Detailed multi-physics simulations have been crucial in elucidating AM process-structure-property relationships and guiding process improvements. However, traditional simulations are limited by their computational expense, and plagued by uncertainties in parameters, properties, and model form. Data-driven methods such as machine learning, on the other hand, can have predictive power but require more data than is typically available from direct measurements, and cannot be reliably extrapolated to new materials or process conditions. In this talk, I will summarize recent work in our research groups to combine the strengths of multi-physics simulation with data-driven methods. Novel approaches include physics-informed machine learning, calibration and optimization methods, data-driven dimensional analysis, and model order reduction. Using these techniques, we are improving the speed and accuracy of process predictions at scales from the melt pool to the full part.