Real-Time Reconstruction of Complex Flow in Nanoporous Media: Linear vs Non-linear Decoding.

Physical field reconstruction from limited real-time data is a topical inverse problem that attracts substantial research effort, and complex geometries present a formidable challenge. The paper describes a reconstruction of the velocity field of a steady fluid flow through a two-dimensional porous structure from the real-time gauge readings (that is, velocity values obtained at specific fixed locations). The dataset is composed of 300 Lattice-Boltzmann simulations of the flow with different boundary conditions. The number of the gauges and their locations are varied. Two reconstruction techniques are applied: neural network (NN) and linear least squares solver. The linear solver outperforms the NN in terms of both speed and precision. Sensor locations are optimized by Monte Carlo method. The porous structure is mapped onto a graph and the optimization is performed by Metropolis type node-to-node trial displacements of the gauges. With 100 gauges, the linear method enables reconstruction of the velocity field in a porous structure discretized on 256 $$\,\times \,$$ 256 2D grid with the normalized error of 0.57%.