A Study on Convolution Neural Network for Reconstructing the Temperature Field of Wall-Bounded Flows

Abstract

In the present study, the capabilities of a new Convolutional Neural Network (CNN) model are explored with the paramount objective of reconstructing the temperature field of wall-bounded flows based on a limited set of measurement points taken at the boundaries of the fluid domain. For that, we employ an algorithm that leverages the CNN capabilities provided with additional information about the governing equations of the physical problem. Great progress has been made in recent years towards reconstructing and characterizing the spatial distribution of physical variables of interest using CNNs. In principle, CNNs can represent any continuous mathematical function with a relatively reduced number of parameters. However, depending on the complexity imposed by the physical problem, this technique becomes unfeasible. The present study employs a Physics Informed Neuron Network technique featuring a data-efficient function approximator. As a proof of concept, the CNN is trained to retrieve the temperature of a heated channel based on a limited number of sensors placed at the boundaries of the domain. In this context, the training data are the temperature fields solutions considering various flows conditions at steady state, e.g varying the Reynolds and the Prandtl numbers. Additionally, a demonstration case considering the more complex geometry of a MSR is also provided. Assessment on the performance of the CNN is done by the mean L2 and the maximum Linf Euclidean norms stemmed from the difference between the actual solutions and the predictions made by the CNN. Finally, a sensitivity analysis is carried out such that the robustness of the CNN is tested considering a potential real application scenario where noise is inevitable. For that, the original test inputs are overlaid with a normal distribution of random numbers targeting to mimic different levels of noise in the measurement points.