Distance Based Similarity Metrics for Artificial Neural Network Estimates of Soot Distribution in Catalytic

Although artificial neural networks have attracted the attention of researchers as potential fast and lightweight substitutes for expensive computational models, their application to real world problems may be hindered by improper choice of training and validation metrics. In this work, we examine the applicability of so called distance based metrics to the problem of soot deposition in porous media and compare their performance with standard pixel-wise metrics such as the root mean square error. Specifically, we showcase the implementation and behavior of the Sliced Wasserstein Distance and the Sinkhorn Distance on a set of benchmarks, and we demonstrate their use with a previously developed artificial neural network for the estimation of soot deposits. Our results suggest that both the Sliced Wasserstein and Sinkhorn distances outperform the root mean squared error; however, their computational complexity may render their use in conjunction with artificial neural networks impractical.