Learnable graph network simulator for modeling granular flows

Abstract

Regional-scale landslide modeling is critical to assess the runout risk on communities. Landslide runout predictions are modeled using mesh-free methods like the Material Point Method (MPM), but such methods are computationally expensive. Uncertainty quantification with thousands of MPM simulations under different loading and boundary conditions is infeasible. An alternative to conventional simulation techniques is to develop differentiable simulators, which learn the physics of granular-flow dynamics from MPM simulations by merely observing the particle position. The learned simulator then predicts the flow behavior with almost the same accuracy as an MPM simulation which uses complex physics. This study develops a Machine Learning (ML)-based Graph Network Simulators (GNS) that operates on graphs to learn the physics of granular dynamics and predict large-deformation flow on inclined planes. The graph network spans the soil 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 physics of granular dynamics, such as momentum and energy exchange, through message passing on the graph. GNS has three components: (a) Encoder, 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. We train the GNS model on small-scale granular collapse and collision problems with 1000 particles for 20 Million steps on Nvidia A100 GPUs. The trained model then accurately predicts (within 5% of error compared to MPM simulations) the granular flow on an inclined plane with 10x the number of particles during its training. GNS models support spatial and permutation equivariance; GNS models are generalizable to simulate different material properties and predict granular flow behavior outside their training domain. The GNS predictions are The GNS code is implemented using PyTorch and is available under the MIT license at https://github.com/geoelements/gns. Hamiltonian GNNs capture the physical interactions between bodies as “message passing” on graphs. These messages are like forces and node features represent Newton’s law of motion. GNNs convert high-dimensional interactions into low-dimensional functional representations (internal functions of edges, vertices, and global variables φe,φv,φu) ideal for Symbolic Regression. We derive analytical expressions for the internal functions (messages) using a mutation-based evolutionary algorithm. We successfully derived the expression of interaction force between spheres.