Summary of Automatic Differentiation Is Essential in Training Neural Networks For Solving Differential Equations, by Chuqi Chen et al.
Automatic Differentiation is Essential in Training Neural Networks for Solving Differential Equations
by Chuqi Chen, Yahong Yang, Yang Xiang, Wenrui Hao
First submitted to arxiv on: 23 May 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Numerical Analysis (math.NA)
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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 Medium Difficulty summary: Neural network-based approaches have shown promise in solving partial differential equations (PDEs) in science and engineering, particularly when dealing with complex domains or empirical data. This paper quantitatively demonstrates the advantage of automatic differentiation (AD) in training neural networks. AD requires only sample points, unlike traditional finite difference (FD) approximations that require nearby local points to compute derivatives. The concept of truncated entropy is introduced to characterize the training property. Experimental and theoretical analyses on random feature models and two-layer neural networks show that truncated entropy serves as a reliable metric for quantifying residual loss in random feature models and training speed in both AD and FD methods. Results demonstrate that, from a training perspective, AD outperforms FD in solving PDEs. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Low Difficulty summary: This paper looks at how well artificial intelligence (AI) can solve complex math problems called partial differential equations (PDEs). The AI method is good because it doesn’t need as much information as other methods do. Scientists found that this way of doing things makes it easier to train the AI, and they were able to create a new way to measure how well the AI does its job. They tested their idea on some math problems and showed that this AI approach works better than another common method. |
Keywords
» Artificial intelligence » Neural network
