title: "Unraveling the design pattern of physics-informed neural networks: Series 01" authors: Shuai Guo year: 2023 URL: https://towardsdatascience.com/unraveling-the-design-pattern-of-physics-informed-neural-networks-series-01-8190df459527 –-

In this post, the author discusses the work by [[@Wu2022a]] in what concerns the adaptive (resampling and refinement) residual point distribution to boost training and accuracy.

Approaches:

• RAD: residual-based adaptive distribution (more expensive)
• RAR-D: residual-based adaptive refinement with distribution (robust)
• Both are less useful under smooth solutions (activate when required)

Key idea: resample with a probability proportional to residual

\[p(x) \propto \frac{\varepsilon^k(x)}{𝔼[\varepsilon^k(x)]}+C\]

Other references of interest are:

• [[@Lu2019a]]: residual-based adaptive refinement (RAR-D with high $k$)
• [[@Nabian2021a]]: importance sampling (RAD with $k=1$ and $c=0$)