{"title":"Learning river water quality models by <i>l1</i>-weighted regularization","authors":"Dinh Nho Hào, Duong Xuan Hiep, Pham Quy Muoi","doi":"10.1093/imamat/hxad023","DOIUrl":null,"url":null,"abstract":"Abstract We investigate the problem of learning a water quality model (BOD-DO model) from given data. Assuming that all parameters in the model are constants, we reformulate the problem as a system of linear equations for the unknown terms. Since in practice the system is often under-determined or over-determined and the observed data are noisy, we use an $l^{1}$-weighted regularization method to find a stable approximate solution. Then, Nesterov’s algorithm is used to solve the regularized problem. Learning models with variable coefficients are also discussed. Numerical examples show that our approach works well with noisy data and has the ability to learn the BOD-DO model.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/imamat/hxad023","RegionNum":4,"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: 0
Abstract
Abstract We investigate the problem of learning a water quality model (BOD-DO model) from given data. Assuming that all parameters in the model are constants, we reformulate the problem as a system of linear equations for the unknown terms. Since in practice the system is often under-determined or over-determined and the observed data are noisy, we use an $l^{1}$-weighted regularization method to find a stable approximate solution. Then, Nesterov’s algorithm is used to solve the regularized problem. Learning models with variable coefficients are also discussed. Numerical examples show that our approach works well with noisy data and has the ability to learn the BOD-DO model.
期刊介绍：
The IMA Journal of Applied Mathematics is a direct successor of the Journal of the Institute of Mathematics and its Applications which was started in 1965. It is an interdisciplinary journal that publishes research on mathematics arising in the physical sciences and engineering as well as suitable articles in the life sciences, social sciences, and finance. Submissions should address interesting and challenging mathematical problems arising in applications. A good balance between the development of the application(s) and the analysis is expected. Papers that either use established methods to address solved problems or that present analysis in the absence of applications will not be considered.
The journal welcomes submissions in many research areas. Examples are: continuum mechanics materials science and elasticity, including boundary layer theory, combustion, complex flows and soft matter, electrohydrodynamics and magnetohydrodynamics, geophysical flows, granular flows, interfacial and free surface flows, vortex dynamics; elasticity theory; linear and nonlinear wave propagation, nonlinear optics and photonics; inverse problems; applied dynamical systems and nonlinear systems; mathematical physics; stochastic differential equations and stochastic dynamics; network science; industrial applications.
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