Despite advances in computational hardware and algorithms in the last 30 years, multiphysics computational methods are still not computationally efficient enough for real-time prediction for online controls, digital twins, or a large number of forward functional evaluations in iterative designs, sensitivity analysis, and uncertainty quantification loops. Among the most challenging industrial processes is steel solidification thermo-mechanical phenomena in continuous casting, responsible for over 90% of the world’s steel production. Two innovative deep learning operator methods are trained with coupled thermo-mechanical data from an advanced steel solidification finite element model and studied for encoding multiple input sequential data to predict complete thermal and mechanical solution fields from a real-world steelmaking process. While both trained sequential operator methods can predict solutions accurately and several orders of magnitude more efficiently than the classical finite element method, the single-branch sequential operator network predicted more accurate results than the multiple-branch operator that encodes thermal and mechanical inputs separately.