Summary of Embedded Nonlocal Operator Regression (enor): Quantifying Model Error in Learning Nonlocal Operators, by Yiming Fan et al.
Embedded Nonlocal Operator Regression (ENOR): Quantifying model error in learning nonlocal operators
by Yiming Fan, Habib Najm, Yue Yu, Stewart Silling, Marta D’Elia
First submitted to arxiv on: 27 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Materials Science (cond-mat.mtrl-sci)
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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 proposes a novel framework called Embedded Nonlocal Operator Regression (ENOR) for bottom-up homogenization in long-term simulations. ENOR combines Nonlocal Operator Regression (NOR), an optimization-based nonlocal kernel learning approach, with an embedded model error term to learn a nonlocal homogenized surrogate model and its structural model error. The framework provides discrepancy-adaptive uncertainty quantification for homogenized material response predictions. Bayesian inference is employed to infer the model error term parameters together with the kernel parameters using a multilevel delayed acceptance Markov chain Monte Carlo (MLDA-MCMC) method. The paper demonstrates the effectiveness of ENOR by applying it to predict long-term wave propagation in a heterogeneous one-dimensional bar, outperforming additive noise models. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper creates a new way to make predictions about how materials will behave over a long time. It uses something called nonlocal operators that can represent big effects and small details at the same time. But sometimes these predictions can be wrong because they don’t account for small errors that add up. To fix this, the researchers developed a new method called ENOR (Embedded Nonlocal Operator Regression) that learns how to predict both the material behavior and the errors that might occur. This helps make more accurate predictions about what will happen in the future. |
Keywords
» Artificial intelligence » Bayesian inference » Optimization » Regression
