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.
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
Keywords
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…
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.