Summary of Piratenets: Physics-informed Deep Learning with Residual Adaptive Networks, by Sifan Wang et al.
PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks
by Sifan Wang, Bowen Li, Yuhan Chen, Paris Perdikaris
First submitted to arxiv on: 1 Feb 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 This study addresses the limitations of physics-informed neural networks (PINNs) when using larger and deeper architectures. The authors identify that the root cause is poor initialization schemes for multi-layer perceptron (MLP) architectures, leading to unstable training of network derivatives. To overcome this, they propose Physics-informed Residual Adaptive Networks (PirateNets), which leverage adaptive residual connections and a novel initialization scheme to facilitate stable training. PirateNets enable the encoding of inductive biases corresponding to a given PDE system into the network architecture, achieving state-of-the-art results across various benchmarks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Physics-informed neural networks (PINNs) are used to solve forward and inverse problems governed by partial differential equations (PDEs). However, their performance degrades when using larger and deeper architectures. The problem is caused by poor initialization schemes for multi-layer perceptron (MLP) architectures, making it hard to train the network derivatives. To fix this, scientists propose a new architecture called PirateNets that uses adaptive residual connections and a special way of initializing the network. This makes training more stable and allows the network to learn from deeper structures. The result is better performance on various benchmark problems. |
