域分解随机特征演化深度神经网络用于非连续高对比系数瞬态压力扩散
Domain-decomposed Evolutional Deep Neural Network with Random Features for Transient Pressure Diffusion with Discontinuous and High-Contrast Coefficients
- Xi’an Jiaotong-Liverpool University（西交利物浦大学）
- University of Liverpool（利物浦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对非均质多孔介质中不连续高对比渗透率的瞬态压力扩散，提出域分解随机特征演化深度神经网络，分离空间与时间，实现结构保持的高效降阶模拟，精度高且可解释。
AI中文摘要：
当渗透率不连续且跨越多个数量级时，非均质多孔介质中的瞬态压力扩散难以高效求解。我们开发了一种域分解随机特征演化深度神经网络（DD RF-EDNN），将空间近似与时间演化分离。渗透率信息随机特征被压缩到正交压力空间中，并将守恒有限体积算子投影到该空间，使得仅需在时间上推进降阶坐标。该公式保留了离散流动问题的耗散结构，无需重复的神经网络优化。分析量化了字典和奇异值截断误差，证明了在能量一致耗散校正下的收缩性，并推导了针对齐次动力学和时间无关数据（允许稳态提升）的条件网格级估计。在低渗透率夹杂物、高导流通道和块体以及三维网格上的实验表明，该方法在不同系数结构下均具有一致的精度。该方法在主要基准中达到最终时间相对$L^2$误差为$9.54\ imes10^{-4}$，并在渗透率对比度为$10^3$时保持误差在$10^{-2}$量级。数值诊断进一步表明，观测到的误差平衡和时间收敛性与分析一致。这些结果支持DD RF-EDNN作为指定非均质介质上瞬态模拟的结构保持且可解释的降阶公式。
英文摘要：
Transient pressure diffusion in heterogeneous porous media becomes difficult to resolve efficiently when permeability is discontinuous and spans several orders of magnitude. We develop a domain-decomposed random-feature evolutional deep neural network (DD RF-EDNN) that separates spatial approximation from temporal evolution. Permeability-informed random features are compressed into an orthonormal pressure space, and a conservative finite-volume operator is projected onto this space so that only the reduced coordinates are advanced in time. This formulation retains the dissipative structure of the discrete flow problem without repeated neural-network optimization. The analysis quantifies dictionary and singular-value truncation errors, proves contractivity under an energy-consistent dissipativity correction, and derives a conditional grid-level estimate for homogeneous dynamics and time-independent data admitting a steady lifting. Experiments on low-permeability inclusions, high-conductivity channels and blocks, and three-dimensional grids demonstrate consistent accuracy across distinct coefficient structures. The method reaches a final-time relative $L^2$ error of $9.54\times10^{-4}$ in the principal benchmark and maintains errors on the order of $10^{-2}$ at a permeability contrast of $10^3$. Numerical diagnostics further show that the observed error balance and temporal convergence are consistent with the analysis. These results support DD RF-EDNN as a structure-preserving and interpretable reduced formulation for transient simulations on prescribed heterogeneous media.
