用自适应采样提升流体模拟精度，比现有方法更准更快。
A Discrete Neural Operator with Adaptive Sampling for Surrogate Modeling of Parametric Transient Darcy Flows in Porous Media
- 结合时间编码与UNet结构，学习参数到流场的映射关系。
- 在有限训练数据下，预测误差显著降低，2D/3D测试均表现更优。
- 基于生成模型动态采样，提升训练效率，适合复杂多孔介质模拟。
本文提出一种新型离散神经算子，用于异质多孔介质中具有随机参数的瞬态达西流场的代理建模。该方法融合时间编码、算子学习与UNet结构，近似随机参数向量空间到时空流场空间的映射关系。相较于最先进的注意力-残差-UNet结构，新方法在预测精度上表现更优。基于有限体积法，以传导率矩阵而非渗透率作为代理模型输入，进一步提升了预测准确性。为提高采样效率，提出一种基于高斯混合模型的生成潜在空间自适应采样方法，用于泛化误差密度估计。在二维与三维单相及两相达西流场预测测试案例中验证，结果表明在训练数据有限的情况下，预测精度持续提升。
原文摘要 · Abstract (English)
This study proposes a new discrete neural operator for surrogate modeling of transient Darcy flow fields in heterogeneous porous media with random parameters. The new method integrates temporal encoding, operator learning and UNet to approximate the mapping between vector spaces of random parameter and spatiotemporal flow fields. The new discrete neural operator can achieve higher prediction accuracy than the SOTA attention-residual-UNet structure. Derived from the finite volume method, the transmissibility matrices rather than permeability is adopted as the inputs of surrogates to enhance the prediction accuracy further. To increase sampling efficiency, a generative latent space adaptive sampling method is developed employing the Gaussian mixture model for density estimation of generalization error. Validation is conducted on test cases of 2D/3D single- and two-phase Darcy flow field prediction. Results reveal consistent enhancement in prediction accuracy given limited training set.
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