The main objective of this project is to explore and expand different non-intrusive reduced order modelling methods (ROM). Ultimately, we aim to allow the industry to produce new or better products. The work is focused on applications relevant for industrial material processes. In this area of work, current limitations of the state of the art of non-intrusive ROM methods will be identified and explored. The goal is to improve these methods in terms of computational efficiency and accuracy. Critical bottlenecks shall be identified to better understand the trade-off between runtime and accuracy. New approaches will be proposed, that may be used to improve real-time modelling capabilities. We have examined some of the mathematical foundations for accuracy in reduced models, and have found interesting results that are especially relevant for applications towards casting.