Summary of Hierarchic Flows to Estimate and Sample High-dimensional Probabilities, by Etienne Lempereur et al.
Hierarchic Flows to Estimate and Sample High-dimensional Probabilities
by Etienne Lempereur, Stéphane Mallat
First submitted to arxiv on: 6 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Fluid Dynamics (physics.flu-dyn)
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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 The abstract presents a novel approach to modeling complex physical fields, such as turbulence, by leveraging hierarchical probability flows from coarse to fine scales. This “inverse renormalization group” is defined by conditional probabilities across scales, using a wavelet basis to avoid the curse of dimensionality. The authors introduce low-dimensional models with robust multiscale approximations of high-order polynomial energies, calculated through a second wavelet transform that defines interactions over two hierarchies of scales. These “wavelet scattering models” are used to generate 2D vorticity fields of turbulence and images of dark matter densities. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Scientists have been trying to understand complex physical phenomena like turbulence for decades. To make this easier, they’re looking at a new way to model these things using probability flows from large scales down to small ones. This helps avoid some big problems that come with dealing with really high-dimensional data. The researchers introduce a new type of model that can handle this kind of complexity and use it to generate pictures of turbulence and dark matter. |
Keywords
» Artificial intelligence » Probability
