Physics-based Finite Element Methods models can be used to investigate the electrical conditions in submerged arc furnaces (SAFs). However, their explicit solution may be very demanding in terms of time and computational resources. This makes these models difficult to employ during control operations and in fast prototyping. To obviate these inconveniences, we developed metamodels that are grounded on the physics-based model. In this context, a metamodel is a surrogate of an original model obtained using statistical analysis tools to determine approximate input–output relationships in a database of simulations from the original model. The metamodels for the SAF electrical conditions are shown to retain the same generalization capabilities as the original model while being computationally lightweight.