发表机构
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 中文总结
本研究开发了物理信息神经网络框架，用于Savage-Hutter深度平均雪崩动力学模型，从一维解析验证到二维实验验证，通过混合物理与数据训练实现准确预测。
AI 中文摘要
准确预测雪崩运动对于山区灾害评估至关重要。本研究开发并评估了一种物理信息神经网络（PINN）框架，用于Savage-Hutter深度平均颗粒流模型，从一维解析验证推进到二维实验验证。首先，针对解析解验证了三个复杂度递增的一维问题：给定速度的高度预测、给定高度的速度预测，以及使用守恒公式对两个场的耦合预测。解耦测试在其他场给定的情况下准确重建了每个场的时空演化。耦合公式在没有给定数据的情况下学习两个场，实现了无量纲单位下平均高度和速度的均方根误差（RMSE）分别为0.043和0.079。超参数敏感性研究评估了网络深度、宽度、配置点密度、学习率和训练轮次的影响。随后，该框架扩展到二维，并针对圆柱形颗粒堆在斜面上坍塌的实验室实验进行了验证，其中TITAN2D提供了数值比较。纯基于物理的训练收敛到平凡零解；通过向损失中添加来自最终堆积剖面的10个稀疏训练点，产生了物理信息、数据辅助的混合框架。峰值流深、深度平均速度、RMSE和润湿面积IoU评估了全局和局部一致性。四个实验案例的全局高度RMSE范围从2.7到6.7毫米，而平均润湿面积IoU范围从69%到81%，表明在不同颗粒质量和斜坡角度的变化下性能一致。
英文摘要
Accurate prediction of avalanche motion is essential for hazard assessment in mountainous terrain. This study develops and evaluates a physics-informed neural network (PINN) framework for the Savage-Hutter model of depth-averaged granular flow, progressing from 1D analytical verification to 2D experimental validation. First, three 1D problems of increasing complexity were verified against the analytical solution: height prediction with prescribed velocity, velocity prediction with prescribed height, and coupled prediction of both fields using the conservative formulation. The decoupled tests accurately reconstructed the spatio-temporal evolution of each field when the other was prescribed. The coupled formulation learned both fields without prescribed data, achieving mean height and velocity RMSEs of 0.043 and 0.079 in non-dimensional units. A hyperparameter sensitivity study evaluated the effects of network depth, width, collocation density, learning rate, and epochs. The framework was then extended to 2D and validated against laboratory experiments of a cylindrical granular pile collapsing on an inclined plane, with TITAN2D providing numerical comparisons. Purely physics-based training converged to the trivial zero solution; augmenting the loss with 10 sparse training points from final deposit profiles produced a physics-informed, data-assisted hybrid framework. Peak flow depth, depth-averaged velocity, RMSE, and wetted-area IoU evaluated global and local agreement. Global height RMSE ranged from 2.7 to 6.7 mm across four experimental cases, while mean wetted-area IoU ranged from 69 to 81 %, demonstrating consistent performance across variations in pile mass and slope angle.
Comments49 pages, 41 figures
