Physics-Informed Surrogate Modelling of Concrete Self-Healing via Coupled FEM-ML with Active Learning

This study presents a physics-informed modelling framework that combines finite element method (FEM) simulations and supervised machine learning (ML) to predict the self-healing performance of microbial concrete. A FEniCS-based FEM platform resolves multiphysics phenomena including nutrient diffusion, microbial CaCO₃ precipitation, and stiffness recovery. These simulations, together with experimental data, are used to train ML models (Random Forest yielding normalized RMSE ≈ 0.10) capable of predicting performance over a wide range of design parameters. Feature importance analysis identifies curing temperature, calcium carbonate precipitation rate, crack width, bacterial strain, and encapsulation method as the most influential parameters. The coupled FEM-ML approach enables sensitivity analysis, design optimization, and prediction beyond the training dataset (consistently exceeding 90% healing efficiency). Experimental validation confirms model robustness in both crack closure and strength recovery. This FEM–ML pipeline thus offers a generalizable, interpretable, and scalable strategy for the design of intelligent, self-adaptive construction materials.