Interpretable machine learning predicts strength of heat-storing microcapsule concrete in external lab tests

Concrete that stores heat could reshape how buildings manage energy, but a stubborn problem has kept phase-change materials out of structural walls: stuffing microcapsules of wax into a cement mix quietly destroys its strength. A new study now tackles that problem from two directions at once, pairing a fresh laboratory testing program with an interpretable machine-learning framework that was validated against data the models had never seen. The result is one of the stricter tests yet of whether artificial intelligence can genuinely predict the behavior of thermally enhanced cementitious composites, rather than simply memorize published numbers.

The research team compiled a database of 271 experimental records drawn from peer-reviewed studies of Portland-cement-based mortars and concretes containing microencapsulated phase change materials, or MPCMs. Each record carried eleven inputs spanning the thermophysical properties of the capsules, such as melting point and latent heat of fusion, the mixture design, including cement, water, fine aggregate, coarse aggregate, and superplasticizer dosages, and the curing age and temperature. The single output was compressive strength. Studies using supplementary cementitious materials were deliberately excluded, so that the observed strength effects could be attributed to MPCM incorporation and mixture-design variables rather than to overlapping pozzolanic reactions.

To guard against the well-known trap of testing a model on data drawn from the same pool used to train it, the researchers reserved an entirely independent laboratory dataset for final evaluation. They produced twelve unique concrete mixtures with water-to-cement ratios of 0.30, 0.35, and 0.40, and MPCM dosages of 0, 3, 6, and 9 percent by mass of cement, introduced by replacing an equivalent volume of fine aggregate. The MPCM was a commercial powder consisting of a paraffin wax core inside a rigid melamine-formaldehyde polymer shell, with a measured peak melting temperature of 30.1 degrees Celsius and a latent heat of 157 kilojoules per kilogram. Each mixture was tested at 28 and 90 days using three replicate 100-millimeter cubes per condition, yielding 72 specimens and 24 averaged strength records that played no role in training, tuning, or model selection.

The laboratory results themselves tell a clear mechanical story. At 28 days, strength ranged from 61.1 megapascals for the plain reference mixture at the lowest water-to-cement ratio down to 36.0 megapascals for the mixture with the highest water content and 9 percent MPCM. At the maximum dosage, the 28-day strength dropped by 29.5, 32.0, and 33.5 percent relative to the corresponding plain references at the three water-to-cement ratios. Notably, the dose-response was non-linear: the first 3 percent of MPCM cost only 6.5 percent of strength, the step from 3 to 6 percent cost a further 12.6 percent, and the step from 6 to 9 percent another 13.6 percent. The authors attribute this acceleration to capsule agglomeration, which concentrates porosity and interfacial weakness into preferential zones for microcrack initiation. Crucially, every modified mixture remained above the commonly adopted 25-megapascal threshold for structural-grade concrete, and all mixes continued to gain strength between 28 and 90 days, with gains of 6.3 to 8.9 percent, showing that MPCM did not suppress later-age hydration.

The strength penalty has a coherent physical explanation. The polymer shells are far more compliant than the mineral aggregate they replace, acting as soft inclusions that concentrate stress under compression. The hydrophobic paraffin core limits formation of a dense calcium silicate hydrate layer at the capsule surface, leaving a weaker, more porous interfacial transition zone than the one that forms around natural aggregates. Water retained near the capsule shells during early hydration also locally modifies the effective water-to-cement ratio in the surrounding paste. Because these mechanisms interact in non-linear ways, traditional code-based strength relations, which contain no term for MPCM content at all, would overestimate strength by the full MPCM-induced reduction, which can exceed 50 percent at high dosages in the broader literature.

On the modeling side, the team trained five regression algorithms: Linear Regression as a transparent baseline, a Decision Tree, Random Forest, Gradient Boosting Machine, and XGBoost, all tuned with Bayesian optimization over a 70/30 training-validation split with 10-fold cross-validation. The ensemble models decisively outperformed the linear baseline, confirming that strength in these composites is governed by non-linear interactions among mixture proportions, capsule characteristics, and curing conditions. On the validation subset, Gradient Boosting achieved the best figures, with an R-squared of 0.962 and a root mean square error of 2.886 megapascals, followed by XGBoost at 0.944 and 3.479 megapascals. Exploratory paired comparisons of fold-wise errors found no statistically significant difference between the two boosting models, a result the authors caution should not be read as proof of equivalence.

The decisive test came on the 24 unseen laboratory records. There, XGBoost achieved the highest R-squared of 0.900 with a root mean square error of 4.663 megapascals, narrowly ahead of Gradient Boosting at 0.880 and 5.088 megapascals, while Random Forest, despite an almost perfect training fit with R-squared of 1.000, fell to 0.847 externally, a signature of overfitting. Linear Regression managed only 0.549 externally. The external R-squared values of roughly 0.88 to 0.90 are lower than the best random-split performances reported in earlier literature, but the authors argue this reflects a far more stringent evaluation: the test data came from newly produced mixtures, a single commercial MPCM product, and a single laboratory, with no leakage into preprocessing or tuning. Under a repeatability-based criterion tied to the coefficient of variation of the triplicate measurements, 91.7 percent of external predictions fell within one times that experimental scatter and 95.8 percent within three times, and only one specimen, the lowest-strength mixture, exceeded the three-standard-deviation threshold.

The study also probed cross-study generalization directly. Using proxy source-study groups defined by combinations of melting point, latent heat, and PCM density, which are effectively constant within any single published study, the team ran grouped cross-validation in which entire studies were withheld from training. XGBoost’s R-squared dropped from 0.927 to 0.851, Gradient Boosting’s from 0.915 to 0.816, and Random Forest’s from 0.876 to 0.787. All three stayed above 0.78, indicating that the models’ accuracy was not primarily driven by memorizing one dominant source study, though the decline quantifies how much easier prediction becomes when fragments of the same study appear on both sides of the split.

Interpretability analysis using SHAP values showed that the winning model had learned physically sensible relationships. PCM content, cement content, curing age, water content, and fine aggregate emerged as the most influential predictors. Increasing PCM dosage pushed predictions downward, while higher cement content and longer curing age pushed them upward, consistent with established mechanisms of compliant inclusions, weak capsule-matrix interfaces, and progressive hydration. The authors were careful about a subtle confound: positive SHAP contributions for PCM at low dosages are measured against a model baseline of about 33.8 megapascals and do not imply that adding MPCM strengthens concrete. Their tertile analysis showed that low-PCM records in the database also tended to have lower water-to-cement ratios, 0.472 versus 0.513, and higher cement contents, 501.2 versus 459.4 kilograms per cubic meter, so PCM dosage co-varies with other strength-relevant variables. Controlled factorial experiments varying PCM content independently will be needed to isolate the true physical effect.

The team also flagged the boundaries of their validation. The external set extrapolates beyond the training domain in three dimensions, since the laboratory MPCM’s melting point of 30.1 degrees Celsius exceeds the training maximum of 29.0 degrees, the lowest laboratory water content of 131 kilograms per cubic meter falls below the training minimum, and the 90-day tests exceed the training maximum curing age of 60 days. All external records came from one MPCM product, one cement supplier, and one laboratory, so inter-manufacturer variability in shell chemistry is not captured. The findings therefore apply to low water-to-cement ratio, conventional-strength MPCM-modified concrete with paraffin and melamine-formaldehyde capsules, and should not be generalized to all MPCM systems. To make the work usable, the researchers deployed the optimized XGBoost model in a public web application that accepts mixture and curing inputs and returns a predicted strength with domain assessment and SHAP interpretation. As a screening tool for preliminary mixture design, the framework suggests that structurally viable, thermally functional concrete is achievable when water-to-cement ratio and MPCM dosage are controlled together, while future work must extend the database to supplementary cementitious materials, higher dosages, and independent laboratories.

Subject of Research: Interpretable machine learning and experimental validation for predicting the compressive strength of microencapsulated phase change material concrete

Article Title: Experimental validation and interpretable machine learning for compressive strength prediction of MPCM-integrated cementitious composites

Article References: Mohsennia, E., Toufigh, V., & Javid, A. (2026). Experimental validation and interpretable machine learning for compressive strength prediction of MPCM-integrated cementitious composites. Case Studies in Construction Materials, 25, Article e06631. https://doi.org/10.1016/j.cscm.2026.e06631

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06631

Keywords: phase change materials, microencapsulated PCM, compressive strength, machine learning, XGBoost, SHAP interpretability, cementitious composites, thermal energy storage, concrete, external validation, building materials, Bayesian optimization