The paper introduces a novel framework integrating Physics-Informed constraints with Message Passing Neural Networks (PI-MPNN) for geometrically irregular structural systems. It encodes the governing equations of solid mechanics directly into the message passing operations of graph neural networks, enabling native handling of arbitrary geometric complexity, embedded physical constraints ensuring physically consistent predictions, and generalization across different structural topologies.
Key findings
PI-MPNN enables handling of arbitrary geometric complexity without regular grid constraints.
Embedded physical constraints ensure physically consistent predictions.
Generalization is achieved across different structural topologies.
The method is validated through benchmark problems in linear elasticity, materially nonlinear analysis, and dynamic structural response.
Limitations & open questions
The paper does not discuss the scalability of the proposed method for very large structural systems.
The generalization performance on unseen geometries needs further extensive testing.