Summary of Total Uncertainty Quantification in Inverse Pde Solutions Obtained with Reduced-order Deep Learning Surrogate Models, by Yuanzhe Wang and Alexandre M. Tartakovsky
Total Uncertainty Quantification in Inverse PDE Solutions Obtained with Reduced-Order Deep Learning Surrogate Models
by Yuanzhe Wang, Alexandre M. Tartakovsky
First submitted to arxiv on: 20 Aug 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 The proposed approximate Bayesian method quantifies total uncertainty in inverse PDE solutions obtained with machine learning surrogate models, including operator learning models. The method accounts for uncertainty in observations, PDEs, and surrogate models by formulating a minimization problem in the reduced space for maximum a posteriori (MAP) inverse solution. Randomizing the MAP objective function generates samples of the posterior distribution, which are tested against iterative ensemble smoother and deep ensembling methods for a non-linear diffusion equation describing groundwater flow. The proposed method provides similar or more descriptive posteriors than the iterative ensemble smoother method, while deep ensembling underestimates uncertainty and provides less informative posteriors. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper is about finding the best way to solve a complex problem using machine learning. It’s like trying to figure out what’s inside a box without opening it. The researchers developed a new method that takes into account different types of uncertainty, which helps them get a better answer. They tested this method with a real-world example of how water flows underground and compared it to other methods. The results show that their approach is more accurate than others. |
Keywords
» Artificial intelligence » Diffusion » Machine learning » Objective function
