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

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.

Figures (11)

• Figure 1: Numerical modeling and dataset construction. (a) Schematic view of the discrete element method (DEM) model showing the geometry, particle size, coordinate system, and representative surfaces of interest, from the observational boundary (Slice 0) to the other boundary plane (Slice 3). (b) Representative DEM results, showing runout velocity $v_x$ profile after packing, during the flow, and after flow stops. (c) Demonstration of the grid-averaging scheme that transfers particle-scale information into the scale of Representative Elementary Volume (REV), with a grid size of 4 mm. (d) Demonstrative grid-averaged results at $t=0.3$ s used for conditional flow matching, including runout velocity $v_x$, granular temperature $T$, mean stress $p$, and deviatoric stress $q$.
• Figure 2: Overview of the proposed framework. The architecture integrates (a) a continuous-time probabilistic flow matching backbone as a kinematic prior $f$, (b) a differentiable neural forward operator $g$ with a gradient guidance mechanism for conditional flow matching to infer internal particle dynamics from partial boundary observations, and (c) a physics decoder $\mathcal{H}$ to infer key physical properties from the reconstructed kinematic fields.
• Figure 3: Empirical cumulative distribution functions (eCDFs) of the three velocity components ($v_x$, $v_y$, and $v_z$). The unguided generative samples show a strong overall match with the DEM ground truth, demonstrating that the model successfully captures the underlying kinematic distribution.
• Figure 4: Reconstruction of internal velocity fields from full boundary observations at $t = 0.56$ s. The top and bottom rows display the streamwise ($v_x$) and vertical ($v_z$) velocity components, respectively. From left to right, the columns present the boundary observation (Slice 0) used as the conditioning input, the DEM ground truth at the deepest internal plane (Slice 3), the corresponding CFM reconstruction, and the absolute error field.
• Figure 5: Reconstruction of internal streamwise velocity fields ($v_x$) from partial boundary observations at $t = 0.56$ s. (a) The masked input boundary observation region, indicated by a pink bounding box. (b) Visualization of the observation window on the boundary (Slice 0) and prediction Slices 1-3. (c) Slice-by-slice comparison across three internal depths (rows: Slices 1, 2, and 3 from top to bottom). The columns display the DEM ground truth with green boxes showing the projection of the boundary observation window, the CFM reconstruction, and the absolute error, respectively.