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Article
Publication date: 22 January 2021

Rainald Löhner, Harbir Antil, Hamid Tamaddon-Jahromi, Neeraj Kavan Chakshu and Perumal Nithiarasu

The purpose of this study is to compare interpolation algorithms and deep neural networks for inverse transfer problems with linear and nonlinear behaviour.

303

Abstract

Purpose

The purpose of this study is to compare interpolation algorithms and deep neural networks for inverse transfer problems with linear and nonlinear behaviour.

Design/methodology/approach

A series of runs were conducted for a canonical test problem. These were used as databases or “learning sets” for both interpolation algorithms and deep neural networks. A second set of runs was conducted to test the prediction accuracy of both approaches.

Findings

The results indicate that interpolation algorithms outperform deep neural networks in accuracy for linear heat conduction, while the reverse is true for nonlinear heat conduction problems. For heat convection problems, both methods offer similar levels of accuracy.

Originality/value

This is the first time such a comparison has been made.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 9
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 18 February 2020

Rainald Löhner and Harbir Antil

The purpose of this study is to determine the possibility of an accurate assessment of the spatial distribution of material properties such as conductivities or impedances from…

59

Abstract

Purpose

The purpose of this study is to determine the possibility of an accurate assessment of the spatial distribution of material properties such as conductivities or impedances from boundary measurements when the governing partial differential equation is a Laplacian.

Design/methodology/approach

A series of numerical experiments were carefully performed. The results were analyzed and compared.

Findings

The results to date show that while the optimization procedure is able to obtain spatial distributions of the conductivity k that reduce the cost function significantly, the resulting conductivity k is still significantly different from the target (or real) distribution sought. While the normal fluxes recovered are very close to the prescribed ones, the tangential fluxes can differ considerably.

Research limitations/implications

At this point, it is not clear why rigorous mathematical proofs yield results of convergence and uniqueness, while in practice, accurate distributions of the conductivity k seem to be elusive. One possible explanation is that the spatial influence of conductivities decreases exponentially with distance. Thus, many different conductivities inside a domain could give rise to very similar (infinitely close) boundary measurements.

Practical implications

This implies that the estimation of field conductivities (or generally field data) from boundary data is far more difficult than previously assumed when the governing partial differential equation in the domain is a Laplacian. This has consequences for material parameter assessments (e.g. for routine maintenance checks of structures), electrical impedance tomography, and many other applications.

Originality/value

This is the first time such a finding has been reported in this context.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 11
Type: Research Article
ISSN: 0961-5539

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