Inverse analysis of granular flows using differentiable graph neural network simulator

TL;DR

This work addresses the computational and differentiability barriers in inverse modeling of granular flows by introducing a differentiable graph neural network simulator (GNS) that supports gradient-based optimization via reverse-mode automatic differentiation. The approach trains a graph-based forward model on MPM-generated data and leverages gradient checkpointing to enable long 3D rollouts, allowing efficient solving of single- and multi-parameter inverse problems as well as barrier-design tasks. Key results include accurate estimation of friction angle $\phi$ with runout errors under 3.5%, recovery of initial layer velocities with a mean-squared error of $8.70\times 10^{-4}$, and successful baffle optimization with a loss as low as $4.68\times 10^{-6}$, all achieved with substantial speedups (up to ~151×) over finite-difference gradient methods. The framework demonstrates generalization beyond training distributions and provides a practical path for rapid, data-driven inverse analysis and design in granular hazard mitigation.

Abstract

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.

Figures (23)

• Figure 1: Overview of the research.
• Figure 1: Evolution of material point flow with normalized time for GNS and MPM for the short column with a = 0.5: (a) $\phi=21 \degree$, (b) $\phi=42 \degree$. The color represents the magnitude of the displacement. Each row corresponds to a column before the flow initiation, $t/\tau_c=1.0$, $t/\tau_c=2.5$, and the final deposit at the last timestep.
• Figure 1: An example of training data for 2D GNS (Flow2D).
• Figure 2: Illustrative representation of inverse problems in granular media: (a) single parameter inverse of determining material property based on the final runout, (b) evaluating the initial boundary conditions (initial velocity) based on the final runout profile, and (c) optimizing the location of barriers based on the target runout distribution.
• Figure 2: Evolution of flow interacting with baffles for GNS and MPM from initial condition to the final deposit. The simulation domain is $1.8 \times 0.8 \times 1.8 \ m$, and the initial geometry of the granular mass is $0.35\times0.25\times1.4 \ m$. The barrier size is $0.15\times0.30\times0.15 \ m$. The center location of the three baffles in the first row is at $(x=0.76, \ z=0.36) \ m$, $(x=0.76, \ z=1.00) \ m$, and $(x=0.76, \ z=1.64) \ m$, and the two baffles in the second row are at $(x=1.26, \ z=0.68) \ m$ and $(x=1.26, \ z=1.32) \ m$.