Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data

Massimiliano Lupo Pasini; Simona Perotto

doi:10.1007/s10915-022-02073-6

Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data

Massimiliano Lupo Pasini, Simona Perotto

Computational Coupled Physics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm. In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach.

Original language	English
Article number	36
Journal	Journal of Scientific Computing
Volume	94
Issue number	2
DOIs	https://doi.org/10.1007/s10915-022-02073-6
State	Published - Jan 2023

Funding

Massimiliano Lupo Pasini thanks Dr. Vladimir Protopopescu for his valuable feedback in the preparation of this manuscript. This work was supported in part by the Office of Science of the Department of Energy and by the Laboratory Directed Research and Development (LDRD) Program of Oak Ridge National Laboratory. This research is sponsored by the Artificial Intelligence Initiative as part of the Laboratory Directed Research and Development (LDRD) Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the US Department of Energy under contract DE-AC05-00OR22725. Simona Perotto acknowledges the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Actions, grant agreement 872442 (ARIA, Accurate Roms for Industrial Applications), and the PRIN research grant n.20204LN5N5 (Advanced Polyhedral Discretisations of Heterogeneous PDEs for Multiphysics Problems). This manuscript has been authored in part by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ).

Funders	Funder number
Artificial Intelligence Initiative as part of the Laboratory Directed Research and Development
Office of Science of the Department of Energy
U.S. Department of Energy	DE-AC05-00OR22725
Oak Ridge National Laboratory
Laboratory Directed Research and Development
Horizon 2020 Framework Programme
H2020 Marie Skłodowska-Curie Actions	20204LN5N5, 872442

Keywords

Machine learning
Numerical analysis
Numerical linear algebra
Partial differential equations
Reduced order models

Access to Document

10.1007/s10915-022-02073-6

Cite this

@article{adec60bc77804612a9ca7d3dbfc77cd2,

title = "Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data",

abstract = "We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm. In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach.",

keywords = "Machine learning, Numerical analysis, Numerical linear algebra, Partial differential equations, Reduced order models",

author = "{Lupo Pasini}, Massimiliano and Simona Perotto",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s).",

year = "2023",

month = jan,

doi = "10.1007/s10915-022-02073-6",

language = "English",

volume = "94",

journal = "Journal of Scientific Computing",

issn = "0885-7474",

publisher = "Springer",

number = "2",

}

TY - JOUR

T1 - Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data

AU - Lupo Pasini, Massimiliano

AU - Perotto, Simona

PY - 2023/1

Y1 - 2023/1

N2 - We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm. In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach.

AB - We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm. In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach.

KW - Machine learning

KW - Numerical analysis

KW - Numerical linear algebra

KW - Partial differential equations

KW - Reduced order models

UR - http://www.scopus.com/inward/record.url?scp=85145677494&partnerID=8YFLogxK

U2 - 10.1007/s10915-022-02073-6

DO - 10.1007/s10915-022-02073-6

M3 - Article

AN - SCOPUS:85145677494

SN - 0885-7474

VL - 94

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 2

M1 - 36

ER -

Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this