Problem
Research questions and friction points this paper is trying to address.
Reduced-order models
closure problem
multi-fidelity learning
uncertainty quantification
Uncertainty-aware Multi-fidelity Closure via Conditional Normalizing Flows
🤖 AI Summary
本文针对ROM闭合问题，提出了一种基于条件归一化流的多保真度不确定性感知框架，通过直接学习和残差学习两种策略提高了预测精度并量化了不确定性。
📝 Abstract
Reduced-order models (ROMs) provide an efficient surrogate for complex multiscale systems, but their predictive accuracy is often compromised by truncation errors and the inadequate representation of interactions between resolved and unresolved scales. The missing effect of truncated (unresolved) scales on ROM (resolved) scales is often denoted as the closure problem. In this work, we formulate ROM closure modeling as a multi-fidelity (MF) learning problem and propose an uncertainty-aware MF framework based on conditional normalizing flow to enhance ROM predictive accuracy. The proposed approach learns a probabilistic mapping from low-fidelity (LF) ROM coefficients to high-fidelity (HF) coefficients, thereby improving predictive fidelity while quantifying the uncertainty associated with the learned closure. Two correction strategies are investigated: direct learning, in which HF coefficients are predicted directly from LF inputs, and residual learning, which learns the discrepancy between LF and HF coefficients and uses it to recover the corrected HF solution. The framework is demonstrated on a vortex merging problem governed by the two-dimensional Navier Stokes equations. Results show that both correction strategies improve ROM accuracy over uncorrected ROM, with residual learning achieving consistently better performance than direct learning. Moreover, the two proposed deep generative model-based strategies provide uncertainty quantification for the corrected ROM coefficients, which is critical for assessing prediction confidence and supporting the reliable use of ROMs in practical applications.
Innovation
Methods, ideas, or system contributions that make the work stand out.
multi-fidelity closure
conditional normalizing flows
uncertainty-aware
reduced-order models (ROMs)
residual learning
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