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Open AccessFeature PaperArticle

The Role of Data in Model Building and Prediction: A Survey Through Examples

1
Dipartimento di Fisica, “Sapienza” Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
2
Istituto dei Sistemi Complessi, CNR, via dei Taurini 19, 00185 Rome, Italy
3
CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
4
Centro Linceo Interdisciplinare “B. Segre”, Accademia dei Lincei, via della Lungara 10, 00165 Rome, Italy
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(10), 807; https://doi.org/10.3390/e20100807
Received: 27 July 2018 / Revised: 18 October 2018 / Accepted: 19 October 2018 / Published: 22 October 2018
(This article belongs to the Special Issue Economic Fitness and Complexity)
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Abstract

The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of quantitative sciences, mean abstract mathematical or algorithmical representations. This short review discusses a few key examples from Physics, taken from dynamical systems theory, biophysics, and statistical mechanics, representing three paradigmatic procedures to build models and predictions from available data. In the case of dynamical systems we show how predictions can be obtained in a virtually model-free framework using the methods of analogues, and we briefly discuss other approaches based on machine learning methods. In cases where the complexity of systems is challenging, like in biophysics, we stress the necessity to include part of the empirical knowledge in the models to gain the minimal amount of realism. Finally, we consider many body systems where many (temporal or spatial) scales are at play—and show how to derive from data a dimensional reduction in terms of a Langevin dynamics for their slow components. View Full-Text
Keywords: models; data; multiscale systems; Langevin equation models; data; multiscale systems; Langevin equation
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Baldovin, M.; Cecconi, F.; Cencini, M.; Puglisi, A.; Vulpiani, A. The Role of Data in Model Building and Prediction: A Survey Through Examples. Entropy 2018, 20, 807.

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