Thermal fatigue in concrete composites critically compromises infrastructure performance and longevity. While data-driven methods have pioneered structural health monitoring (SHM), conventional approaches suffer from high training costs, overfitting risk, poor interpretability, overlooking physical principles, and limited generalizability. This study presents an innovative physics-informed white-box framework integrated with ultrasonic signal features for diagnosing and prognosing thermal fatigue in concrete composites. A novel physics-informed symbolic regression (SR) is developed as an interpretable platform according to underlying physical laws with low training costs. In parallel, a plain SR is established as a baseline for comparison. An evolutionary algorithm with a multi-objective fitness function addresses regression problems and reduces computational costs. High-performance concrete is used to generate training and testing data through a comprehensive experimental fatigue program. A hierarchical data structure enables systematic evaluation of the interpolation property. As a result, ultrasonic signal features robustly predict the key mechanical parameters. Additionally, the paste volume fraction demonstrates a pivotal role in damage modeling. Out-of-distribution data assess the extrapolation property and potential for overfitting. In particular, the physics-informed SR captures influential degradation mechanisms by highlighting the significance of paste integrity and thermal expansion mismatch. Bayesian regression extends the learned physical mechanism to other concrete materials and thermal patterns. The results outperform standards and previous studies in terms of strength and stiffness predictions. This work introduces a promising SHM system that supports field deployment, pre-crack estimation, real-time monitoring, and transparent decision-making.