| --- |
| license: mit |
| tags: |
| - graph-neural-network |
| - surrogate-model |
| - finite-element-method |
| - structural-mechanics |
| datasets: |
| - Junghunl/Deformed-ABC |
| --- |
| |
| # Global Weight Deep Equilibrium Attention |
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|
| This is a Global Weight Deep Equilibrium Attention model trained on the [DeformedABC](https://huggingface.co/datasets/Junghunl/Deformed-ABC) 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](https://huggingface.co/datasets/Junghunl/Deformed-ABC). |
|
|
| ## 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. |
