HEStacked-FSML: Data-Efficient Prediction of Nano-Modified Concrete Compressive Strength

Abstract The necessity of precise prediction of compressive strength in nano-modified concrete is of great essence in promoting sustainable and high-performance building materials. Nevertheless, the traditional empirical and machine learning (ML) models are likely to fail at generalization in low-data scenarios, due especially to the highly nonlinear nature of the behavior that is induced by nanomaterial additives. This paper will suggest a new type of hybrid-based predictive model that can overcome these drawbacks by employing hybrid ensemble stacking (HEStacked) and few-shot meta-learning using the Reptile algorithm (FSML-Reptile). Training and testing of the models were conducted using a carefully curated data set consisting of 90 nano-concrete mixes and rigorous 10-fold cross-validation and hold-out testing. The FSML-Reptile model achieved a mean squared error (MSE) of 19.30 and a coefficient of determination ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R squared" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> ) of 0.963, demonstrating improved performance compared with conventional ML models such as extreme gradient boosting (XGBoost) (MSE = 34.67 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R squared equals 0.889" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.889</mml:mn> </mml:math> ). HEStacked also demonstrated strong performance (MSE = 23.13 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R squared equals 0.953" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.953</mml:mn> </mml:math> ), confirming the robustness of ensemble learning under limited-data regimes. Statistical significance was established via paired <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="t" display="inline" overflow="scroll"> <mml:mi>t</mml:mi> </mml:math> -tests, validating the superiority of FSML-Reptile over HEStacked ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p less than 0.05" display="inline" overflow="scroll"> <mml:mi>p</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0.05</mml:mn> </mml:math> ) and conventional models ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p much less than 0.01" display="inline" overflow="scroll"> <mml:mi>p</mml:mi> <mml:mo>≪</mml:mo> <mml:mn>0.01</mml:mn> </mml:math> ). Beyond predictive accuracy, shapley additive explanations (SHAP)-based interpretability provided an analysis of how cement, fine aggregate, and water-to-cement ratio contributed most to the results, and the subtlety of the role of nanomaterials was also quantified. The framework proposed could enable rapid and data-efficient mix development, minimizing the need for numerous laboratory tests and aligning with the concept of a sustainable economy. These findings reinforce that meta-ensemble learning may revolutionize the development of intelligent materials in civil engineering practices.