AI 中文总结
研究通过物理信息神经网络计算卡拉比-丘三维流形上的数值扭曲IIB通量背景，应用于五次曲面德沃克族的两个通量真空，研究奇异体问题，还对CY度量数值研究技术有改进，如改进采样算法等。
AI 中文摘要
我们按照吉丁斯、卡奇鲁和波钦斯基的构造，计算卡拉比-丘三维流形上的数值扭曲IIB通量背景。利用物理信息神经网络，我们近似GKP设置所需的所有三个要素：里奇平坦的卡拉比-丘度量、表示虚自对偶三形式通量的调和(2,1)形式以及在内部流形上求解源泊松方程的翘曲因子。我们将我们的管道应用于五次曲面的德沃克族，用于两个不同的通量真空，一个靠近锥形奇点，一个远离它，后者用作数值交叉检查。借助这些工具，我们研究了奇异体问题，发现对于我们靠近锥形奇点的基准点，大约0.5%的卡拉比-丘总体积位于喉部，并且翘曲因子比主体大一个数量级。我们还对用于CY度量及其派生量的数值研究的技术进行了一些改进，这些改进可能独立于我们的应用而受到关注。这些改进包括一种改进的点采样算法，该算法在卡拉比-丘测度下产生更均匀的样本，一种用于度量的特征工程谱网络，多步物理信息训练，以及一种针对具有高度不均匀源的刚性偏微分方程量身定制的加权胡贝尔损失。
英文摘要
We compute numerical warped Type IIB flux backgrounds on Calabi-Yau threefolds following the construction of Giddings, Kachru, and Polchinski. Using physics-informed neural networks, we approximate all three ingredients required by the GKP setup: the Ricci-flat Calabi-Yau metric, the harmonic (2,1)-forms representing the imaginary self-dual three-form flux, and the warp factor, which solves a sourced Poisson equation on the internal manifold. We apply our pipeline to the Dwork family of quintics for two different flux vacua, one near a conifold point and one away from it, the latter serving as a numerical cross-check. With these tools, we study the singular bulk problem, and find that for our benchmark point close to the conifold, approximately 0.5 percent of the total Calabi-Yau volume sits in the throat, and the warp factor is an order of magnitude larger as compared to the bulk. We also introduce several improvements to techniques used for numerical studies of CY metrics and quantities derived from them that might be of interest independently of our application. These include an improved point sampling algorithm that produces samples that are more uniform under the Calabi-Yau measure, a feature-engineered spectral network for the metric, multi-step physics-informed training, and a weighted Huber loss tailored to stiff PDEs with highly non-uniform sources.
Comments34 pages, 9 figures
