Summary of Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularization, by Xiaoyu Xie et al.
Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularization
by Xiaoyu Xie, Saviz Mowlavi, Mouhacine Benosman
First submitted to arxiv on: 23 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Engineering, Finance, and Science (cs.CE); Mathematical Physics (math-ph); Numerical Analysis (math.NA)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper introduces a novel approach for spatiotemporal modeling, addressing the limitations of current data-driven reduced-order models (ROMs) that neglect temporal correlations. The proposed framework, combining an implicit neural representation-based autoencoder and a neural ODE latent dynamics model, incorporates jerk regularization to promote smoothness and sparsity in the compressed latent space. This yields improved accuracy, convergence speed, and extrapolation ability over time. The effectiveness of this approach is demonstrated through simulations of a two-dimensional unsteady flow problem governed by the Navier-Stokes equations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Spatiotemporal modeling is important for many areas of science and engineering. However, it can be hard to make accurate predictions when we don’t have complete information about the system. One way to solve this problem is to use reduced-order models (ROMs), which are like simplified versions of the real thing. But these ROMs often don’t take into account how things change over time, which makes them less accurate. To fix this issue, researchers developed a new framework that adds an extra layer of complexity to the ROMs. This helps make more accurate predictions and speeds up the process. |
Keywords
* Artificial intelligence * Autoencoder * Latent space * Regularization * Spatiotemporal
