Speaker
Description
Modeling flow and transport in large, heterogeneous networks—such as fractured, karstic, or pore-scale systems—often requires substantial model reduction while preserving global hydraulic behavior. We propose a systematic coarse-graining framework for resistor networks that combines resistance-distance–based upscaling with gradient-based optimization to construct physically consistent coarse networks with effective conductivities.
Starting from a fine-scale network, the method defines coarse vertices as sets of fine nodes obtained from a prescribed partition. Effective resistance distances between coarse vertex pairs are computed by solving constrained energy-minimization problems on the fine network, generalizing classical resistance distance concepts to sets of nodes. These coarse resistance distances encode global flow information and naturally account for long-range connectivity effects.
Given the coarse network topology and a set of target resistance distances, we formulate an inverse problem to estimate the effective conductivities of coarse edges. This problem is cast as a nonlinear least-squares minimization and solved using a Gauss–Newton algorithm. An analytical expression for the Jacobian shows that the sensitivity of resistance distances to edge conductivities is directly related to energy dissipation on the corresponding edges, enabling the simultaneous computation of resistance distances and gradients with negligible additional cost.
The methodology is validated on two- and three-dimensional percolation networks with lognormally distributed conductivities, over a range of heterogeneity levels and distances to the percolation threshold. When coarse resistance distances are prescribed, the inverse problem for estimating effective coarse conductivities is well posed and can be solved efficiently, with rapid and robust convergence in most tested configurations, including highly heterogeneous networks.
When coarse resistance distances are computed directly from fine-scale networks, their estimation is found to depend on long-range connectivity and on the choice of partitioning strategy. This sensitivity highlights the nonlocal nature of resistance distances and motivates further investigation into their consistent definition and numerical stabilization at the coarse scale. Overall, the proposed framework provides a flexible basis for physics-informed network coarsening, and offers insight into how global flow information can be transferred from fine to coarse representations.
| Country | France |
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