A Convolutional Neural Network-based Approach to Field Reconstruction
- URL: http://arxiv.org/abs/2108.13517v1
- Date: Fri, 27 Aug 2021 00:16:44 GMT
- Title: A Convolutional Neural Network-based Approach to Field Reconstruction
- Authors: Roberto Ponciroli and Andrea Rovinelli and Lander Ibarra
- Abstract summary: In many applications, the spatial distribution of a field needs to be carefully monitored to detect spikes, discontinuities or dangerous heterogeneities.
In this work, a physics-informed, data-driven algorithm that allows addressing these requirements is presented.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: This work has been submitted to the IEEE for possible publication. Copyright
may be transferred without notice, after which this version may no longer be
accessible.
In many applications, the spatial distribution of a field needs to be
carefully monitored to detect spikes, discontinuities or dangerous
heterogeneities, but invasive monitoring approaches cannot be used. Besides,
technical specifications about the process might not be available by preventing
the adoption of an accurate model of the system. In this work, a
physics-informed, data-driven algorithm that allows addressing these
requirements is presented. The approach is based on the implementation of a
boundary element method (BEM)-scheme within a convolutional neural network.
Thanks to the capability of representing any continuous mathematical function
with a reduced number of parameters, the network allows predicting the field
value in any point of the domain, given the boundary conditions and few
measurements within the domain. The proposed approach was applied to
reconstruct a field described by the Helmholtz equation over a
three-dimensional domain. A sensitivity analysis was also performed by
investigating different physical conditions and different network
configurations. Since the only assumption is the applicability of BEM, the
current approach can be applied to the monitoring of a wide range of processes,
from the localization of the source of pollutant within a water reservoir to
the monitoring of the neutron flux in a nuclear reactor.
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