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

원문 초록

Transient pressure diffusion in heterogeneous porous media becomes difficult to resolve efficiently when permeability is discontinuous and spans several orders of magnitude. In this paper, 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. Numerical experiments on low-permeability inclusions, high-conductivity blocks and channels, and three-dimensional grids assess the accuracy of the method across distinct coefficient configurations. 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.