物理信息神经网络用于弯曲地形上深度平均颗粒雪崩动力学
Physics-Informed Neural Networks for Depth-Averaged Granular Avalanche Dynamics on Curved Topography
- Indian Institute of Technology Mandi（曼迪印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究将物理信息神经网络扩展至弯曲地形上的深度平均颗粒雪崩动力学，采用分阶段时间课程和策略性观测放置，显著降低轨迹预测误差，验证了训练策略与数据位置的关键作用。
AI中文摘要：
物理信息神经网络（PINNs）提供了一种无网格框架用于求解控制方程，但其在弯曲地形上的颗粒雪崩动力学应用仍 largely unexplored。本研究将基于Savage-Hutter方程的深度平均PINN公式扩展到具有空间变化倾角和应变率依赖的Mohr-Coulomb土压力闭合的指数弯曲滑槽。模型通过与实验室颗粒雪崩实验中测量的前缘和后缘轨迹进行验证，部分观测数据被保留不用于训练。分阶段的时间课程被证明对准确预测至关重要，与从一开始就在整个时间域上训练相比，将保留轨迹误差减少了约两个数量级。稀疏数据实验进一步表明，在所测试的配置中，观测位置比观测数量更具影响力。四个跨越加速到减速转变的观测点达到了与八观测参考配置几乎相同的精度，而聚集在早期或晚期的观测点表现较差。结果表明，在将PINNs应用于弯曲地形上的颗粒流时，训练策略和信息性数据放置都至关重要。
英文摘要：
Physics-informed neural networks (PINNs) provide a mesh-free framework for solving governing equations, but their application to granular avalanche dynamics over curved terrain remains largely unexplored. This study extends a depth-averaged PINN formulation based on the Savage-Hutter equations to an exponentially curved chute with spatially varying inclination and a strain-rate-dependent Mohr-Coulomb earth-pressure closure. The model is validated against measured front- and rear-edge trajectories from a laboratory granular-avalanche experiment, with selected observations withheld from training. A staged temporal curriculum proved essential for accurate prediction, reducing the held-out trajectory error by approximately two orders of magnitude compared with training over the full time domain from the outset. Sparse-data experiments further showed that observation placement was more influential than observation number within the configurations tested. Four observations bracketing the transition from acceleration to deceleration achieved nearly the same accuracy as the eight-observation reference configuration, whereas observations clustered at early or late times performed poorly. The results demonstrate the importance of both training strategy and informative data placement when applying PINNs to granular flows over curved topography.
