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

arXiv: https://arxiv.org/abs/2604.04453 · HTML: https://mlsanity.com/paper/2604.04453/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 8 of its 58 references that are in the map.
- First posted on arXiv 6 Apr 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 8 of 8)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Physics Informed Neural Network for Dynamic Stress Prediction](https://mlsanity.com/paper/2211.16190/) (2022)

## Abstract (arXiv)

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 and a novel sparsity-aware gradient guidance mechanism. This mechanism avoids the gradient dilution inherent to standard mean-squared-error approaches, preserves the absolute physical scale of observation errors, 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, and it suggests potential applicability for inverse problems in particulate and multiphase systems.