{"title":"基于 SMT 的非线性连续和混合动力学参数可识别组合检测","authors":"Devleena Ghosh, C. Mandal","doi":"10.1145/3665920","DOIUrl":null,"url":null,"abstract":"Parameter identifiability is an important aspect of parameter estimation of dynamic system modelling. Several methods exist to determine identifiability of parameter sets using the model definition and analysis of experimental data. There is also the possibility of some parameters being independently unidentifiable but forming identifiable parameter combinations. These identifiable parameter combinations are useful in model reparameterisation to estimate parameters experimentally. Multiple numerical and algebraic methods exist to detect identifiable parameter combinations of dynamic system models represented as ordinary differential equations (ODE). Local identifiability analysis of hybrid system models are available in the literature. However, methods for structural identifiability analysis and identifiable combination detection for hybrid systems are not explored. Here, we have developed a parameter identifiable combination detection method for non-linear hybrid systems along with ODE systems using an SMT based parameter space exploration method. For higher dimensional systems and larger parameter space, SMT based approaches may easily become computationally intractable. This problem has been mitigated to a large extent by heuristically limiting the parameter space to be explored, using Gaussian process regression and gradient based approaches. The developed method has been demonstrated for some simple hybrid models, biochemical models of ODE systems and non-linear hybrid systems.","PeriodicalId":50432,"journal":{"name":"Formal Aspects of Computing","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SMT based parameter identifiable combination detection for non-linear continuous and hybrid dynamics\",\"authors\":\"Devleena Ghosh, C. Mandal\",\"doi\":\"10.1145/3665920\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Parameter identifiability is an important aspect of parameter estimation of dynamic system modelling. Several methods exist to determine identifiability of parameter sets using the model definition and analysis of experimental data. There is also the possibility of some parameters being independently unidentifiable but forming identifiable parameter combinations. These identifiable parameter combinations are useful in model reparameterisation to estimate parameters experimentally. Multiple numerical and algebraic methods exist to detect identifiable parameter combinations of dynamic system models represented as ordinary differential equations (ODE). Local identifiability analysis of hybrid system models are available in the literature. However, methods for structural identifiability analysis and identifiable combination detection for hybrid systems are not explored. Here, we have developed a parameter identifiable combination detection method for non-linear hybrid systems along with ODE systems using an SMT based parameter space exploration method. For higher dimensional systems and larger parameter space, SMT based approaches may easily become computationally intractable. This problem has been mitigated to a large extent by heuristically limiting the parameter space to be explored, using Gaussian process regression and gradient based approaches. The developed method has been demonstrated for some simple hybrid models, biochemical models of ODE systems and non-linear hybrid systems.\",\"PeriodicalId\":50432,\"journal\":{\"name\":\"Formal Aspects of Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-06-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Formal Aspects of Computing\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1145/3665920\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Formal Aspects of Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1145/3665920","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
SMT based parameter identifiable combination detection for non-linear continuous and hybrid dynamics
Parameter identifiability is an important aspect of parameter estimation of dynamic system modelling. Several methods exist to determine identifiability of parameter sets using the model definition and analysis of experimental data. There is also the possibility of some parameters being independently unidentifiable but forming identifiable parameter combinations. These identifiable parameter combinations are useful in model reparameterisation to estimate parameters experimentally. Multiple numerical and algebraic methods exist to detect identifiable parameter combinations of dynamic system models represented as ordinary differential equations (ODE). Local identifiability analysis of hybrid system models are available in the literature. However, methods for structural identifiability analysis and identifiable combination detection for hybrid systems are not explored. Here, we have developed a parameter identifiable combination detection method for non-linear hybrid systems along with ODE systems using an SMT based parameter space exploration method. For higher dimensional systems and larger parameter space, SMT based approaches may easily become computationally intractable. This problem has been mitigated to a large extent by heuristically limiting the parameter space to be explored, using Gaussian process regression and gradient based approaches. The developed method has been demonstrated for some simple hybrid models, biochemical models of ODE systems and non-linear hybrid systems.
期刊介绍:
This journal aims to publish contributions at the junction of theory and practice. The objective is to disseminate applicable research. Thus new theoretical contributions are welcome where they are motivated by potential application; applications of existing formalisms are of interest if they show something novel about the approach or application.
In particular, the scope of Formal Aspects of Computing includes:
well-founded notations for the description of systems;
verifiable design methods;
elucidation of fundamental computational concepts;
approaches to fault-tolerant design;
theorem-proving support;
state-exploration tools;
formal underpinning of widely used notations and methods;
formal approaches to requirements analysis.