Summary of Spectral Informed Neural Network: An Efficient and Low-memory Pinn, by Tianchi Yu et al.
Spectral Informed Neural Network: An Efficient and Low-Memory PINN
by Tianchi Yu, Yiming Qi, Ivan Oseledets, Shiyi Chen
First submitted to arxiv on: 29 Aug 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Numerical Analysis (math.NA); Computational Physics (physics.comp-ph)
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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 A novel neural network architecture is introduced that efficiently solves partial differential equations (PDEs) while reducing computational requirements compared to traditional physics-informed neural networks (PINNs). The key innovation is replacing automatic differentiation with a spectral-based multiplication, allowing for lower memory usage and shorter training times. This approach also achieves higher accuracy thanks to the exponential convergence of the spectral basis. Two strategies are proposed to handle the different domains of physics and spectra during network training. The method’s effectiveness is demonstrated through comprehensive experiments. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A new way to solve partial differential equations using a special kind of neural network is presented. This approach, called a spectral-based neural network, is more efficient than previous methods because it doesn’t need to use automatic differentiation. Instead, it uses multiplication to solve the problem. This makes it faster and uses less memory. The method is also very accurate because it uses a special basis that gets closer to the correct answer as you go. To make sure this approach works well in different situations, two ways of training the network are proposed. The results show that this new approach is better than previous methods. |
Keywords
» Artificial intelligence » Neural network
