A Query-Time Framework for Transient 2D Pore-Scale Flow Prediction and Generative Design

This study addresses the high computational cost of repeated lattice Boltzmann method (LBM) simulations in porous media engineering. The authors develop a large-scale benchmark, QSGS-Transient-7606, containing 7,606 two-dimensional porous structures with transient flow data. They propose CT-PoreFlow, a continuous-time surrogate model that uses a geometry-conditioned encoder-decoder architecture. The model integrates topology-aware geometry encoding (including pore masks, Euclidean distance transforms, and geodesic graph distances) with compressed spectral mixing via Fourier Neural Operators (FNO) and log-time conditioning. This allows the model to predict velocity and pressure fields at any requested time point without sequential time-stepping.

CT-PoreFlow demonstrates superior predictive accuracy compared to standard U-Net and FNO baselines, achieving a velocity relative L2 error of 0.2248 and a terminal permeability error of 12.81% on unseen geometries. A key finding is that minimizing pixel-averaged field error does not necessarily optimize engineering transport quantities; therefore, the authors incorporate a late-time flux-calibration objective to improve terminal permeability and hydraulic tortuosity recovery. The surrogate is successfully integrated into an inverse design workflow, where it screens thousands of candidates generated by GAN and diffusion models. Guided GAN sampling achieved a 72.28% conditional design success rate, significantly outperforming random selection and diffusion-based generation in this specific configuration.

By replacing iterative LBM solvers with a query-time surrogate, this framework enables high-throughput screening of porous structures for specific transport properties. It bridges the gap between generative microstructure design and physical verification, allowing researchers to explore vast design spaces for applications like groundwater remediation, carbon sequestration, and battery electrode optimization. The study highlights that effective design requires considering both permeability and hydraulic tortuosity as complementary structural dimensions, rather than relying on bulk porosity alone.