Systems & control transactions最新文献

筛选

英文中文

Selection of Fitness Criteria for Learning Interpretable PDE Solutions via Symbolic Regression. 符号回归学习可解释PDE解的适应度标准选择。

Systems & control transactions Pub Date : 2025-07-01 Epub Date: 2025-06-27 DOI: 10.69997/sct.199083

Benjamin G Cohen, Burcu Beykal, George M Bollas

{"title":"Selection of Fitness Criteria for Learning Interpretable PDE Solutions via Symbolic Regression.","authors":"Benjamin G Cohen, Burcu Beykal, George M Bollas","doi":"10.69997/sct.199083","DOIUrl":"10.69997/sct.199083","url":null,"abstract":"Physics-Informed Symbolic Regression (PISR) offers a pathway to discover human-interpretable solutions to partial differential equations (PDEs). This work investigates three fitness metrics within a PISR framework: PDE fitness, Bayesian Information Criterion (BIC), and a fitness metric proportional to the probability of a model given the data. Through experiments with Laplace's equation, Burgers' equation, and a nonlinear wave equation, we demonstrate that incorporating information theoretic criteria like BIC can yield higher fidelity models while maintaining interpretability. Our results show that BIC-based PISR achieved the best performance, identifying an exact solution to Laplace's equation and finding solutions with <math> <mrow><msup><mi>R</mi> <mn>2</mn></msup> </mrow> </math> -values of 0.998 for Burgers' equation and 0.957 for the nonlinear wave equation. The inclusion of the Bayes D-optimality criterion in estimating model probability strongly constrained solution complexity, limiting models to 3-4 parameters and reducing accuracy. These findings suggest that a two-stage approach-using simpler complexity metrics during initial solution discovery followed by a post-hoc identifiability analysis may be optimal for discovering interpretable and mathematically identifiable PDE solutions.","PeriodicalId":520222,"journal":{"name":"Systems & control transactions","volume":"4 ","pages":"1837-1842"},"PeriodicalIF":0.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12425483/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145067516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Data-Driven Chance-Constrained Mixed Integer Nonlinear Bi-level Optimisation Via Copulas: Application To Integrated Planning And Scheduling Problems. 基于copula的数据驱动机会约束混合整数非线性双级优化：在综合计划和调度问题中的应用。

Systems & control transactions Pub Date : 2025-01-01 Epub Date: 2025-06-27 DOI: 10.69997/sct.169891

Syu-Ning Johnn, Hasan Nikkhah, Meng-Lin Tsai, Styliani Avraamidou, Burcu Beykal, Vassilis M Charitopoulos

{"title":"Data-Driven Chance-Constrained Mixed Integer Nonlinear Bi-level Optimisation Via Copulas: Application To Integrated Planning And Scheduling Problems.","authors":"Syu-Ning Johnn, Hasan Nikkhah, Meng-Lin Tsai, Styliani Avraamidou, Burcu Beykal, Vassilis M Charitopoulos","doi":"10.69997/sct.169891","DOIUrl":"10.69997/sct.169891","url":null,"abstract":"Planning and scheduling are integral components of process supply chains. The presence of data correlation, particularly multivariate demand data dependency, can pose significant challenges to the decision-making process. This necessitates the consideration of dependency structures inherent in the underlying data to generate good-quality, feasible solutions to optimisation problems such as planning and scheduling. This work proposes a chance-constrained optimisation framework integrated with copulas, a non-parametric data estimation technique to forecast uncertain demand levels in accordance with specified risk thresholds in the context of a planning and scheduling problem. We focus on the integrated planning and scheduling problem following a bi-level optimisation formulation. The estimated demand forecasts are subsequently utilised within the Data-driven Optimisation of bi-level Mixed-Integer NOnlinear problems (DOMINO) framework to solve the integrated optimisation problem, and derive decisions with guaranteed demand satisfaction rates. Computational experiments demonstrate that our proposed copula-based chance-constrained optimisation framework can incorporate demand correlation and achieve higher joint demand satisfaction rate, lower total costs with higher efficiency.","PeriodicalId":520222,"journal":{"name":"Systems & control transactions","volume":"4 ","pages":"117-122"},"PeriodicalIF":0.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12425488/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145067542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

From Then to Now and Beyond: Exploring How Machine Learning Shapes Process Design Problems. 从过去到现在，再到未来：探索机器学习如何塑造流程设计问题。

Systems & control transactions Pub Date : 2024-01-01 Epub Date: 2024-07-10 DOI: 10.69997/sct.116002

Burcu Beykal

引用次数: 0