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Including prior knowledge is important for effective machine learning models in physics, and is usually achieved by explicitly adding loss terms or constraints on model architectures. Prior knowledge embedded in the physics computation itself rarely draws attention. We show that solving the Kohn-Sham equations when training neural networks for the exchange-correlation functional provides an implicit regularization that greatly improves generalization. Two separations suffice for learning the entire one-dimensional H2 dissociation curve within chemical accuracy, including the strongly correlated region. Our models also generalize to unseen types of molecules and overcome self-interaction error.
While additive manufacturing (AM) has facilitated the production of complex structures, it has also highlighted the immense challenge inherent in identifying the optimum AM structure for a given application. Numerical methods are important tools for optimization, but experiment remains the gold standard for studying nonlinear, but critical, mechanical properties such as toughness. To address the vastness of AM design space and the need for experiment, we develop a Bayesian experimental autonomous researcher (BEAR) that combines Bayesian optimization and high-throughput automated experimentation. In addition to rapidly performing experiments, the BEAR leverages iterative experimentation by selecting experiments based on all available results. Using the BEAR, we explore the toughness of a parametric family of structures and observe an almost 60-fold reduction in the number of experiments needed to identify high-performing structures relative to a grid-based search. These results show the value of machine learning in experimental fields where data are sparse.