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Research in physics is often concerned with establishing the governing equations of a dynamical system. As systems become increasingly complex and data more abundant, machine learning (ML) is becoming a standard approach for modeling physics, yet the full power of statistical learning is rarely used. Consequently, the learning algorithms offer no guarantees and the resulting discoveries need external human validation. For the same reason, results do not generalize from one problem to the next; a human expert must inspect and interpret the results, and this interpretation is the transferable knowledge. The human expert does not benefit from specialized data analytic tools to separate the artifacts introduced by the algorithm from the data features. In other words, the ML algorithms are black boxes from the point of view of the physicist. This workshop will showcase how to employ mathematical aspects of statistical / information theoretic approaches in ML for the discovery of physical laws from data. Offering statistical guarantees along with the learned models is critical in physics and in areas such as aeronautics, climate science, chemistry, biology, and robotics. We will consider model selection, robust statistics, model-free and adaptive learning, and model validation in the context of both static and dynamic models, such as equations of motion.