{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,8]],"date-time":"2025-09-08T06:00:32Z","timestamp":1757311232458},"reference-count":60,"publisher":"MIT Press","issue":"4","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In many engineering fields and scientific disciplines, the results of experiments are in the form of time series, which can be quite problematic to interpret and model. Genetic programming tools are quite powerful in extracting knowledge from data. In this work, several upgrades and refinements are proposed and tested to improve the explorative capabilities of symbolic regression (SR) via genetic programming (GP) for the investigation of time series, with the objective of extracting mathematical models directly from the available signals. The main task is not simply prediction but consists of identifying interpretable equations, reflecting the nature of the mechanisms generating the signals. The implemented improvements involve almost all aspects of GP, from the knowledge representation and the genetic operators to the fitness function. The unique capabilities of genetic programming, to accommodate prior information and knowledge, are also leveraged effectively. The proposed upgrades cover the most important applications of empirical modeling of time series, ranging from the identification of autoregressive systems and partial differential equations to the search of models in terms of dimensionless quantities and appropriate physical units. Particularly delicate systems to identify, such as those showing hysteretic behavior or governed by delayed differential equations, are also addressed. The potential of the developed tools is substantiated with both a battery of systematic numerical tests with synthetic signals and with applications to experimental data.<\/jats:p>","DOI":"10.1162\/evco_a_00330","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T18:06:53Z","timestamp":1682964413000},"page":"401-432","update-policy":"http:\/\/dx.doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":4,"title":["Upgrades of Genetic Programming for Data-Driven Modeling of Time Series"],"prefix":"10.1162","volume":"31","author":[{"given":"A.","family":"Murari","sequence":"first","affiliation":[{"name":"Consorzio RFX (CNR, ENEA, INFN, Universit\u00e0 di Padova, Acciaierie Venete SpA), Corso Stati Uniti 4, 35127 Padova, Italy Istituto per la Scienza e la Tecnologia dei Plasmi, CNR, Padova, Italy andrea.murari@istp.cnr.it"}]},{"given":"E.","family":"Peluso","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Rome \u201cTor Vergata,\u201d via del Politecnico 1, Roma, Italy emmanuele.peluso@uniroma2.it"}]},{"given":"L.","family":"Spolladore","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Rome \u201cTor Vergata,\u201d via del Politecnico 1, Roma, Italy luca.spolladore@uniroma2.it"}]},{"given":"R.","family":"Rossi","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Rome \u201cTor Vergata,\u201d via del Politecnico 1, Roma, Italy riccardo.rossi.en@gmail.com"}]},{"given":"M.","family":"Gelfusa","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Rome \u201cTor Vergata,\u201d via del Politecnico 1, Roma, Italy gelfusa@ing.uniroma2.it"}]}],"member":"281","published-online":{"date-parts":[[2023,12,1]]},"reference":[{"issue":"2","key":"2023120113073566200_B1","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1162\/EVCO_a_00110","article-title":"Genetic programming and serial processing for time series classification","volume":"22","author":"Alfaro-Cid","year":"2014","journal-title":"Evolutionary Computation"},{"key":"2023120113073566200_B2","volume-title":"Methods of information geometry","author":"Amari","year":"2000"},{"issue":"1","key":"2023120113073566200_B3","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10710-009-9084-3","article-title":"The influence of mutation on population dynamics in multiobjective genetic programming","volume":"11","author":"Badran","year":"2010","journal-title":"Genetic Programming and Evolvable Machines"},{"key":"2023120113073566200_B4","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316757","author":"Bates","year":"1988","journal-title":"Nonlinear regression analysis and its applications"},{"key":"2023120113073566200_B5","volume-title":"Hysteresis in magnetism: For physicists, materials scientists, and engineers","author":"Bertotti","year":"1998"},{"key":"2023120113073566200_B6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-12601-7","volume-title":"Extracting knowledge from time series: An introduction to nonlinear empirical modeling","author":"Bezruchko","year":"2010"},{"key":"2023120113073566200_B7","volume-title":"Model selection and multi-model influence: A practical information theoretic approach","author":"Burnham.","year":"2002"},{"key":"2023120113073566200_B8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-0835-9","volume-title":"Genetic algorithms and genetic programming in computational finance","author":"Chen","year":"2002"},{"key":"2023120113073566200_B9","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1137\/0806023","article-title":"An interior trust-region approach for nonlinear minimization subject to bounds","volume":"6","author":"Coleman","year":"1996","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"2023120113073566200_B10","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/BF01582221","article-title":"On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds","volume":"67","author":"Coleman","year":"1994","journal-title":"Mathematical Programming"},{"key":"2023120113073566200_B18","doi-asserted-by":"crossref","DOI":"10.1002\/9781118165881","volume-title":"Nonparametric statistics for non-statisticians: A step-by-step approach","author":"Corder, G. 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