Hybrid AI model finds balanced mix for marine coral concrete

A hybrid artificial-intelligence model identified a computationally optimized blend of silica fume and nano-silica for coral aggregate concrete, with the proposed mix balancing mechanical strength against water seepage. The predicted compromise contains 8.0% silica fume and 2.1% nano-silica and is estimated to produce 28-day compressive strength of 57.61 megapascals, splitting tensile strength of 6.48 megapascals and a water seepage height of 7.16 millimetres. These are model predictions rather than independently tested outcomes: the researchers did not experimentally validate the optimized formulation, and the underlying study used a fixed water-to-binder ratio without evaluating long-term durability.

The work addresses a practical materials problem for island and reef construction in the South China Sea, where locally available coral debris is used to make concrete mixed with seawater. Coral aggregate can reduce reliance on imported material, but its high porosity and weak interfacial transition zone—the boundary between aggregate and cement paste—can limit strength and increase permeability. The research team combined response surface methodology, which represents material behavior with explicit polynomial equations, with a fully connected neural network that can learn more flexible nonlinear relationships. The central aim was to preserve the statistical model’s broad, interpretable trends while using neural-network training to correct local deviations.

Because laboratory testing of concrete is expensive, the analysis began with a small dataset: 28 unique mixes from a two-factor full-factorial experiment. Silica fume content ranged from 0% to 12%, while nano-silica ranged from 0% to 3%. The responses were 28-day compressive strength, splitting tensile strength and water seepage height after seawater curing. The center-point formulation, containing 8% silica fume and 2% nano-silica, had been tested in triplicate, and the mean response was used in the machine-learning dataset to avoid treating replicates as independent samples. Response surface analysis and analysis of variance used 30 observations in total, comprising the 28 unique mixes and two additional replicate center-point tests.

The researchers compared quadratic, cubic and quartic response surface models. Cubic equations were selected for all three properties because they provided the strongest balance between fit and prediction. Their coefficients of determination were 0.9294 for compressive strength, 0.9434 for splitting tensile strength and 0.9367 for water seepage height, with predicted R² values of 0.8085, 0.8462 and 0.8336, respectively. Higher-order quartic models slightly increased ordinary fit for some responses but reduced predicted R², indicating overfitting. The cubic models were considered globally useful for describing the combined and higher-order effects of the two supplementary cementitious materials, although the model terms and data do not by themselves establish a physical mechanism.

To give the neural network a broader starting point, the team generated virtual formulations from the response surface equations. Latin hypercube sampling produced 600 points across silica-fume contents of 6% to 10% and nano-silica contents of 0% to 3%, followed by 300 additional points in the higher-performance region where nano-silica was between 1.5% and 2.5%. Values were rounded to practical increments of 0.5 percentage point for silica fume and 0.1 percentage point for nano-silica. After duplicate removal, 462 virtual samples remained. These were not new laboratory measurements; they were computational outputs of the fitted polynomial models and therefore inherited any errors in those models.

The fully connected network expanded the two input variables into five normalized polynomial features and passed them through hidden layers of 64, 32 and 16 neurons. Rectified-linear-unit activation, a 0.2 dropout rate, L2 weight decay and early stopping were used to limit overfitting. Performance was assessed through fivefold cross-validation on the 28 unique experimental mixes, with 22 or 23 training observations in each fold. Preprocessing parameters were fitted only on each fold’s training data. The hybrid procedure pre-trained a fresh network on 462 response-surface-generated samples and then fine-tuned it on the real data from that fold, allowing every prediction reported for the hybrid to remain out of fold.

Standalone neural networks produced out-of-fold R² values of 0.8416 for compressive strength, 0.8338 for splitting tensile strength and 0.8131 for water seepage height. They outperformed random forest, support vector regression and Gaussian process regression, although residuals showed enough dispersion to indicate instability in the small-sample setting. Support vector regression performed best among the three conventional alternatives, with R² values from 0.6802 to 0.8088; random forest ranked last, with R² as low as 0.4000. Adding response-surface pre-training raised the hybrid model’s R² to 0.9035, 0.8657 and 0.8862 for the three responses. An ablation comparison, in which the hybrid and standalone neural network otherwise shared the same architecture and training settings, linked the improvement specifically to pre-training: root mean square error fell by 22.0% for compressive strength, 10.1% for splitting tensile strength and 22.0% for seepage height.

The trained hybrid model was then used to predict 775 candidate formulations defined by engineering-scale increments: silica fume from 0% to 12% in 0.5-point steps and nano-silica from 0% to 3% in 0.1-point steps. Maximizing compressive strength alone selected 7.0% silica fume and 2.2% nano-silica, whereas minimizing water seepage selected 9.0% silica fume and 2.0% nano-silica. This shift exposed a trade-off in the modeled responses. The researchers attributed it to a difference between the responses of the pore network and those of bulk mechanical properties: in their interpretation, silica fume subdivides larger capillary pores, while nano-silica fills smaller voids and supplies nucleation sites for hydration products. The original experimental work also reported that excessive nano-silica could agglomerate, impair dispersion and introduce microcracks at the interfacial transition zone.

Non-dominated sorting identified a Pareto set of formulations for simultaneously maximizing compressive and splitting tensile strength while minimizing water seepage. An equally weighted geometric-mean desirability function was used to select a compromise without assigning one engineering priority over another. The resulting 8.0% silica-fume and 2.1% nano-silica formulation received an overall desirability of 0.993 and sat near the knee of the Pareto front. Its proximity to the experimentally observed center-point optimum of 8% and 2% provides indirect consistency with the source dataset, but it is not independent validation of the hybrid model. The researchers explicitly identify the principal limitations: the optimized mix remains untested, the polynomial surrogate can transmit bias into pre-training, the water-to-binder ratio was fixed, and long-term marine durability was outside the study. Future work would need experimental confirmation and broader design variables, including aggregate gradation and time-dependent performance.

Subject of Research: Small-sample machine-learning optimization of silica-fume and nano-silica modified coral aggregate concrete

Article Title: Hybrid RSM-FCNN model for multi-objective optimization of coral aggregate concrete modified with silica fume and nano-silica

Article References: Su, S., Wang, Q., Wu, J., Liu, Z., Zhao, J., & Zhang, Y. (2026). Hybrid RSM-FCNN model for multi-objective optimization of coral aggregate concrete modified with silica fume and nano-silica. Results in Engineering, 32, Article 113600. https://doi.org/10.1016/j.rineng.2026.113600

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113600

Keywords: coral aggregate concrete, silica fume, nano-silica, neural networks, response surface methodology, multi-objective optimization, marine construction materials, permeability, compressive strength, transfer learning, Hybrid, RSM-FCNN