Summary of An Efficient Wavelet-based Physics-informed Neural Networks For Singularly Perturbed Problems, by Himanshu Pandey et al.
An efficient wavelet-based physics-informed neural networks for singularly perturbed problems
by Himanshu Pandey, Anshima Singh, Ratikanta Behera
First submitted to arxiv on: 18 Sep 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 Physics-informed neural networks (PINNs) are a type of deep learning model that incorporates physics in the form of differential equations to tackle complex problems. However, solving differential equations with rapid oscillations, steep gradients, or singular behavior can be challenging for PINNs. To address this, researchers designed an efficient wavelet-based PINNs (W-PINNs) model, which represents the solution in wavelet space using smooth-compactly supported wavelets. This framework reduces the number of degrees of freedom while retaining complex physical dynamics. The proposed model does not require automatic differentiations or prior knowledge about solution behavior. W-PINNs excel at capturing localized nonlinear information, making them suitable for problems with abrupt features. The model is demonstrated in various 1D and 2D test problems, including the FitzHugh-Nagumo (FHN) model, the Helmholtz equation, the Maxwell’s equation, lid-driven cavity flow, and the Allen-Cahn equation. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper talks about a new way to use computers to solve complex math problems. It’s called Physics-informed neural networks (PINNs). PINNs are good at solving some kinds of math problems, but they can struggle with others. To make them better, the researchers created a new version called Wavelet-based PINNs (W-PINNs). W-PINNs work by breaking down the math problem into smaller pieces and looking at each piece in a special way. This makes it easier to solve the problem and get an accurate answer. The new method is tested on several different kinds of math problems, and it works better than older methods. |
Keywords
» Artificial intelligence » Deep learning
