Machine learning, in particular neural networks-based approaches have shown great success in recent years due to its function approximation ability and feature representation learning through its network architecture. However, additional considerations need to be made when dealing with scientific data since they tend to be noisier and uncertain. The goal of this project to develop robust deep learning approaches that are interpretable, parsimonious and able to quantify uncertainty in their predictions. Applications include spatio-temporal image processing, chemical synthesis, materials design and strong gravitational lensing.