Summary of Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds For Surrogate Modeling and Uncertainty Quantification, by Dimitris G. Giovanis et al.
Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification
by Dimitris G. Giovanis, Dimitrios Loukrezis, Ioannis G. Kevrekidis, Michael D. Shields
First submitted to arxiv on: 30 Jan 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Dynamical Systems (math.DS)
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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 novel approach to uncertainty quantification in high-dimensional stochastic systems. The authors develop a manifold learning-based surrogate modeling framework that efficiently parameterizes the response of complex computational models. They use Principal Geodesic Analysis on the Grassmann manifold to identify low-dimensional descriptors, and then employ Riemannian K-means and Frechet variance minimization to identify “local” principal geodesic submanifolds representing different system behavior. The method is demonstrated on four test cases, including a toy-example, Lotka-Volterra dynamics, a chemical reactor system, and Rayleigh-Benard convection. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand complex systems better. It creates a new way to model uncertainty in big systems that are hard to calculate exactly. The method works by looking at patterns in the data and finding simple ways to describe it. They test this on four different examples, like a ball bouncing around or chemical reactions happening in a tank. |
Keywords
* Artificial intelligence * K means * Manifold learning
