In the field of numerical simulations, accuracy is of course one of the main considered aspects. In the last decades, however, the increasing computational capacity has allowed to control the accuracy of ever more complex models, by providing a larger computational power. However, in several contexts, a balanced trade-off between the required computational cost and the achieved accuracy is usually prefered, as for example during the optimization of industrial processes or artefacts. Such demand has induced the development of recent techniques to accelerate the computing time for numerical simulations. Reduced order models (ROMs) and scientific machine learning (ML) are two examples of methodologies that have gained a lot of popularity thanks to their capability to reduce the computing time for numerical simulations. In this session, we aim to collect several applications where the usage of such techniques led to enable new industrial workflows, to accelerate and/or to improve the existing ones, and more in general to reduce the computational cost for numerical simulations. We encourage contributions regarding applications that involve recent methods — that include, but are not limited to, ROMs and ML — to tackle computational bottlenecks in industrial simulations. Contributions from industry, spinoffs and startups are encouraged, but not limited to.