Summary of Ensemble and Mixture-of-experts Deeponets For Operator Learning, by Ramansh Sharma et al.
Ensemble and Mixture-of-Experts DeepONets For Operator Learning
by Ramansh Sharma, Varun Shankar
First submitted to arxiv on: 20 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 presents two novel deep neural network architectures for operator learning. The first is the ensemble DeepONet, which allows multiple trunk networks to be combined to improve expressivity and generalization capabilities. The second is a spatial mixture-of-experts (MoE) DeepONet trunk network architecture that utilizes a partition-of-unity (PoU) approximation to promote spatial locality and model sparsity. Both architectures are shown to be universal approximators, and ensemble DeepONets achieve 2-4x lower relative _2 errors than standard DeepONets on operator learning problems involving partial differential equations (PDEs). The PoU-MoE formulation provides a natural way to incorporate spatial locality and model sparsity into any neural network architecture. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about two new ways to improve how computers learn to solve math problems. It presents special kinds of neural networks that can do this better than usual networks. These networks, called DeepONets, are good at solving math problems that involve partial differential equations (PDEs). The first new way combines multiple networks together to make a stronger one. The second way uses a clever trick to make the network more efficient and accurate. |
Keywords
» Artificial intelligence » Generalization » Mixture of experts » Neural network
