Uncertainty quantification in neural networks: Application to the automated measure of particle size of TiO2

The growing use of technological solutions based on deep learning algorithms has exploded in recent years, due to their performance on tasks such as object detection, image and video segmentation and classification, in many fields such as medicine, finance, autonomous driving... In this context, deep learning research is increasingly focusing on improving the performance and understanding of the algorithms used, by attempting to quantify the uncertainty associated with their predictions. Providing this uncertainty is key to the mass dissemination of these new tools in industry, and to overcoming the current obstacles to their use, particularly in critical systems. Indeed, providing information on uncertainty may be of regulatory importance in certain sectors of activity.

This manuscript presents the work on uncertainty quantification in neural networks. To begin with, we provide an in-depth overview, explaining the key concepts involved in a metrological framework. Next, the focus is chosen to be on the propagation of input uncertainty through an already-trained neural network, in response to a pressing industrial need. The proposed input uncertainty propagation method, named WGMprop, models the network outputs as mixtures of Gaussians, whose uncertainty propagation is ensured by a Split&Merge algorithm equipped with a divergence measure chosen as the Wasserstein distance. Then the focus is on quantifying the uncertainty inherent in the network parameters. In this context, a comparative study of state-of-the-art methods was carried out. In particular, this study led to propose a method for local characterization of deep ensembles, which is currently the standard. The developed methodology, named WEUQ, enables an exploration of the basins of attraction of the neural network parameter landscape, taking into account the diversity of predictors. Finally, the case study is presented, involving the automated measurement of the size distribution of titanium dioxide (TiO₂) nanoparticles from images acquired by scanning electron microscopy (SEM). The development of the technology used is described, and the methodological choices for quantifying the uncertainties arising from this research.

Uncertainty, Deep learning, Neural network, Segmentation, Nanoparticles, Applied mathematics