AI 中文总结
本研究针对扩散蒙特卡洛（DMC）电子密度的统计噪声，利用密度泛函理论密度作为先验，通过方差稳定化的回归方法结合3D UNET等技术去噪，将DMC模拟成本降低10-100倍，为噪声敏感任务提供新途径。
AI 中文摘要
获得准确的电子密度对分子和凝聚态体系的基础描述以及下一代密度泛函的开发至关重要。扩散蒙特卡洛（DMC）以产生基准质量的数据而闻名，但预测的实空间电子密度包含大量统计噪声。本研究以信息论的Jensen-Shannon散度为基准，研究DMC密度的去噪方法。该去噪通过利用密度泛函理论（DFT）密度作为物理先验的近似异方差到同方差变换实现。我们系统比较了多种去噪技术，包括傅里叶变换、回归和3D UNET，研究对象为密度变化范围广泛的材料：碳金刚石、蓝磷和金红石VO2。结果表明，简单的扁平化机器学习模型和基于2D图像的模型会引入线条伪影，且难以捕捉完整的空间相关性。相比之下，使用方差稳定化时，回归方法在所有材料的高噪声和低噪声极限下均优于其他所有方法。最佳去噪器将生成密度的DMC模拟所需成本降低了10-100倍，为应用于DFT泛函反演等对噪声敏感的任务提供了有前景的途径。
英文摘要
Obtaining accurate electron densities is important for the fundamental description of molecular and condensed matter systems, as well as for the development of next-generation density functionals. Diffusion Monte Carlo (DMC), in particular, is known to produce benchmark-quality data; however, the predicted real-space electron densities contain substantial amounts of statistical noise. In this work, we study denoising approaches for DMC densities, judged on the basis of the information-theoretic Jensen-Shannon divergence. The denoising is facilitated by an approximate heteroscedastic to homoscedastic transformation leveraging the density functional theory density as a physical prior. We systematically compare a range of denoising techniques-including Fourier transform, regression, and 3D UNETs-on materials showing a wide range of density variations: carbon diamond, blue phosphorus, and rutile VO2. Our results indicate that simple flattened machine learning models and 2D image-based models introduce line artifacts and struggle to capture the full spatial correlation. In contrast, when using variance stabilization, regression methods outperform all others in both the high and low- noise limits across all materials considered. The best denoisers reduce the required cost of density-generating DMC simulations by 10-100x, providing a promising route forward for application in noise-sensitive tasks such as DFT functional inversion.
