This invited session (IS) provides a forum to discuss the synergies between machine learning (ML) and reduced order models (ROM) with IGA in general, as well as IGA based enabling technologies for predictive Digital Twins (DT). Any contributions to the subject termed Scientific Machine Learning (SciML) which aim to exploit the complementary perspectives of computational science and computer science to develop accurate, robust, and efficient methods for addressing challenging problems in science and engineering are in particular welcomed. We adopt here the following definition of a Digital Twin: A digital twin is defined as a virtual representation of a physical asset, or a process enabled through data and simulators for real-time prediction, optimization, monitoring, control, and decision-making. Enabling methods and techniques for digital twins include, but are not restricted to, advanced numerical methods for multi-physics systems, error control, reduced order modelling, data assimilation, scientific machine learning, and uncertainty quantification. This IS focuses on IGA technologies both for virtual (or descriptive) and predictive digital twins. Regarding virtual twins, the advantage of IGA for bridging the gap between geometric modelling and analysis is highly relevant, as it aims to drastically reduce human intervention in the simulation of the (multi-)physics behaviour for a geometric model. Instead, to enable predictive twins, one may utilize Hybrid Analysis and Modelling (HAM) that combines classical Physics Based Methods (PBM) accelerated by means of Reduced Order Modelling (ROM) together with Data Driven Methods (DDM) based on sensor measurements analysed by use of Machine Learning (ML).