Summary of Physics Informed Cell Representations For Variational Formulation Of Multiscale Problems, by Yuxiang Gao et al.
Physics informed cell representations for variational formulation of multiscale problems
by Yuxiang Gao, Soheil Kolouri, Ravindra Duddu
First submitted to arxiv on: 27 May 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 This paper proposes a novel approach to Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) with multiscale features. The limitation of traditional PINNs in converging slowly and accurately is addressed by introducing physics-informed cell representations, using multilevel multiresolution grids coupled with multilayer perceptrons (MLPs). A gradient-descent based optimization determines the grid parameters and MLP parameters. A variational loss function accelerates computation, allowing linear interpolation of feature vectors within grid cells. The proposed model uses a decoupled training scheme for Dirichlet boundary conditions and a parameter-sharing scheme for periodic boundary conditions, achieving superior accuracy compared to traditional PINNs. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about a new way to use artificial intelligence (AI) to solve complex math problems called partial differential equations (PDEs). These PDEs are used in many fields like physics and engineering. The current method of using AI for this, called Physics-Informed Neural Networks (PINNs), has some limitations. To overcome these limits, the authors propose a new approach that divides the problem into smaller parts and uses multiple levels of detail to solve it. This new method is tested on several examples and shows improved accuracy and speed compared to traditional PINNs. |
Keywords
» Artificial intelligence » Gradient descent » Loss function » Optimization
