Accelerating Heterogeneous Multiscale Simulations of Advanced Materials Properties with Graph‐Based Clustering

Maxime Vassaux (1) , Krishnakumar Gopalakrishnan (1) , Robert Sinclair (1) , Robin Richardson (1) , Peter Coveney (1)

1 Centre for Computational Science

Heterogeneous multiscale methods (HMM) capable of simulating asynchronously multiple scales concurrently are now tractable with the advent of exascale supercomputers. However, naive implementations display a large number of redundancies and are very costly. The macroscale model typically requires computations of a large number of very similar microscale simulations. In hierarchical methods, this is barely an issue as phenomenological constitutive models are inexpensive. However, when microscale simulations require, for example, high-dimensional molecular dynamics (MD) or finite element (FE) simulations, redundancy must be avoided. A clustering algorithm suited for HMM workflows is proposed that automatically sorts and eliminates redundant microscale simulations. The algorithm features a combination of splines to render a low-dimension representation of the parameter configurations of microscale simulations and a graph network representation based on their similarity. The algorithm enables the clustering of similar parameter configurations into a single one in order to reduce to a minimum the number of microscale simulations required. An implementation of the algorithm in the context of an HMM application coupling FE and MD to predict the chemically specific mechanical behavior of polymer-graphene nanocomposites. The algorithm furnishes a threefold reduction of the computational effort with limited loss of accuracy

Mots clés: multiscale modelling; model reduction; unsupervised learning; clustering; spline; graph theory; multiscale modelling

Domaines: Mécanique des matériaux [physics.class-ph]; Modélisation et simulation

Maxime Vassaux, Krishnakumar Gopalakrishnan, Robert Sinclair, Robin Richardson, Peter Coveney. Accelerating Heterogeneous Multiscale Simulations of Advanced Materials Properties with Graph‐Based Clustering. Advanced Theory and Simulations, 2021, 4 (2), pp.2000234. ⟨10.1002/adts.202000234⟩. ⟨hal-03452472⟩