{"title":"A new high-precision numerical method for solving the HIV infection model of CD4(+) cells","authors":"","doi":"10.1016/j.physa.2024.130090","DOIUrl":null,"url":null,"abstract":"<div><p>This paper proposes a new method called the “Special Neural Network” to solve the HIV infection model of CD4(+) cells using a novel approximation approach. Unlike traditional methods that involve constructing loss functions and performing inverse matrix operations, our method discretizes the differential equations at configuration points, combines them, and transforms the system into a set of nonlinear equations. Parameters in the neural network are then iteratively solved using optimization to obtain an approximate solution. Additionally, when using the neural network as an approximate solution to the differential equations, we provide a form that satisfies the initial conditions through construction, eliminating the need to handle initial conditions during the solving process and thus streamlining the method. Finally, by comparing with other numerical methods using two sets of models and parameters, the Special Neural Network achieves high precision results and further demonstrates the advantages of our approach.</p></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica A: Statistical Mechanics and its Applications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378437124005995","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
This paper proposes a new method called the “Special Neural Network” to solve the HIV infection model of CD4(+) cells using a novel approximation approach. Unlike traditional methods that involve constructing loss functions and performing inverse matrix operations, our method discretizes the differential equations at configuration points, combines them, and transforms the system into a set of nonlinear equations. Parameters in the neural network are then iteratively solved using optimization to obtain an approximate solution. Additionally, when using the neural network as an approximate solution to the differential equations, we provide a form that satisfies the initial conditions through construction, eliminating the need to handle initial conditions during the solving process and thus streamlining the method. Finally, by comparing with other numerical methods using two sets of models and parameters, the Special Neural Network achieves high precision results and further demonstrates the advantages of our approach.
期刊介绍:
Physica A: Statistical Mechanics and its Applications
Recognized by the European Physical Society
Physica A publishes research in the field of statistical mechanics and its applications.
Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents.
Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.