Inverse analysis of granular flows using differentiable graph neural network simulator

Abstract

Inverse problems in granular flows, such as landslides and debris flows, involve estimating material parameters or boundary conditions based on a target runout profile. Traditional high-fidelity simulators for these inverse problems are computationally expensive, restricting the number of possible simulations. These simulators are also non-differentiable, making efficient gradient-based optimization methods for high-dimensional spaces inapplicable. Machine learning-based surrogate models offer computational efficiency and differentiability. However, they often struggle to generalize beyond their training data due to relying 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) that combines 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 timestep, given the current state. The differentiable GNS demonstrates 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 solves inverse problems with orders of magnitude faster convergence than the conventional gradient-based optimization approach using finite difference.