Generative modeling of granular flow on inclined planes using conditional flow matching

TL;DR

This paper introduces a novel conditional flow matching framework for reconstructing interior granular flow fields from sparse boundary data, leveraging generative modeling and physics-guided guidance to improve accuracy and uncertainty estimation.

Contribution

It presents the first CFM approach for granular flow reconstruction, combining physics-guided guidance with generative modeling to handle sparse data and ill-posed inverse problems.

Findings

Accurately recovers interior flow from 16% of data

Effective with only 11% of data in highly sparse scenarios

Outperforms deterministic CNN baseline in ill-posed regimes

Abstract

Granular flows govern many natural and industrial processes, yet their interior kinematics and mechanics remain largely unobservable, as experiments access only boundaries or free surfaces. Conventional numerical simulations are computationally expensive for fast inverse reconstruction, and deterministic models tend to collapse to over-smoothed mean predictions in ill-posed settings. This study, to the best of the authors' knowledge, presents the first conditional flow matching (CFM) framework for granular-flow reconstruction from sparse boundary observations. Trained on high-fidelity particle-resolved discrete element simulations, the generative model is guided at inference by a differentiable forward operator with a sparsity-aware gradient guidance mechanism, which enforces measurement consistency without hyperparameter tuning and prevents unphysical velocity predictions in non-material regions. A physics decoder maps the reconstructed velocity fields to stress states and energy fluctuation quantities, including mean stress, deviatoric stress, and granular temperature. The framework accurately recovers interior flow fields from full observation to only 16% of the informative window, and it remains effective under strongly diluted spatial resolution with only 11% of data. It also outperforms a deterministic CNN baseline in the most ill-posed reconstruction regime and provides spatially resolved uncertainty estimates through ensemble generation. These results demonstrate that conditional generative modeling offers a practical route for non-invasive inference of hidden bulk mechanics in granular media, with broader applicability for inverse problems in particulate and multiphase systems.