用生成模型从稀疏观测重建斜面颗粒流内部运动,提升逆问题求解效率与精度。
Generative modeling of granular flow on inclined planes using conditional flow matching

- 基于条件流匹配框架,结合可微前向算子与稀疏感知梯度机制
- 在仅16%观测数据下仍能准确恢复内部速度场,11%数据时仍有效
- 提供空间解析的不确定性估计,适合颗粒与多相系统逆问题研究
颗粒流主导众多自然与工业过程,但其内部运动与力学特性难以直接观测,实验仅能获取边界或自由表面信息。传统数值模拟计算成本高,且在不适定条件下确定性模型易坍缩为过平滑的均值预测。本文首次提出基于条件流匹配(CFM)的颗粒流重构框架,利用高保真粒子解析离散元模拟训练生成模型,并在推理阶段通过可微前向算子与新颖的稀疏感知梯度引导机制进行指导。该机制避免标准均方误差方法的梯度稀释问题,保留观测误差的绝对物理尺度,无需超参数调优即可强制测量一致性,并防止非物质区域产生不合理的速度预测。物理解码器将重构的速度场映射至应力状态与能量涨落量,包括平均应力、偏应力和颗粒温度。该框架可在全观测到仅16%有效窗口的数据下精确恢复内部流场,在空间分辨率严重稀疏(仅11%数据)时仍保持有效性,且在最不适定重建场景中优于确定性CNN基线,并通过集成生成提供空间分辨的不确定性估计。结果表明,条件生成建模为非侵入式推断颗粒介质隐藏体力学提供了可行路径,也暗示其在颗粒与多相系统逆问题中的应用潜力。
原文摘要 · Abstract (English)
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.
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