Résumé
Digital Twins are receiving significant attention. However, despite individual success stories, broad industrial adoption remains limited. We observe barriers similar to those that slowed Computer Aided Engineering adoption over past decades, including the complexity of setting up simulations with appropriate meshing and discretization parameter selection, as well as difficulties in assessing accuracy and uncertainties. Achieving widespread adoption requires novel perspectives that combine AI and Machine Learning with classical algorithm innovation in Digital Modeling.
In this talk, we present opportunities at the intersection of Artificial Intelligence, Machine Learning, and classical numerical methods, demonstrated through real-world examples. We unify our discussion around mesh-free methods, covering Cartesian PDE solvers with immersed boundary methods as well as reduced-order modeling based on proper orthogonal decomposition and autoregressive operator inference. Importantly, we highlight specific opportunities for novel mathematical research, aiming to inspire future algorithmic advances.
We conclude by exploring Artificial Intelligence—particularly large language models—and the emerging impact on Digital Twins, offering an outlook on future opportunities in this space.
