Uncertain identification of damage in short bridges via physics-informed VAE

Damage identification in civil infrastructure through vibrations represents one of the most complex inverse problems in structural engineering. Uncertainty caused by measurement noise, sensor scarcity, and environmental variability turns any diagnosis into a technical challenge. Deterministic approaches, although powerful, lack reliable uncertainty quantification and can produce physically inconsistent results. Faced with this reality, the scientific community has begun to explore probabilistic models that integrate physical knowledge with machine learning. A promising example is the use of physics-informed variational autoencoders, such as the recently proposed PI-GCVAE framework, which incorporates a differentiable eigenvalue solver directly into the architecture to ensure that latent solutions satisfy structural dynamics equations. Furthermore, by employing a Gaussian copula instead of independence assumptions, spatial correlations between adjacent elements are captured, defining feasible solutions even with high dimensionality. These advances not only improve posterior distribution coverage—reaching 77.2% in synthetic validations—but also open the door to real-world applications in operational bridges. For these solutions to transcend the laboratory, robust technological platforms integrating artificial intelligence, cloud data management, and advanced visualization are necessary. At Q2BSTUDIO, as a company specialized in developing custom applications, we understand that modern structural engineering demands software tools that combine probabilistic models with scalable infrastructure. Therefore, we offer services ranging from implementing AI agents for continuous monitoring to using AWS and Azure cloud services to process large volumes of sensor data. The combination of artificial intelligence with cybersecurity ensures that critical information from bridges and other structures is protected, while business intelligence services tools like Power BI allow engineers to visualize the evolution of damage indicators in real time. Ultimately, the integration of AI for businesses with physics-informed models represents a qualitative leap in the reliability of structural diagnosis, and at Q2BSTUDIO we accompany organizations in this transformation with custom software solutions that address both the algorithmic and operational aspects.