Inverse problems in granular flows, such as landslides and debris flows, involve estimating material parameters or boundary conditions based on target runout profile. Traditional high-fidelity simulators for these inverse problems are computationally demanding, restricting the number of simulations possible. Additionally, their non-differentiable nature makes gradient-based optimization methods, known for their efficiency in high-dimensional problems, inapplicable. While machine learning-based surrogate models offer computational efficiency and differentiability, they often struggle to generalize beyond their training data due to their reliance on low-dimensional input-output mappings that fail to capture the complete physics of granular flows. We propose a novel differentiable graph neural network simulator (GNS) by combining reverse mode automatic differentiation of graph neural networks with gradient-based optimization for solving inverse problems. GNS learns the dynamics of granular flow by representing the system as a graph and predicts the evolution of the graph at the next time step, given the current state. The differentiable GNS shows optimization capabilities beyond the training data. We demonstrate the effectiveness of our method for inverse estimation across single and multi-parameter optimization problems, including evaluating material properties and boundary conditions for a target runout distance and designing baffle locations to limit a landslide runout. Our proposed differentiable GNS framework offers an orders of magnitude faster solution to these inverse problems than the conventional finite difference approach to gradient-based optimization.

翻译：颗粒流（如滑坡和泥石流）中的反演问题涉及根据目标堆积剖面估算材料参数或边界条件。传统高保真模拟器在解决这类反演问题时计算成本高昂，限制了可执行的模拟次数。此外，其不可微特性使得以梯度优化方法（在高维问题中效率显著）无法适用。基于机器学习的代理模型虽具备计算高效性和可微性，但由于依赖无法完整刻画颗粒流物理过程的低维输入-输出映射，常难以泛化至训练数据之外。我们提出一种新型可微图神经网络模拟器（GNS），通过结合图神经网络的反向模式自动微分与基于梯度的优化方法来解决反演问题。GNS将系统表示为图结构来学习颗粒流动力学，并根据当前状态预测下一时刻的图演化。可微GNS展现出超越训练数据的优化能力。我们通过单参数和多参数优化问题验证了该方法在反演估计中的有效性，包括基于目标堆积距离评估材料属性与边界条件，以及设计挡板位置以限制滑坡堆积范围。与传统的基于有限差分法的梯度优化方法相比，我们提出的可微GNS框架在求解此类反演问题时的速度提升了数个数量级。