用变分自编码器生成更灵活的先验样本，提升马尔可夫链蒙特卡洛效率。
Variational Autoencoder for Generating Broader-Spectrum prior Proposals in Markov chain Monte Carlo Methods
- 用VAE从数据中学习相关结构，无需预设协方差函数。
- 在已知相关长度时精度相当，偏离真实值时显著优于KLE。
- 大幅降低随机维度，适合高维贝叶斯反演问题。
本研究采用变分自编码器（VAE）方法，提升马尔可夫链蒙特卡洛（McMC）方法的效率与适用性，通过生成更广谱的先验提案。传统方法如Karhunen-Loève展开（KLE）需预先知晓协方差函数，实际应用中常不可得。VAE框架实现数据驱动，灵活捕捉贝叶斯反演问题中的多种相关结构，尤其适用于地下水流建模。在合成地下水流动反演问题中，利用压力数据估计渗透率场。数值实验表明：当相关长度已知时，基于VAE的参数化精度与KLE相当；当假设相关长度偏离真实值时，性能显著超越KLE。此外，该方法显著降低随机维度，提升计算效率。结果表明，将深度生成模型引入McMC可实现更适应、高效的高维贝叶斯推断。
原文摘要 · Abstract (English)
This study uses a Variational Autoencoder method to enhance the efficiency and applicability of Markov Chain Monte Carlo (McMC) methods by generating broader-spectrum prior proposals. Traditional approaches, such as the Karhunen-Loève Expansion (KLE), require previous knowledge of the covariance function, often unavailable in practical applications. The VAE framework enables a data-driven approach to flexibly capture a broader range of correlation structures in Bayesian inverse problems, particularly subsurface flow modeling. The methodology is tested on a synthetic groundwater flow inversion problem, where pressure data is used to estimate permeability fields. Numerical experiments demonstrate that the VAE-based parameterization achieves comparable accuracy to KLE when the correlation length is known and outperforms KLE when the assumed correlation length deviates from the true value. Moreover, the VAE approach significantly reduces stochastic dimensionality, improving computational efficiency. The results suggest that leveraging deep generative models in McMC methods can lead to more adaptable and efficient Bayesian inference in high-dimensional problems.
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