Probabilistic Super-Resolution for High-Fidelity Physical System Simulations with Uncertainty Quantification
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912232190771200 |
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| author | Zhang, Pengyu Duffin, Connor Glyn-Davies, Alex Vadeboncoeur, Arnaud Girolami, Mark |
| author_facet | Zhang, Pengyu Duffin, Connor Glyn-Davies, Alex Vadeboncoeur, Arnaud Girolami, Mark |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10280 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probabilistic Super-Resolution for High-Fidelity Physical System Simulations with Uncertainty Quantification Zhang, Pengyu Duffin, Connor Glyn-Davies, Alex Vadeboncoeur, Arnaud Girolami, Mark Machine Learning 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. |
| title | Probabilistic Super-Resolution for High-Fidelity Physical System Simulations with Uncertainty Quantification |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.10280 |