Physics‐informed deep learning with dual theoretical bound constraints for shear strength prediction of deep beams

Abstract Predicting the shear strength of reinforced‐concrete deep beams (DBs) is challenging because geometry, material properties, and reinforcement detailing jointly govern multiple shear‐transfer mechanisms, while most purely data‐driven models ignore mechanics. This study proposes a physics‐informed deep learning framework that embeds dual theoretical bounds—an upper bound based on a strut‐and‐tie mechanism and a lower bound associated with diagonal‐tension failure—directly into model training. A literature database of 1577 DB tests is compiled and used to benchmark conventional regressors against three physics‐informed models: (i) a bounded‐loss DNN and two uncertainty‐aware variants based on MC‐dropout and distributional regression. All physics‐informed models outperform purely data‐driven baselines, reaching test‐set R 2 ≈0.98. The distributional model achieves the best accuracy (RMSE = 78.6 kN) and yields conservative 95% prediction intervals (98.7% empirical coverage). In a small‐sample setting (training with 20% of the original training set), the physics‐informed models remain stable ( R 2 up to 0.96), whereas conventional models degrade markedly ( R 2 ≈0.83). The proposed framework provides a mechanics‐consistent and uncertainty‐aware surrogate for rapid shear assessment of DBs and can be extended to other shear‐critical RC members.