GNS: A generalizable Graph Neural Network-basedsimulator for particulate and fluid modeling
Krishna Kumar, Joseph P. Vantassel
Abstract
Graph Network-based Simulator (GNS) is a framework for developing generalizable, efficient, and accurate machine learning (ML)-based surrogate models for particulate and fluid systems using Graph Neural Networks (GNNs).GNNs are the state-of-the-art geometric deep learning (GDL) that operates on graphs to represent rich relational information (Scarselli et al., 2008), which maps an input graph to an output graph with the same structure but potentially different node, edge, and global feature attributes.The graph network in GNS spans the physical domain with nodes representing an individual or a collection of particles, and the edges connecting the vertices representing the local interaction between particles or clusters of particles.The GNS computes the system dynamics via learned message passing.Figure 1 shows an overview of how GNS learns to simulate n-body dynamics.The GNS has three components: (a) Encoder, which embeds particle information to a latent graph, the edges represent 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.The GNS learns the dynamics, such as momentum and energy exchange, through a form of messages passing (Gilmer et al., 2017), where latent information propagates between nodes via the graph edges.The GNS edge messages ( ′ ← ( , , , )) are a learned linear combination of the interaction forces.The edge messages are aggregated at every node exploiting the principle of superposition ē′ ← ∑ = ′ .The node then encodes the connected edge features and its local features using a neural network: ′ ← ( ē , , ).