Summary of Physics-constrained Polynomial Chaos Expansion For Scientific Machine Learning and Uncertainty Quantification, by Himanshu Sharma et al.
Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification
by Himanshu Sharma, Lukáš Novák, Michael D. Shields
First submitted to arxiv on: 23 Feb 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Data Analysis, Statistics and Probability (physics.data-an)
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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 A novel physics-constrained polynomial chaos expansion is proposed as a surrogate modeling method that can perform both scientific machine learning (SciML) and uncertainty quantification (UQ) tasks. The method integrates SciML into UQ and vice versa, allowing it to quantify uncertainties in SciML tasks effectively and leverage SciML for improved uncertainty assessment during UQ-related tasks. The surrogate model can incorporate various physical constraints, such as PDEs with initial and boundary conditions, inequality-type constraints, and a priori information, ensuring physically realistic predictions and reducing the need for expensive computational evaluations. Additionally, the method has a built-in UQ feature to estimate output uncertainties. Applications include linear/non-linear PDEs with deterministic and stochastic parameters, data-driven surrogate modeling of complex physical systems, and UQ of stochastic systems with random field parameters. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper proposes a new way to do scientific machine learning and uncertainty quantification. It’s like having a superpower that lets you predict things and know how sure you are about those predictions! This method is special because it can take into account the rules of physics, like how water flows or how heat moves, which makes its predictions more realistic. It also helps to figure out how certain you should be about your predictions, which is important for making good decisions. |
Keywords
* Artificial intelligence * Machine learning
