标题： 用于马尔可夫链蒙特卡洛方法中生成更广谱先验建议的变分自编码器 显示英文标题

标题： Variational Autoencoder for Generating Broader-Spectrum prior Proposals in Markov chain Monte Carlo Methods

摘要： 本研究使用变分自编码器方法，通过生成更广谱的先验提议来提高马尔可夫链蒙特卡洛（McMC）方法的效率和适用性。传统的做法，如Karhunen-Loève展开（KLE），需要先验知识的协方差函数，在实际应用中通常不可用。VAE框架使一种数据驱动的方法能够灵活地捕捉贝叶斯反问题中的更广泛的相关结构，特别是在地下水流建模中。该方法在合成地下水流动反演问题上进行了测试，其中使用压力数据来估计渗透率场。数值实验表明，当相关长度已知时，基于VAE的参数化方法与KLE具有可比的准确性，并且当假设的相关长度偏离真实值时，其表现优于KLE。此外，VAE方法显著降低了随机维度，提高了计算效率。结果表明，在McMC方法中利用深度生成模型可以在高维问题中实现更适应性和更高效的贝叶斯推断。 显示英文摘要

摘要： 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-Lo\`eve 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.