value gradually increases,the degree of fitting between the corresponding result model and the known time course also gradually decreases.through the experimental results and analysis,it is verified that the LHS-PSO algorithm can simultaneously derive the ODE model that matches the known time process data.In addition,compared with the experimental results of the standard particle swarm algorithm,the model that the LHS-PSO algorithm finds has a better fit with the known time-course data.