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

Pore-scale flow governs transport and permeability behaviour in porous media engineering applications, yet repeated lattice Boltzmann method (LBM) simulation across many geometries and design queries remains costly for repeated deployment. This study formulates transient pore-scale flow prediction as a geometry-conditioned query-time operator and introduces QSGS-Transient-7606, a benchmark of 7,606 two-dimensional porous structures each paired with 30 logarithmically sampled LBM states. The proposed continuous-time pore-scale flow surrogate model (CT-PoreFlow) integrates topology-aware geometry encoding, compressed spectral mixing, and log-time conditioning with a late-time flux-calibration objective. On unseen test geometries, CT-PoreFlow achieves a velocity relative L2 of 0.2248 and a terminal permeability error of 12.81%. Frozen morphology and computed tomography image audits confirm reasonable cross-geometry robustness without fine-tuning. The surrogate is then embedded in an inverse design workflow, screening 9,216 generative adversarial network and diffusion candidates across 18 property targets prior to LBM verification. Guided GAN sampling attains 98.11% through-connectivity and 72.28% conditional design success, exceeding diffusion-based generation. The framework unifies transient flow prediction, transport-aware screening, and LBM-verified inverse design for porous media.

A Two-Stage Learning PINN Approach for Solving the Inverse Problem of the 1D Porous Medium Equation

The Porous Medium Equation (PME), given by $u_t = Δ(u^m)$ for $m > 1$, is a degenerate nonlinear parabolic partial differential equation that arises in various physical applications such as fluid flow in porous media, heat transfer in plasmas, and population dynamics. It is known for its nonlinear diffusion and finite propagation speed. In this paper, we study numerical solutions of the one-dimensional direct and inverse PME using Physics-Informed Neural Networks (PINNs), and compare them with classical numerical methods and available analytical and manufactured solutions. While PINNs provide a flexible framework for solving both forward and inverse problems, we show that the standard inverse formulation suffers from a strong sensitivity to the initial guess, leading to only local convergence. To address this issue, we propose a novel two-stage PINN training framework for the inverse problem, which significantly improves convergence stability and allows reliable recovery of the unknown parameter even for poor initial guesses. Overall, the proposed approach demonstrates that PINNs are a flexible and accurate alternative to classical methods for the 1D PME, and the introduced two-stage training strategy substantially improves their robustness in inverse problems, providing a solid basis for extensions to more complex geometries and higher-dimensional cases.

Denoising 3D images: robustness of persistent homology measures

When computing sub/super-level-set persistent homology (PH), the effect of noise may introduce millions of (short-lived) topological generators, presenting an obstacle to both the computation of PH of large 3D images, and any analysis of PH that incorporates the number of generators. As such, it is often necessary to denoise the data before computing its PH. We analyze the PH of synthetic 3D images of porous media in the presence of spatially uncorrelated noise, and perform a comparative analysis of various topological measures (e.g. bottleneck distance, Wasserstein distance, persistence statistics and persistence images) to assess their robustness to both noise and the denoising process (i.e. adding spatially uncorrelated Gaussian noise, and denoising by either a Gaussian convolution or a machine learning approach).

Physics-Guided Generative AI for Property-Targeted 3D Porous Media Design

Inverse design of three-dimensional porous media is central to applications in filtration, catalysis, energy storage, fuel cells, thermal management, and biomedical scaffolds, but remains challenging because many distinct pore geometries can share similar porosity or permeability while small structural changes can strongly affect transport behaviour. This paper proposes a physics-guided generative AI framework for property-targeted porous media design, combining a property-aware variational autoencoder, a conditional latent diffusion model, and an independently trained differentiable structure-to-property surrogate. The framework learns a compact, physically informative latent design space, generates porous structures conditioned on target porosity and directional permeability, and refines generated samples using property-level feedback during denoising and decoding. Experiments on procedurally generated structures and real micro-CT porous-media datasets show improved target-property matching, directional permeability control, and property correlation compared with representative property-aware variational-autoencoder and latent-diffusion baselines. The results demonstrate a scalable route towards controllable inverse design of complex porous geometries and establish a foundation for simulation-informed generative AI tools in engineering and advanced materials discovery.

Property-Constrained 3D Porous Media Reconstruction from 2D Images via Conditional Generative Adversarial Networks

This study presents a conditional Generative Adversarial Network (cGAN) framework for generating 3D porous media volumes with controlled porosity, trained exclusively on 2D thin section images. The key innovation lies in combining property-conditioned generation with 2D-to-3D reconstruction, eliminating the need for expensive 3D training data while maintaining control over petrophysical properties. The framework employs a hybrid architecture with a 3D generator and 2D discriminator, where multi-axis slice extraction enables learning 3D-consistent structures from 2D training data. Porosity labels are extracted using an Enhanced U-Net segmentation model. The methodology was demonstrated on two carbonate samples with different lithologies: dolomite-anhydrite and pure dolomite. Results show that the framework successfully generates realistic 3D volumes capturing lithological features such as anhydrite inclusions and fine crystalline textures. Porosity control achieved an $R^2$ of 0.93, with mean absolute errors of 0.019 and 0.010 for the heterogeneous and homogeneous samples, respectively.