Summary of Parametric Encoding with Attention and Convolution Mitigate Spectral Bias Of Neural Partial Differential Equation Solvers, by Mehdi Shishehbor et al.
Parametric Encoding with Attention and Convolution Mitigate Spectral Bias of Neural Partial Differential Equation Solvers
by Mehdi Shishehbor, Shirin Hosseinmardi, Ramin Bostanabad
First submitted to arxiv on: 22 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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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 Deep neural networks (DNNs) are increasingly used to solve partial differential equations (PDEs), which naturally arise while modeling various physical phenomena. However, as PDE complexity increases, DNN accuracy decreases due to spectral bias, where they tend to learn low-frequency solution characteristics. To address this issue, we introduce Parametric Grid Convolutional Attention Networks (PGCANs) that can solve PDE systems without labeled data in the domain. PGCAN parameterizes the input space with a grid-based encoder connected to a DNN decoder via attention, prioritizing feature training and avoiding overfitting. Our encoder provides localized learning and improves information propagation from boundaries to the interior. We test PGCAN on various PDE systems, showing it effectively addresses spectral bias and provides more accurate solutions than competing methods. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Imagine trying to solve complex math problems without much help. That’s what happens when we try to use computers to solve certain kinds of math problems called partial differential equations (PDEs). These PDEs describe how things change over time or space, like how a ball bounces or water flows. Computers can do this job pretty well, but the more complex the problem is, the worse they do. This is because computers tend to focus on simple patterns and miss important details. To fix this, we created a new way of using computers called Parametric Grid Convolutional Attention Networks (PGCANs). PGCANs can solve these math problems without needing any help from human experts. We tested PGCANs on many different types of math problems and found that they work much better than other methods. |
Keywords
* Artificial intelligence * Attention * Decoder * Encoder * Overfitting
