Nonlinear reduction strategies for data compression: a comprehensive comparison from diffusion to advection problems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917274974158848 |
|---|---|
| author | Gonnella, Isabella Carla Pichi, Federico Rozza, Gianluigi |
| author_facet | Gonnella, Isabella Carla Pichi, Federico Rozza, Gianluigi |
| contents | This work presents an overview of several nonlinear reduction strategies for data compression from various research fields, and a comparison of their performance when applied to problems characterized by diffusion and/or advection terms. We aim to create a common framework by unifying the notation referring to a common two-stage pipeline. At the same time, we underline their main differences and objectives by highlighting the diverse choices made for each stage. We test the considered approaches on three test cases belonging to the family of Advection-Diffusion problems, also focusing on the pure Advection and pure Diffusion benchmarks, studying their reducibility while varying the latent dimension. Finally, we interpret the numerical results under the lens of the discussed theoretical considerations, offering a comprehensive landscape for nonlinear reduction methods for general Advection-Diffusion dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear reduction strategies for data compression: a comprehensive comparison from diffusion to advection problems Gonnella, Isabella Carla Pichi, Federico Rozza, Gianluigi Numerical Analysis This work presents an overview of several nonlinear reduction strategies for data compression from various research fields, and a comparison of their performance when applied to problems characterized by diffusion and/or advection terms. We aim to create a common framework by unifying the notation referring to a common two-stage pipeline. At the same time, we underline their main differences and objectives by highlighting the diverse choices made for each stage. We test the considered approaches on three test cases belonging to the family of Advection-Diffusion problems, also focusing on the pure Advection and pure Diffusion benchmarks, studying their reducibility while varying the latent dimension. Finally, we interpret the numerical results under the lens of the discussed theoretical considerations, offering a comprehensive landscape for nonlinear reduction methods for general Advection-Diffusion dynamics. |
| title | Nonlinear reduction strategies for data compression: a comprehensive comparison from diffusion to advection problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.12816 |