An Interpretable Graph-Based Multi-Task Framework for Classroom Acoustic Quality Prediction and Design Exploration

Classroom acoustic quality is strongly influenced by spatial configuration, source–receiver relationships, and node-specific acoustic properties, making rapid and interpretable prediction valuable for building-acoustic assessment and design. This study develops an interpretable graph-based multi-task learning framework for classroom acoustic quality prediction and design-space exploration. A classroom configuration is represented as a 14-node spatial graph, and a graph convolutional network (GCN) learns a shared representation for jointly predicting six Strength (G), six Clarity (C50), and three Speech Transmission Index (STI) indicators. The framework was evaluated against a multilayer perceptron, random forest, XGBoost, graph attention network, and equivariant graph neural network using 10,816 simulated samples and five random seeds. The GCN attained a mean absolute error of 0.10112, an RMSE of 0.14802, and an R2 of 0.99967. These scores are only marginally better than those of the multilayer perceptron (MAE = 0.10138). The principal contribution is therefore not a large gain in accuracy, but a spatial graph representation that preserves source–receiver–surface relationships, supports node- and interaction-level interpretation, and serves as a surrogate for constrained design-space exploration. Explainability analysis showed that receiver-to-node distances accounted for 67.1% of the aggregated SHAP attribution and that node 2 was the most influential spatial component. A GCN ensemble combined with constrained NSGA-II was then used to explore surrogate-optimal candidates within the training bounds. The resulting configurations require independent verification before use as engineering solutions.