Differentiable Graph Neural Network Simulator for the Back-Analysis of Post-Liquefaction Residual Strength from Flow Failure Runout

Abstract: This study introduces Differentiable Graph Neural Network Simulators (Diff-GNS) as a physics-informed and automated framework for estimating post-liquefaction residual strengths ($S_r$). Traditional approaches to estimate $S_r$ rely on simplified physics, manual iterations, and assumptions about runout development. Diff-GNS overcomes these limitations by integrating a Graph Neural Network Simulator (GNS) that simulates granular flows, with gradient-based optimization through automatic differentiation. GNS accelerates forward runout simulations that are otherwise computationally intensive with conventional numerical methods, while gradient-based optimization automates the inversion to back-calculate $S_r$. The GNS is trained on simulations with the material point method on geometries informed by case-history runout failures, enabling focused learning of realistic runout mechanisms and the ability to simulate slopes across small and large scales. The Diff-GNS framework is validated using two well-documented liquefaction-induced flow failure case histories: the Lower San Fernando dam and La Marquesa dam. In the two cases, the inferred $S_r$ agrees closely with published estimates and reproduces physically consistent runout behaviors. The framework also has the ability to jointly infer multiple interacting parameters, extending beyond single-parameter back-analyses. By embedding the physics of runout processes, minimizing manual intervention, and accelerating the inversion process to estimate $S_r$, Diff-GNS provides an efficient, reproducible, and physically grounded approach for geotechnical analysis of liquefaction-induced flow failures.