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Data-Driven Corrections of Partial Lotka–Volterra Models

In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a given reaction) and in epidemiological models (only certain...

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Autor principal: Morrison, Rebecca E.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7712089/
https://www.ncbi.nlm.nih.gov/pubmed/33287078
http://dx.doi.org/10.3390/e22111313
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author Morrison, Rebecca E.
author_facet Morrison, Rebecca E.
author_sort Morrison, Rebecca E.
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description In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a given reaction) and in epidemiological models (only certain subpopulations are consequential). Thus, it is common to use greatly reduced or partial models in which only the interactions among the species of interest are known. In this work, we explore the use of an embedded, sparse, and data-driven discrepancy operator to augment these partial interaction models. Preliminary results show that the model error caused by severe reductions—e.g., elimination of hundreds of terms—can be captured with sparse operators, built with only a small fraction of that number. The operator is embedded within the differential equations of the model, which allows the action of the operator to be interpretable. Moreover, it is constrained by available physical information and calibrated over many scenarios. These qualities of the discrepancy model—interpretability, physical consistency, and robustness to different scenarios—are intended to support reliable predictions under extrapolative conditions.
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spelling pubmed-77120892021-02-24 Data-Driven Corrections of Partial Lotka–Volterra Models Morrison, Rebecca E. Entropy (Basel) Article In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a given reaction) and in epidemiological models (only certain subpopulations are consequential). Thus, it is common to use greatly reduced or partial models in which only the interactions among the species of interest are known. In this work, we explore the use of an embedded, sparse, and data-driven discrepancy operator to augment these partial interaction models. Preliminary results show that the model error caused by severe reductions—e.g., elimination of hundreds of terms—can be captured with sparse operators, built with only a small fraction of that number. The operator is embedded within the differential equations of the model, which allows the action of the operator to be interpretable. Moreover, it is constrained by available physical information and calibrated over many scenarios. These qualities of the discrepancy model—interpretability, physical consistency, and robustness to different scenarios—are intended to support reliable predictions under extrapolative conditions. MDPI 2020-11-18 /pmc/articles/PMC7712089/ /pubmed/33287078 http://dx.doi.org/10.3390/e22111313 Text en © 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Morrison, Rebecca E.
Data-Driven Corrections of Partial Lotka–Volterra Models
title Data-Driven Corrections of Partial Lotka–Volterra Models
title_full Data-Driven Corrections of Partial Lotka–Volterra Models
title_fullStr Data-Driven Corrections of Partial Lotka–Volterra Models
title_full_unstemmed Data-Driven Corrections of Partial Lotka–Volterra Models
title_short Data-Driven Corrections of Partial Lotka–Volterra Models
title_sort data-driven corrections of partial lotka–volterra models
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7712089/
https://www.ncbi.nlm.nih.gov/pubmed/33287078
http://dx.doi.org/10.3390/e22111313
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