CompMoE: Compositional mixture-of-experts neural network for sustainable mix optimization of fiber-reinforced ultra-high-performance concrete

Fiber-reinforced ultra-high-performance concrete (UHPC) exhibits exceptional mechanical properties, yet its high cement content and steel fiber dosage generate a substantial environmental footprint. This study proposes a Compositional Mixture-of-Experts (CompMoE) neural network for predicting the 28-day compressive strength of fiber-reinforced UHPC and for multi-objective sustainable mix optimization. CompMoE introduces three novel mechanisms that exploit the physics-informed subsystem decomposition of UHPC constituents, including Compositional Attention Gating (CAG), which models interactions among five material subsystems through cross-attention, a Physics-Informed Residual Path (PIRP) that decomposes the prediction into a linear component and a nonlinear expert-routed residual, and Hierarchical Expert Diversity (HED), which assigns experts of varying architectural complexity to different compositional regimes. To the best of the authors’ knowledge, this is the first mixture-of-experts surrogate that embeds the compositional structure of concrete mix design directly into the network topology. On the test set, the CompMoE model achieved a coefficient of variation ( 𝑅 2 ) of 0.854, mean absolute error (MAE) of 9.05 MPa, and root mean squared error (RMSE) of 12.76 MPa, outperforming baseline models evaluated on the identical data split. The trained surrogate is coupled with the non-dominated sorting genetic algorithm III (NSGA-III) multi-objective optimization, which resulted in Pareto optimal fiber-reinforced UHPC mixes that simultaneously balance compressive strength, embodied CO 2 emissions, and material cost. From this Pareto front, a single preferred mix can be selected through multi-criteria decision-making (MCDM) by assigning relative weights to the three objectives. The balanced knee-point mix attains a predicted compressive strength of 203 MPa with a 28% reduction in embodied CO 2 and a 54% reduction in material cost relative to the means of the database. The complete framework has been deployed as an interactive web-based prediction and optimization tool.