{"title":"求解 CD4(+)细胞艾滋病毒感染模型的新型高精度数值方法","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":"{\"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}","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
摘要
本文提出了一种名为 "特殊神经网络 "的新方法,利用新颖的近似方法求解 CD4(+) 细胞的 HIV 感染模型。与涉及构建损失函数和执行逆矩阵运算的传统方法不同,我们的方法在配置点上离散微分方程,将它们组合起来,并将系统转换为一组非线性方程。然后使用优化方法对神经网络中的参数进行迭代求解,以获得近似解。此外,在使用神经网络作为微分方程的近似解时,我们通过构造提供了一种满足初始条件的形式,从而无需在求解过程中处理初始条件,从而简化了方法。最后,通过与其他使用两组模型和参数的数值方法进行比较,特殊神经网络获得了高精度结果,进一步证明了我们方法的优势。
A new high-precision numerical method for solving the HIV infection model of CD4(+) cells
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.