Summary of Operator Learning with Gaussian Processes, by Carlos Mora et al.
Operator Learning with Gaussian Processes
by Carlos Mora, Amin Yousefpour, Shirin Hosseinmardi, Houman Owhadi, Ramin Bostanabad
First submitted to arxiv on: 6 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 This paper introduces a hybrid Gaussian Process (GP) and Neural Network (NN)-based framework for operator learning, which focuses on approximating mappings between infinite-dimensional spaces of functions. This approach is particularly suitable for solving parametric nonlinear partial differential equations (PDEs). The authors combine the strengths of GPs and NNs to approximate the associated real-valued bilinear form, allowing them to recover the original function-valued operator. They develop a robust training mechanism based on maximum likelihood estimation (MLE) that can leverage physics involved in certain applications. Numerical benchmarks demonstrate improved performance compared to base neural operators and enable zero-shot data-driven models for accurate predictions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Operator learning is about finding connections between infinite-dimensional spaces of functions. This paper shows how combining Gaussian Processes (GPs) and Neural Networks (NNs) can help solve complex problems like nonlinear partial differential equations (PDEs). By using a GP to approximate the bilinear form, they can recover the original function-valued operator. The authors also develop a way to train this hybrid model that can make use of physical laws in certain cases. This leads to better results and even allows for predictions without any training data. |
Keywords
» Artificial intelligence » Likelihood » Neural network » Zero shot
