Domain-decomposed Evolutional Deep Neural Network with Random Features for Transient Pressure Diffusion with Discontinuous and High-Contrast Coefficients

2026-09-17

AI Summary

本文提出了一种域分解随机特征进化深度神经网络(DD RF-EDNN)，用于解决具有不连续和高对比度系数的瞬态压力扩散问题，通过将空间近似与时间演化分离来提高计算效率。

Abstract

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.

Problem

• Transient Pressure Diffusion
• Discontinuous Permeability
• Heterogeneous Porous Media
• High-Contrast Coefficients

Innovation

• Domain-decomposed
• Random Features
• Evolutional Deep Neural Network
• Discontinuous Coefficients
• High-Contrast