Summary of Cono: Complex Neural Operator For Continous Dynamical Physical Systems, by Karn Tiwari et al.
CoNO: Complex Neural Operator for Continous Dynamical Physical Systems
by Karn Tiwari, N M Anoop Krishnan, A P Prathosh
First submitted to arxiv on: 1 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV); Neural and Evolutionary Computing (cs.NE)
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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 introduces Complex Neural Operator (CoNO), a novel extension of neural operators that parameterizes the integral kernel using Fractional Fourier Transform (FrFT). Unlike traditional neural operators, CoNO is designed to better represent non-stationary signals in a complex-valued domain. Theoretically, the authors prove the universal approximation capability of CoNO. In an extensive empirical evaluation, CoNO achieves state-of-the-art performance on seven challenging partial differential equations (PDEs), including regular grids, structured meshes, and point clouds, with an average relative gain of 10.9%. Additionally, CoNO outperforms other models in zero-shot super-resolution and robustness to noise tasks. The authors also demonstrate that CoNO can learn from small amounts of data, achieving the same performance as the next best model with just 60% of the training data. Overall, CoNO presents a robust and superior model for modeling continuous dynamical systems, with potential applications in scientific machine learning. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper creates a new way to analyze complex signals that change over time or space. They call it Complex Neural Operator (CoNO). The authors want to make sure their method works well on different kinds of data and problems, so they test it on many challenging tasks. Their results show that CoNO is better than other methods in many cases. This new approach can be used for things like predicting how something will change over time or improving images from blurry pictures. |
Keywords
» Artificial intelligence » Machine learning » Super resolution » Zero shot
