The thesis focuses on deep learning methods applied to discovery of gravitational lensing events in the universe. Publicly available I-band images of the known gravitational lenses were combined with simulated ones and randomly sampled cutouts of the galaxies and stars. Deep convolutional networks outperform the conventional discovery methods and achieve up to 0.9984 mean ROC AUC and 0.9895 mean F1-score on the out-of-sample 7-fold cross-validation. The models demonstrated excellent agreement with the latest list of 92 candidates published in the literature and created with combination of deep learning and manual analysis by professional astronomers.

A biological cell is the elementary unit of life. Despite being actively studied for the last three centuries, many details of how cells are organized remain mysterious. One of the reasons in conventionally accepted optical microscopy that imposes high costs on experimental studies, limits scalability, and slows down the progress. In order to address this, numerous label-free imaging techniques were proposed by the biomedical engineering community. Among them is electrical impedance tomography (EIT), a low-cost and label-free imaging method based on electrical stimulations. Mathematically, EIT is ill-posed which severely limits its applications. Moreover, it was initially developed for human thorax imaging and its micro-scale version is yet to be established. In this dissertation, we shrink EIT for single-cell applications and demonstrate how to image a cell and its interior organelles using only a few microelectrodes.

We start by studying electrical properties of cells and build a scalable model of cellular electrical response. The proposed method mimics biodiversity among four common cell types and accurately represents complex three-dimensional geometries. By combining it with modern shape optimization methods and a customized microelectrode array we extend EIT to single-cell imaging. Along the way, we provide solutions to several well-known EIT problems such as low contrast images and numerical instability. To further expand cellular EIT to nucleus imaging we take a data-driven approach. We explore a variety of machine learning methods previously applied to inverse imaging problems and discuss their pros and cons. We then propose a novel deep learning model specifically adjusted for EIT. Finally, we evaluate and experimentally demonstrate live cell nucleus imaging, driven by pure electrical excitations and the proposed deep neural network.