<p>Process engineering of materials determines not only materials properties, but also cost, yield and production capacity. Although process design is generally based on the experience of process engineers, mathematical/data-science modeling is a key challenge for future process optimization. Here we create new opportunities for process optimization in YBa₂Cu₃O₇ film fabrication through data/model-driven process design. We show integrated modelling of substrate temperature and critical current density in YBa₂Cu₃O₇ films. Gaussian process regression augmented by transfer learning and physics knowledge was constructed from a small amount of data to show substrate temperature dependence of critical current density. Non-numerical factors such as chamber design and substrate material were included in the transfer learning, and physics-aided techniques extended the model to different magnetic fields. Magnetic field dependence of critical current density was successfully predicted for a given substrate temperature for a five-sample series deposited using different pulsed laser deposition systems. Our integrated process and property modelling strategy enables data/model-driven process design for YBa₂Cu₃O₇ film fabrication for coated conductor applications.</p>