Probabilistic Super-Resolution for High-Fidelity Physical System Simulations with Uncertainty Quantification
This work addresses the challenge of reliable uncertainty quantification in super-resolution for physical system simulations, which is crucial for real-world engineering applications.
The authors tackled the problem of super-resolution for physical system simulations with uncertainty quantification, achieving high-fidelity predictions with a computational speed-up. Their method eliminated the need for extensive labeled datasets and provided reliable uncertainty estimates.
Super-resolution (SR) is a promising tool for generating high-fidelity simulations of physical systems from low-resolution data, enabling fast and accurate predictions in engineering applications. However, existing deep-learning based SR methods, require large labeled datasets and lack reliable uncertainty quantification (UQ), limiting their applicability in real-world scenarios. To overcome these challenges, we propose a probabilistic SR framework that leverages the Statistical Finite Element Method and energy-based generative modeling. Our method enables efficient high-resolution predictions with inherent UQ, while eliminating the need for extensive labeled datasets. The method is validated on a 2D Poisson example and compared with bicubic interpolation upscaling. Results demonstrate a computational speed-up over high-resolution numerical solvers while providing reliable uncertainty estimates.