We develop a PyTorch-based Graph Network Simulator (GNS) that learns physics and predicts the flow behavior of particulate and fluid systems. GNS discretizes the domain with nodes representing a collection of material points and the links connecting the nodes representing the local interaction between particles or clusters of particles. The GNS learns the interaction laws through message passing on the graph. GNS has three components: (a) Encoder, which embeds particle information to a latent graph, the edges are learned functions; (b) Processor, which allows data propagation and computes the nodal interactions across steps; and (c) Decoder, which extracts the relevant dynamics (e.g., particle acceleration) from the graph. We introduce physics-inspired simple inductive biases, such as an inertial frame that allows learning algorithms to prioritize one solution (constant gravitational acceleration) over another, reducing learning time. The GNS implementation uses semi-implicit Euler integration to update the next state based on the predicted accelerations. GNS trained on trajectory data is generalizable to predict particle kinematics in complex boundary conditions not seen during training. The trained model accurately predicts within a 5\% error of its associated material point method (MPM) simulation. The predictions are 5,000x faster than traditional MPM simulations (2.5 hours for MPM simulations versus 20 s for GNS simulation of granular flow). GNS surrogates are popular for solving optimization, control, critical-region prediction for in situ viz, and inverse-type problems. The GNS code is available under the open-source MIT license at https://github.com/geoelements/gns.
We present a novel method of using explainability techniques to design physics-aware neural networks. We demonstrate our approach by developing a convolutional neural network (CNN) for solving an inverse problem for shallow subsurface imaging. Although CNNs have gained popularity in recent years across many fields, the development of CNNs remains an art, as there are no clear guidelines regarding the selection of hyperparameters that will yield the best network. While optimization algorithms may be used to select hyperparameters automatically, these methods focus on developing networks with high predictive accuracy while disregarding model explainability (descriptive accuracy). However, the field of Explainable Artificial Intelligence (XAI) addresses the absence of model explainability by providing tools that allow developers to evaluate the internal logic of neural networks. In this study, we use the explainability methods Score-CAM and Deep SHAP to select hyperparameters, such as kernel sizes and network depth, to develop a physics-aware CNN for shallow subsurface imaging. We begin with a relatively deep Encoder-Decoder network, which uses surface wave dispersion images as inputs and generates 2D shear wave velocity subsurface images as outputs. Through model explanations, we ultimately find that a shallow CNN using two convolutional layers with an atypical kernel size of 3x1 yields comparable predictive accuracy but with increased descriptive accuracy. We also show that explainability methods can be used to evaluate the network's complexity and decision-making. We believe this method can be used to develop neural networks with high predictive accuracy while also providing inherent explainability.
An experimental technique is presented to quantify the lateral restraint provided by a geogrid embedded in granular soil at the particle level. Repeated load triaxial tests were done on transparent sand specimens with geosynthetic inclusions simulating geogrids. Particle outlines on laser illuminated planes through the specimens were segmented using a deep learning-based segmentation algorithm. The particle outlines were characterized in terms of Fourier shape descriptors and tracked across sequentially captured images. The accuracy of the particle displacement measurements was validated against Digital Image Correlation (DIC) measurements. In addition, the method's resolution and repeatability is presented. Based on the measured particle displacements and rotations, a state boundary line between probable and improbable particle motions was identified for each test. The size of the zone of probable motions could be used to quantify the lateral restraint provided by the inclusions. Overall, the tests results revealed that the geosynthetic inclusions restricted both particle displacements and rotations. However, the particle displacements were found to be restrained more significantly than the rotations. Finally, a unique relationship was found between the magnitude of the permanent strains of the specimens and the size of the zone of probable motions.
Shear stress history controls the pore pressure response in liquefiable soils. The excess pore pressure does not increase under cyclic loading when shear stress amplitude is lower than the peak prior amplitude -- the shielding effect. Many sophisticated constitutive models fail to capture the shielding effect observed in the cyclic liquefaction experiments. We develop a data-driven machine learning model based on the LSTM neural network to capture the liquefaction response of soils under cyclic loading. The LSTM model is trained on 12 laboratory cyclic simple shear tests on Nevada sand in loose and dense conditions subjected to different cyclic simple shear loading conditions. The LSTM model features include the relative density of soil and the previous stress history to predict the pore water pressure response. The LSTM model successfully replicates the pore pressure response for three cyclic simple test results considering the shielding and density effects.
Graph network-based simulators (GNS) have demonstrated strong potential for learning particle-based physics (such as fluids, deformable solids, and granular flows) while generalizing to unseen geometries due to their inherent inductive biases. However, existing models are typically trained for a single material type and fail to generalize across distinct constitutive behaviors, limiting their applicability in real-world engineering settings. Using granular flows as a running example, we propose a parameter-efficient conditioning mechanism that makes the GNS model adaptive to material parameters. We identify that sensitivity to material properties is concentrated in the early message-passing (MP) layers, a finding we link to the local nature of constitutive models (e.g., Mohr-Coulomb) and their effects on information propagation. We empirically validate this by showing that fine-tuning only the first few (1-5) of 10 MP layers of a pretrained model achieves comparable test performance as compared to fine-tuning the entire network. Building on this insight, we propose a parameter-efficient Feature-wise Linear Modulation (FiLM) conditioning mechanism designed to specifically target these early layers. This approach produces accurate long-term rollouts on unseen, interpolated, or moderately extrapolated values (e.g., up to 2.5 degrees for friction angle and 0.25 kPa for cohesion) when trained exclusively on as few as 12 short simulation trajectories from new materials, representing a 5-fold data reduction compared to a baseline multi-task learning method. Finally, we validate the model's utility by applying it to an inverse problem, successfully identifying unknown cohesion parameters from trajectory data. This approach enables the use of GNS in inverse design and closed-loop control tasks where material properties are treated as design variables.
Accurate simulation of granular flow dynamics is crucial for assessing various geotechnical risks, including landslides and debris flows. Granular flows involve a dynamic rearrangement of particles exhibiting complex transitions from solid-like to fluid-like responses. Traditional continuum and discrete numerical methods are limited by their computational cost in simulating large-scale systems. Statistical or machine learning-based models offer an alternative. Still, they are largely empirical, based on a limited set of parameters. Due to their permutation-dependent learning, traditional machine learning-based models require huge training data to generalize. To resolve these problems, we use a graph neural network, a state-of-the-art machine learning architecture that learns local interactions. Graphs represent the state of dynamically changing granular flows and the interaction laws, such as energy and momentum exchange between grains. We develop a graph neural network-based simulator (GNS) that takes the current state of granular flow and predicts the next state using Euler explicit integration by learning the local interaction laws. We train GNS on different granular trajectories. We then assess the performance of GNS by predicting granular column collapse. GNS accurately predicts flow dynamics for column collapses with different aspect ratios unseen during training. GNS is hundreds of times faster than high-fidelity numerical simulators. The model also generalizes to domains much larger than the training data, handling more than twice the number of particles than it was trained on.