用不确定性感知模型从稀疏数据重建流场，提升预测可信度。
Uncertainty-Aware Flow Field Reconstruction Using SVGP Kolmogorov-Arnold Networks
- 基于SVGP-KAN网络实现稀疏速度测量下的流场重构
- 在0.5%~10%采样率下保持高精度，且不确定性估计可靠
- 适合需要可信预测的周期性流动实验设计
从时间稀疏的速度测量中重建时变流场，对复杂热流系统表征至关重要。本文提出一种基于稀疏变分高斯过程与柯尔莫戈洛夫-阿诺德网络结构（SVGP-KAN）的机器学习框架，实现不确定性感知的流场重构。该方法在经典线性随机估计（LSE）和谱分析模态法（SAMM）基础上，支持合理的认知不确定性量化。通过脉冲冲击射流的合成数据，在0.5%至10%的分数化PIV采样率下系统对比了本方法与传统重建方法及卡尔曼滤波性能。评估指标包括重构误差、泛化差距、结构保持度和不确定性校准。结果表明，SVGP-KAN在精度上媲美现有方法，同时提供准确的不确定性估计，能可靠指示预测质量下降的位置与时刻。该框架为具有明确不确定性量化的数据驱动流场重建提供了鲁棒解决方案，并为周期性流动的实验设计提供实用指导。
原文摘要 · Abstract (English)
Reconstructing time-resolved flow fields from temporally sparse velocimetry measurements is critical for characterizing many complex thermal-fluid systems. We introduce a machine learning framework for uncertainty-aware flow reconstruction using sparse variational Gaussian processes in the Kolmogorov-Arnold network topology (SVGP-KAN). This approach extends the classical foundations of Linear Stochastic Estimation (LSE) and Spectral Analysis Modal Methods (SAMM) while enabling principled epistemic uncertainty quantification. We perform a systematic comparison of our framework with the classical reconstruction methods as well as Kalman filtering. Using synthetic data from pulsed impingement jet flows, we assess performance across fractional PIV sampling rates ranging from 0.5% to 10%. Evaluation metrics include reconstruction error, generalization gap, structure preservation, and uncertainty calibration. Our SVGP-KAN methods achieve reconstruction accuracy comparable to established methods, while also providing well-calibrated uncertainty estimates that reliably indicate when and where predictions degrade. The results demonstrate a robust, data-driven framework for flow field reconstruction with meaningful uncertainty quantification and offer practical guidance for experimental design in periodic flows.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。