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

arXiv: https://arxiv.org/abs/2608.22235 · HTML: https://mlsanity.com/paper/2608.22235/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 23 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Deep learning-aided inverse design of porous metamaterials](https://mlsanity.com/paper/2507.17907/) (2025)

## Abstract (arXiv)

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.