  We consider quantitative analyses of spectral data using laser-induced
breakdown spectroscopy. We address the small size of training data available,
and the validation of the predictions during inference on unknown data. For the
purpose, we build robust calibration models using deep convolutional multitask
learning architectures to predict the concentration of the analyte, alongside
additional spectral information as auxiliary outputs. These secondary
predictions can be used to validate the trustworthiness of the model by taking
advantage of the mutual dependencies of the parameters of the multitask neural
networks. Due to the experimental lack of training samples, we introduce a
simulation-based data augmentation process to synthesise an arbitrary number of
spectra, statistically representative of the experimental data. Given the
nature of the deep learning model, no dimensionality reduction or data
selection processes are required. The procedure is an end-to-end pipeline
including the process of synthetic data augmentation, the construction of a
suitable robust, homoscedastic, deep learning model, and the validation of its
predictions. In the article, we compare the performance of the multitask model
with traditional univariate and multivariate analyses, to highlight the
separate contributions of each element introduced in the process.
