Probabilistic Super-Resolution for High-Fidelity Physical System Simulations with Uncertainty Quantification

A long standing challenge in the engineering sciences is accurately modelling physical systems, most notably when these are described by partial differential equations (PDEs). Highresolution simulations are critical in fields such as automotive and structural engineering [1, 2], where precise modelling of subtle physical behaviours is essential to inform engineering decisions. However, repeated evaluations of high-fidelity simulations using traditional numerical solvers, such as the Finite Element Method (FEM), has high computational costs and significant time requirements. This limitation poses challenges in applications like optimal design, where iterative simulations across varied parameter sets are necessary to achieve optimal configurations, making the process both slow and resource-intensive [3]. With the growing reliance on simulation-based predictions, ensuring computational efficiency alongside accuracy in high-fidelity simulations is paramount. To address some of these challenges, researchers have proposed using super-resolution (SR) techniques, from the field of computer vision [4, 5], to learn a mapping from low-resolution (LR) images to high-resolution (HR) images.