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.

Alpha-Pinene Alleviates Motor Activity in Animal Model of Huntington's Disease via Enhancing Antioxidant Capacity.

Huntington's disease (HD) is a progressive, neurodegenerative, and inherited disease. Antioxidants have been shown to be effective in slowing disease progression in animal models of HD and are under investigation in human clinical trials. α-pinene, a member of the monoterpene class, has been shown to exert antioxidant activity. Therefore, this study aimed to investigate the impact of α-pinene on animal model of HD. Thirty-two male Wistar rats received 3-Nitropropionic acid (3-NP) for induction of the disease model or treated with α-pinene + 3-NP in different groups. Motor skill, and biochemical evaluations to detect oxidant/antioxidant markers in rat cortex and striatum were performed in all groups. We found that α-pinene significantly improved 3-NP-induced changes in the body weight, rotarod activity, time taken to cross the narrow beam, and locomotor activity. Biochemical analysis revealed that α-pinene significantly decreased the 3NP-induced elevation in oxidant markers, nitrite, and malondialdehyde in both cortex and striatum. In addition, α-pinene counteracted the 3-NP-induced fall in antioxidant enzymes, including superoxide dismutase, catalase, and glutathione in the cortex and striatum. In conclusion, we found that α-pinene prevented the motor dysfunction induced by 3-NP in the animal model of Huntington's disease. Oxidants-antioxidant balance might be involved in the protective effect of α-pinene.