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

TL;DR

This work addresses the challenge of back-analyzing post-liquefaction residual strength $S_r$ by introducing Diff-GNS, a Differentiable Graph Neural Network Simulator that couples a learned GNS for granular flow with gradient-based inversion through automatic differentiation. Trained on MPM-based simulations and informed by case-history geometries, two scale-specific GNS models enable efficient, physics-consistent back-analyses and multi-parameter inversions (e.g., $S_r$ and friction angles) for slopes spanning tens to hundreds of meters. The framework is validated on Lower San Fernando and La Marquesa dam failures, yielding $S_r$ and related parameters in close agreement with literature and reproducing key runout features, while offering substantial speedups over high-fidelity MPM. Altogether, Diff-GNS provides a reproducible, automated, and scalable tool for geotechnical back-analysis of liquefaction-induced flow failures with potential to streamline design and assessment workflows.

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.

Figures (17)

• Figure 1: Conceptual illustration of (a) the Kinetics method (after olson2001liquefaction_kinetics) and (b) the Zero Inertial Factor (ZIF) method (after kramer2015empirical_zif) for back-analysis of post-liquefaction residual strength $S_r$.
• Figure 2: Schematic of the Graph Neural Network Simulator (GNS) architecture.
• Figure 3: Differentiable graph neural network simulator (Diff-GNS)-based framework for solving inverse problems in granular flows (after choi2025differentiable_multilayers). Given the initial condition and parameters $\boldsymbol{\theta}$ for a slope system at time $0$, $\hat{\mathbf{X}}_0(\boldsymbol{\theta})$, Diff-GNS runs the forward simulation and generates $\hat{\mathbf{X}}_t(\boldsymbol{\theta})$, granular flow state at time $t$. It then evaluates the loss compared to $X_t^{\text{obs}}$, the observed state. $\boldsymbol{\theta}$ is updated using gradient-based optimization with optional given constraints.
• Figure 4: Scale-specific separate GNS training strategy. A single GNS cannot efficiently accommodate the wide range of slope dimensions due to resolution and memory constraints: large slopes require an excessive number of material points, exceeding the GPU device's memory limits, while small slopes demand finer material point resolution than a large-scale model can provide. We train separate GNS models for large and small-scale slopes, each with its own representative material point and cell resolution of the underlying MPM training data.
• Figure 5: Pre-failure configurations to generate training data for the large-scale GNS. Dimensions for training the small-scale GNS are scaled down by 0.25. The figures are not in scale. (a), (b), and (c) configurations are informed by the case histories listed in \ref{['table:appendix_dam_dimensions']} in \ref{['sec:appendix_training_data']}. Examples are included as figure insets (i.e., North Dike of Wachusett dam, Sgurigrad dam, La Palma dam). (d) and (e) are additional configurations to complement the GNS learning process (see discussions in the text). The numbers in square brackets indicate the indices of the polygon vertices. Solid lines connecting these vertices define the overall shape of granular masses, with brown solid lines denoting the bedrock boundary. The x and y coordinates of the polygon vertices are randomly perturbed; the bars at each vertex represent the perturbation. \ref{['table:appendix_training_data']} in \ref{['sec:appendix_training_data']} provides the variation range for the corresponding vertex indices. Strength properties for Soil 1, Soil 2, and Soil 3 are drawn from distributions in \ref{['table:training_datasets']}. In subfigures a-c, the inscribed figures are examples of case histories that we design to emulate. In subfigure e, the black arrow shows the randomly imposed initial velocity.