Mesh-based GNN surrogates for time-independent PDEs.

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of requiring long-range exchange of information across the computational domain for obtaining accurate predictions. In the context of graph neural networks (GNNs), this calls for deeper networks, which, in turn, may compromise or slow down the training process. In this work, we present two GNN architectures to overcome this challenge-the edge augmented GNN and the multi-GNN. We show that both these networks perform significantly better than baseline methods, such as MeshGraphNets, when applied to time-independent solid mechanics problems. Furthermore, the proposed architectures generalize well to unseen domains, boundary conditions, and materials. Here, the treatment of variable domains is facilitated by a novel coordinate transformation that enables rotation and translation invariance. By broadening the range of problems that neural operators based on graph neural networks can tackle, this paper provides the groundwork for their application to complex scientific and industrial settings.

Nest signature changes throughout colony cycle and after social parasite invasion in social wasps.

Social insects recognize their nestmates by means of a cuticular hydrocarbon signature shared by colony members, but how nest signature changes across time has been rarely tested in longitudinal studies and in the field. In social wasps, the chemical signature is also deposited on the nest surface, where it is used by newly emerged wasps as a reference to learn their colony odor. Here, we investigate the temporal variations of the chemical signature that wasps have deposited on their nests. We followed the fate of the colonies of the social paper wasp Polistes biglumis in their natural environment from colony foundation to decline. Because some colonies were invaded by the social parasite Polistes atrimandibularis, we also tested the effects of social parasites on the nest signature. We observed that, as the season progresses, the nest signature changed; the overall abundance of hydrocarbons as well as the proportion of longer-chain and branched hydrocarbons increased. Where present, social parasites altered the host-nest signature qualitatively (adding parasite-specific alkenes) and quantitatively (by interfering with the increase in overall hydrocarbon abundance). Our results show that 1) colony odor is highly dynamic both in colonies controlled by legitimate foundresses and in those controlled by social parasites; 2) emerged offspring contribute little to colony signature, if at all, in comparison to foundresses; and 3) social parasites, that later mimic host signature, initially mark host nests with species-specific hydrocarbons. This study implies that important updating of the neural template used in nestmate recognition should occur in social insects.