Browsing by Subject "Gradient-based optimization"

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Forward and inverse modeling of granular flows using differentiable graph neural network simulator
(2024-05) Choi, Yongjin; Kumar, Krishna (Engineering geologist); Mrinal Sen; Berkin Dortdivanlioglu; Ellen M Rathje
Granular flows such as landslides can cause extensive damage to infrastructure and pose significant hazards. Accurate forward and inverse modeling granular flows are critical for developing effective risk mitigation strategies and designs. However, conventional high-fidelity forward simulators, like the material point method (MPM), or discrete element method (DEM), are computationally intensive, which limits their ability to efficiently solve inverse problems like parameter optimization or optimal design. 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. This study introduces a differentiable graph neural network simulator (GNS) as a generalizable surrogate model for high-fidelity simulators to accelerate forward simulation for granular flows. Graphs represent the state of dynamically changing granular flows and their interactions. By learning the interaction law that governs the granular flow behavior, GNS is generalizable to predict granular flow dynamics not seen during training. It also shows great computation efficiency compared to the high-fidelity model (CB-Geo MPM) by showing up to 2000x speed up. We then propose a novel approach for solving inverse problems by combining differentiable GNS with gradient-based optimization leveraging reverse mode automatic differentiation (AD) of GNNs. The AD-GNS solves various inverse problems in granular flows. Besides the forward and inverse modeling of granular flows, this study addresses a machine learning approach to predicting pore water pressure response in liquefiable sands under cyclic loading. The pore pressure response in liquefiable sands is largely affected by the history of the cyclic shear stress. When the amplitude of cyclic shear stress is lower than the previous peak amplitude, excess pore pressure does not increase—an effect known as shielding. Many advanced constitutive models do not accurately capture this shielding effect observed in cyclic simple shear tests. We develop a data-driven machine learning model based on the long short-term memory (LSTM) neural network to capture the liquefaction response of soils under cyclic loading. We train the LSTM model on the data from 12 laboratory cyclic simple shear tests performed on Nevada sand samples with varying relative densities and subjected to different cyclic simple shear loading conditions. The model inputs include the soil's relative density and previous stress history to predict the pore water pressure response. The LSTM model successfully replicated the pore pressure response for three cyclic simple shear test cases, accounting for the shielding and density effects.