Finite-element-assisted interpretable graph attention learning for high-fidelity prediction of mass transport in fibrin biomaterials

Abstract

Abstract Accurate prediction of spatial concentration fields within biomaterials is important for mass-transfer analysis and computational modeling of transport processes. This study develops an interpretable data-driven framework for spatially resolved mass-transport prediction by coupling finite element mass-transfer simulations with an attention-based graph neural network (ATGNN). A fibrin biomaterial matrix intended for tissue-regeneration applications was modeled together with adjacent nerve tissue and surrounding medium. Diffusion, reversible binding, dissolution, and enzyme-mediated matrix degradation were incorporated into the numerical model, and more than 26,000 concentration samples were extracted from the biomaterial domain in cylindrical coordinates. Following the train–test partition, LOF-based outlier screening and Min–Max normalization were fitted using the training data only, while the independent test set remained unfiltered. ATGNN, Gaussian process regression, multilayer perceptron, and extreme gradient boosting models were optimized by grid search and evaluated using an 80:20 train-test split and five-fold cross-validation. ATGNN achieved the highest predictive accuracy under the conventional random-split evaluation, while additional spatially blocked and isolated-region validation was used to assess sensitivity to spatial dependence, yielding a test R² of 0.99903, RMSE of 2.33 × 10⁻⁶, MAE of 1.16 × 10⁻⁶, and MAPE of 0.00174%. Its predictions closely reproduced the finite element concentration field and remained stable across validation folds. Graph-attention coefficients and SHAP analysis provided complementary model-based diagnostics of the spatial response, although the two measures were not assumed to provide identical feature rankings or physical interpretations. The proposed framework demonstrates that attention-based graph learning can provide high-fidelity surrogate predictions of the FEM-generated concentration field together with complementary model-based diagnostics of the learned spatial response. The findings are restricted to the simulated physical conditions investigated here and should not be interpreted as evidence of therapeutic efficacy, tissue-regeneration benefit, or clinical performance.