Summary of A Resolution Independent Neural Operator, by Bahador Bahmani et al.
A Resolution Independent Neural Operator
by Bahador Bahmani, Somdatta Goswami, Ioannis G. Kevrekidis, Michael D. Shields
First submitted to arxiv on: 17 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Engineering, Finance, and Science (cs.CE); Computational Physics (physics.comp-ph); Machine Learning (stat.ML)
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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 The Deep Operator Network (DeepONet) is a neural architecture that maps between infinite-dimensional function spaces using two neural networks. While effective, it requires input functions to be discretized at identical locations, limiting practical applications. To address this limitation, researchers introduce a general framework for operator learning from input-output data with arbitrary sensor locations and counts. They propose a resolution-independent DeepONet (RI-DeepONet) that handles input functions discretized arbitrarily but sufficiently finely. This is achieved through two dictionary learning algorithms that adaptively learn continuous basis functions from correlated signals on arbitrary point clouds. These basis functions project input function data onto a finite-dimensional embedding space, making it compatible with DeepONet without architectural changes. The proposed framework uses sinusoidal representation networks (SIRENs) as trainable INR basis functions and demonstrates robustness and applicability in handling arbitrarily sampled input and output functions during both training and inference through several numerical examples. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The researchers developed a new way to learn from data that can be used with any type of data, no matter how it’s collected. They created a new neural network architecture called the Resolution Independent Neural Operator (RINO) that can handle different types of input and output data. This means that RINO can be used in many different situations, such as predicting weather patterns or analyzing medical images. |
Keywords
» Artificial intelligence » Embedding space » Inference » Neural network
