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

TL;DR

This paper introduces a probabilistic super-resolution framework for physical system simulations that provides high-fidelity results with uncertainty quantification, reducing data requirements and computational costs.

Contribution

It combines the Statistical Finite Element Method with energy-based generative modeling to enable efficient, uncertainty-aware super-resolution without large labeled datasets.

Findings

Achieves faster predictions compared to traditional solvers.

Provides reliable uncertainty estimates in super-resolution outputs.

Validated on 2D Poisson problem with positive results.

Abstract

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.