Global_Weight_Deep_Equilibrium_Attention

Global Weight Deep Equilibrium Attention

This is a Global Weight Deep Equilibrium Attention model trained on the DeformedABC dataset for predicting nodal displacements in linear-elastic FEM problems.

Model description

The model constructs a sparse global weight matrix from mesh connectivity via the direct stiffness method, introducing an inductive bias toward a diagonally dominant structure to mitigate over-smoothing. The resulting matrix is iteratively applied until convergence, allowing information to propagate globally without stacking additional message-passing layers. The iterative process is formulated as a Deep Equilibrium Model (DEQ) to reduce memory consumption, while Anderson acceleration is employed to accelerate convergence.

Intended uses & limitations

This model is intended for predicting nodal displacements in linear-elastic, mesh-based structural mechanics problems with geometries similar to those in DeformedABC. It has not been validated for nonlinear material behavior, other physical domains (e.g., fluid dynamics, thermal), or geometries substantially outside the training distribution. Predictions should not be used as a substitute for validated FEM solvers in safety-critical design decisions without further verification.

Training data

Trained on DeformedABC.

Training procedure

Full training details (optimizer, learning rate schedule, hardware, etc.) are provided in the Methods section and Supplementary Information of the associated paper.

Evaluation results

Full evaluation results across all test sets are reported in the Results section and Supplementary Data of the associated paper.

Source code

https://github.com/AiPEX-Lab/GDEA_and_Deformed_ABC

Citation

Currently, this paper is under review. We will upload the final version as soon as it is published.