用神经网络调校湍流模型不确定性，更准且更可信。
Physics-Guided Machine Learning for Uncertainty Quantification in Turbulence Models
- 用卷积神经网络动态调节物理方法的扰动强度
- 在典型算例中不确定性区间更紧致，校准度显著提升
- 适合需要高可靠性预测的工程与流体模拟场景
预测湍流演化是科学与工程的核心问题。现有研究多依赖湍流模型的数值模拟，但其经验性简化会引入认知不确定性。特征空间扰动法（EPM）是一种广泛应用的物理驱动方法，用于量化模型形式不确定性，但纯物理方法常过度高估不确定性边界。本文提出一种基于卷积神经网络（CNN）的EPM扰动幅度调制方法，在保持物理一致性的同时提升校准精度。在多个典型算例中，混合机器学习-EPM框架生成的不确定性估计显著更紧致、校准更优，优于基准EPM方法。
原文摘要 · Abstract (English)
Predicting the evolution of turbulent flows is central across science and engineering. Most studies rely on simulations with turbulence models, whose empirical simplifications introduce epistemic uncertainty. The Eigenspace Perturbation Method (EPM) is a widely used physics-based approach to quantify model-form uncertainty, but being purely physics-based it can overpredict uncertainty bounds. We propose a convolutional neural network (CNN)-based modulation of EPM perturbation magnitudes to improve calibration while preserving physical consistency. Across canonical cases, the hybrid ML-EPM framework yields substantially tighter, better-calibrated uncertainty estimates than baseline EPM alone.
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