Differential Elimination for Dynamical Models via Projections with Applications to Structural Identifiability

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED
Rui-Tao Dong, Christian Goodbrake, H. Harrington, G. Pogudin
{"title":"Differential Elimination for Dynamical Models via Projections with Applications to Structural Identifiability","authors":"Rui-Tao Dong, Christian Goodbrake, H. Harrington, G. Pogudin","doi":"10.1137/22m1469067","DOIUrl":null,"url":null,"abstract":"Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies on computing input-output relations via differential algebraic elimination. Determining identifiability, a natural prerequisite for meaningful parameter estimation, is often prohibitively expensive for medium to large systems due to the computationally expensive task of elimination. We propose an algorithm that computes a description of the set of differential-algebraic relations between the input and output variables of a dynamical system model. The resulting algorithm outperforms general-purpose software for differential elimination on a set of benchmark models from literature. We use the designed elimination algorithm to build a new randomized algorithm for assessing structural identifiability of a parameter in a parametric model. A parameter is said to be identifiable if its value can be uniquely determined from input-output data assuming the absence of noise and sufficiently exciting inputs. Our new algorithm allows the identification of models that could not be tackled before. Our implementation is publicly available as a Julia package at https://github.com/SciML/StructuralIdentifiability.jl.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Algebra and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1469067","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 17

Abstract

Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies on computing input-output relations via differential algebraic elimination. Determining identifiability, a natural prerequisite for meaningful parameter estimation, is often prohibitively expensive for medium to large systems due to the computationally expensive task of elimination. We propose an algorithm that computes a description of the set of differential-algebraic relations between the input and output variables of a dynamical system model. The resulting algorithm outperforms general-purpose software for differential elimination on a set of benchmark models from literature. We use the designed elimination algorithm to build a new randomized algorithm for assessing structural identifiability of a parameter in a parametric model. A parameter is said to be identifiable if its value can be uniquely determined from input-output data assuming the absence of noise and sufficiently exciting inputs. Our new algorithm allows the identification of models that could not be tackled before. Our implementation is publicly available as a Julia package at https://github.com/SciML/StructuralIdentifiability.jl.
基于投影的动力模型微分消除及其在结构可识别性中的应用
在分析(可能是非线性的)动力系统模型时,通常需要消除微分方程系统中的未知数,其中只有一部分变量是可见的。一种这样的分析,可辨识性,通常依赖于通过微分代数消去计算输入-输出关系。确定可辨识性是有意义的参数估计的自然先决条件,由于消除任务的计算成本很高,因此对于中型到大型系统来说,确定可辨识性通常是非常昂贵的。我们提出了一种算法,用于计算动力系统模型的输入和输出变量之间的微分代数关系集的描述。所得算法在一组来自文献的基准模型上优于通用的微分消除软件。我们使用设计的消去算法建立了一个新的随机算法来评估参数模型中参数的结构可识别性。一个参数是可识别的,如果它的值可以唯一地确定从输入输出数据假设没有噪声和足够激励的输入。我们的新算法允许识别以前无法解决的模型。我们的实现可以在https://github.com/SciML/StructuralIdentifiability.jl上作为Julia包公开获得。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
2.20
自引率
0.00%
发文量
19
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信