Solving inverse problems using differentiable graph neural network simulator

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.

This DesignSafe repository contains data required to run the inverse analysis for our three demonstration cases (`inverse_friction`, `inverse_velocity`, `inverse_barrier`). Each includes GNS models (along with their metadata), inverse analysis configurations, and ground truth data for optimization targets. To run the inverse analysis with these data, please refer to our differentiable GNS code provided in the GitHub repository "Related Work (https://github.com/geoelements/gns-inverse-examples)".

针对滑坡与泥石流等颗粒流反问题，需基于目标流距剖面估算材料参数或边界条件。传统高保真模拟器求解此类反问题时计算开销高昂，限制了可开展的模拟次数；同时其不可微分的特性，使得在高维问题中表现高效的基于梯度的优化方法无法适用。基于机器学习的代理模型虽具备计算效率与可微分性，但因依赖无法捕捉颗粒流完整物理机制的低维输入输出映射，往往难以在训练数据之外实现泛化。
为此，我们提出一种新型可微分图神经网络模拟器（GNS），将图神经网络的反向模式自动微分与基于梯度的优化相结合以求解反问题。该模拟器将系统表征为图结构，基于当前状态学习颗粒流动力学并预测图在下一时间步的演化。此可微分GNS具备超出训练数据的优化能力。我们在单参数与多参数优化任务中验证了该方法的反演有效性，包括针对目标流距评估材料属性与边界条件，以及设计挡板位置以限制滑坡流距。相较于传统基于梯度优化的有限差分方法，所提可微分GNS框架求解此类反问题的速度提升可达数个数量级。

本DesignSafe仓库包含我们三个演示案例（`inverse_friction`、`inverse_velocity`、`inverse_barrier`）开展反分析所需的全部数据。每个案例均包含GNS模型（及其元数据）、反分析配置文件与优化目标的真值数据。如需使用这些数据开展反分析，请参考我们在GitHub仓库"Related Work (https://github.com/geoelements/gns-inverse-examples)"中提供的可微分GNS代码。