Many design problems in modern engineering and operations research can be formulated as an inverse problem: Given the target specifications, identify the initial conditions or design parameters that result in the most desired performance. This includes a vast domain of problems in energy systems design, biomedical imaging, inference and diagnostics, remote sensing, optimal control, etc. Newly discovered tools in machine learning and statistics such as Deep Learning, Bayesian and Meta-model Optimization, non-paremetric regression techniques, etc. can help improve or expedite the solutions to many such problems by learning from data and past experience. Part of the research at ECO Lab is dedicated to identifying problems in energy technologies, material design and bio-engineering that have not yet benefited from such modern computational approaches.