Generalized neural closure models with interpretability
Abstract Improving the predictive capability and computational cost of dynamical models is often at the heart of augmenting computational physics with machine learning (ML). However, most learning results are limited in interpretability and generalization over different computational grid resolution...
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ftdoajarticles:oai:doaj.org/article:e77d383fd9674677801f008bc391011c 2023-07-30T04:06:06+02:00 Generalized neural closure models with interpretability Abhinav Gupta Pierre F. J. Lermusiaux 2023-06-01T00:00:00Z https://doi.org/10.1038/s41598-023-35319-w https://doaj.org/article/e77d383fd9674677801f008bc391011c EN eng Nature Portfolio https://doi.org/10.1038/s41598-023-35319-w https://doaj.org/toc/2045-2322 doi:10.1038/s41598-023-35319-w 2045-2322 https://doaj.org/article/e77d383fd9674677801f008bc391011c Scientific Reports, Vol 13, Iss 1, Pp 1-21 (2023) Medicine R Science Q article 2023 ftdoajarticles https://doi.org/10.1038/s41598-023-35319-w 2023-07-09T00:37:49Z Abstract Improving the predictive capability and computational cost of dynamical models is often at the heart of augmenting computational physics with machine learning (ML). However, most learning results are limited in interpretability and generalization over different computational grid resolutions, initial and boundary conditions, domain geometries, and physical or problem-specific parameters. In the present study, we simultaneously address all these challenges by developing the novel and versatile methodology of unified neural partial delay differential equations. We augment existing/low-fidelity dynamical models directly in their partial differential equation (PDE) forms with both Markovian and non-Markovian neural network (NN) closure parameterizations. The melding of the existing models with NNs in the continuous spatiotemporal space followed by numerical discretization automatically allows for the desired generalizability. The Markovian term is designed to enable extraction of its analytical form and thus provides interpretability. The non-Markovian terms allow accounting for inherently missing time delays needed to represent the real world. Our flexible modeling framework provides full autonomy for the design of the unknown closure terms such as using any linear-, shallow-, or deep-NN architectures, selecting the span of the input function libraries, and using either or both Markovian and non-Markovian closure terms, all in accord with prior knowledge. We obtain adjoint PDEs in the continuous form, thus enabling direct implementation across differentiable and non-differentiable computational physics codes, different ML frameworks, and treatment of nonuniformly-spaced spatiotemporal training data. We demonstrate the new generalized neural closure models (gnCMs) framework using four sets of experiments based on advecting nonlinear waves, shocks, and ocean acidification models. Our learned gnCMs discover missing physics, find leading numerical error terms, discriminate among candidate functional forms in ... Article in Journal/Newspaper Ocean acidification Directory of Open Access Journals: DOAJ Articles Scientific Reports 13 1 |
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Medicine R Science Q Abhinav Gupta Pierre F. J. Lermusiaux Generalized neural closure models with interpretability |
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Medicine R Science Q |
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Abstract Improving the predictive capability and computational cost of dynamical models is often at the heart of augmenting computational physics with machine learning (ML). However, most learning results are limited in interpretability and generalization over different computational grid resolutions, initial and boundary conditions, domain geometries, and physical or problem-specific parameters. In the present study, we simultaneously address all these challenges by developing the novel and versatile methodology of unified neural partial delay differential equations. We augment existing/low-fidelity dynamical models directly in their partial differential equation (PDE) forms with both Markovian and non-Markovian neural network (NN) closure parameterizations. The melding of the existing models with NNs in the continuous spatiotemporal space followed by numerical discretization automatically allows for the desired generalizability. The Markovian term is designed to enable extraction of its analytical form and thus provides interpretability. The non-Markovian terms allow accounting for inherently missing time delays needed to represent the real world. Our flexible modeling framework provides full autonomy for the design of the unknown closure terms such as using any linear-, shallow-, or deep-NN architectures, selecting the span of the input function libraries, and using either or both Markovian and non-Markovian closure terms, all in accord with prior knowledge. We obtain adjoint PDEs in the continuous form, thus enabling direct implementation across differentiable and non-differentiable computational physics codes, different ML frameworks, and treatment of nonuniformly-spaced spatiotemporal training data. We demonstrate the new generalized neural closure models (gnCMs) framework using four sets of experiments based on advecting nonlinear waves, shocks, and ocean acidification models. Our learned gnCMs discover missing physics, find leading numerical error terms, discriminate among candidate functional forms in ... |
format |
Article in Journal/Newspaper |
author |
Abhinav Gupta Pierre F. J. Lermusiaux |
author_facet |
Abhinav Gupta Pierre F. J. Lermusiaux |
author_sort |
Abhinav Gupta |
title |
Generalized neural closure models with interpretability |
title_short |
Generalized neural closure models with interpretability |
title_full |
Generalized neural closure models with interpretability |
title_fullStr |
Generalized neural closure models with interpretability |
title_full_unstemmed |
Generalized neural closure models with interpretability |
title_sort |
generalized neural closure models with interpretability |
publisher |
Nature Portfolio |
publishDate |
2023 |
url |
https://doi.org/10.1038/s41598-023-35319-w https://doaj.org/article/e77d383fd9674677801f008bc391011c |
genre |
Ocean acidification |
genre_facet |
Ocean acidification |
op_source |
Scientific Reports, Vol 13, Iss 1, Pp 1-21 (2023) |
op_relation |
https://doi.org/10.1038/s41598-023-35319-w https://doaj.org/toc/2045-2322 doi:10.1038/s41598-023-35319-w 2045-2322 https://doaj.org/article/e77d383fd9674677801f008bc391011c |
op_doi |
https://doi.org/10.1038/s41598-023-35319-w |
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