Parsimonious neural networks learn interpretable physical laws

Abstract Machine learning is playing an increasing role in the physical sciences and significant progress has been made towards embedding domain knowledge into models. Less explored is its use to discover interpretable physical laws from data. We propose parsimonious neural networks (PNNs) that comb...

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Autores principales:	Saaketh Desai, Alejandro Strachan
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/7b24e1e0a740421f8df33a3f6cfc3068
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spelling	oai:doaj.org-article:7b24e1e0a740421f8df33a3f6cfc30682021-12-02T17:24:10ZParsimonious neural networks learn interpretable physical laws10.1038/s41598-021-92278-w2045-2322https://doaj.org/article/7b24e1e0a740421f8df33a3f6cfc30682021-06-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-92278-whttps://doaj.org/toc/2045-2322Abstract Machine learning is playing an increasing role in the physical sciences and significant progress has been made towards embedding domain knowledge into models. Less explored is its use to discover interpretable physical laws from data. We propose parsimonious neural networks (PNNs) that combine neural networks with evolutionary optimization to find models that balance accuracy with parsimony. The power and versatility of the approach is demonstrated by developing models for classical mechanics and to predict the melting temperature of materials from fundamental properties. In the first example, the resulting PNNs are easily interpretable as Newton’s second law, expressed as a non-trivial time integrator that exhibits time-reversibility and conserves energy, where the parsimony is critical to extract underlying symmetries from the data. In the second case, the PNNs not only find the celebrated Lindemann melting law, but also new relationships that outperform it in the pareto sense of parsimony vs. accuracy.Saaketh DesaiAlejandro StrachanNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Saaketh Desai Alejandro Strachan Parsimonious neural networks learn interpretable physical laws
description	Abstract Machine learning is playing an increasing role in the physical sciences and significant progress has been made towards embedding domain knowledge into models. Less explored is its use to discover interpretable physical laws from data. We propose parsimonious neural networks (PNNs) that combine neural networks with evolutionary optimization to find models that balance accuracy with parsimony. The power and versatility of the approach is demonstrated by developing models for classical mechanics and to predict the melting temperature of materials from fundamental properties. In the first example, the resulting PNNs are easily interpretable as Newton’s second law, expressed as a non-trivial time integrator that exhibits time-reversibility and conserves energy, where the parsimony is critical to extract underlying symmetries from the data. In the second case, the PNNs not only find the celebrated Lindemann melting law, but also new relationships that outperform it in the pareto sense of parsimony vs. accuracy.
format	article
author	Saaketh Desai Alejandro Strachan
author_facet	Saaketh Desai Alejandro Strachan
author_sort	Saaketh Desai
title	Parsimonious neural networks learn interpretable physical laws
title_short	Parsimonious neural networks learn interpretable physical laws
title_full	Parsimonious neural networks learn interpretable physical laws
title_fullStr	Parsimonious neural networks learn interpretable physical laws
title_full_unstemmed	Parsimonious neural networks learn interpretable physical laws
title_sort	parsimonious neural networks learn interpretable physical laws
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/7b24e1e0a740421f8df33a3f6cfc3068
work_keys_str_mv	AT saakethdesai parsimoniousneuralnetworkslearninterpretablephysicallaws AT alejandrostrachan parsimoniousneuralnetworkslearninterpretablephysicallaws
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Parsimonious neural networks learn interpretable physical laws

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