Physics-informed deep learning for civil infrastructure: a review framework integrating the PIFI index and P-D-E triad

The safety and sustainability of civil infrastructure are facing increasingly severe challenges, creating an urgent need for smarter, more reliable data-driven methods to support its lifecycle management and decision-making. Existing deep learning methods face key bottlenecks in civil engineering applications, including data scarcity, insufficient model credibility, high computational costs, and ethical compliance issues. Physics-informed deep learning, by embedding physical knowledge, offers a new paradigm for overcoming these limitations. This paper first systematically reviews the research progress of physics-informed deep learning in the field of civil engineering, followed by the proposal of an original evaluation framework. Based on a systematic analysis of 243 publications (2000–2025), it explores in depth the technological evolution, engineering adaptability, and inherent limitations of core architectures such as CNNs, RNNs, and PINNs. On this basis, the paper presents two original contributions: First, the Physics-Informed Fusion Index–which quantifies a model’s comprehensive performance by balancing physical consistency ( \({E}_{\text {physics}}\) ) and predictive accuracy ( \({D}_{\text {accuracy}}\) ) through weighting; this represents the first attempt to incorporate the trade-off between physical constraints and data fitting into a unified evaluation metric. Second, the Physics–Data–Engineering Triangular Model–a quantitative selection framework that assesses the applicability of technical solutions across three orthogonal dimensions: physicality, data dependency, and engineering adaptability. Unlike existing reviews that primarily compile methodologies, the proposed PIFI-P-D-E framework traces the trajectory of technological evolution and examines the trade-offs between physical embedding depth, data utility boundaries, and engineering implementation constraints, providing a systematic perspective and decision-making tools for the transition from technological exploration to engineering governance. Building on this foundation, this paper outlines an interdisciplinary development pathway centred on ‘mechanism–data integration’, advocating for a new paradigm in civil informatics.