The convergence of artificial intelligence (AI) with engineering and scientific disciplines has catalyzed transformative advancements in both structural health monitoring (SHM) and the modeling of complex physical systems. This dissertation explores the development and application of AI-driven methodologies with a focus on anomaly detection and inverse modeling for domain-specific and other scientific problems.SHM is vital for the safety and longevity of structures like buildings and bridges. With the growing scale and potential impact of structural failures, there is a dire need for scalable, cost-effective, and passive SHM techniques tailored to each structure without relying on complex baseline models. Mechanics-Informed Damage Assessment of Structures, MIDAS, is introduced, which continuously adapts a bespoke baseline model by learning from the structure's undamaged state. Numerical simulations and experiments show that incorporating mechanical characteristics into the autoencoder improves minor damage detection and localization by up to 35% compared to standard autoencoders.In addition to anomaly detection, NeuralSI was introduced for structural identification, estimating key nonlinear parameters in mechanical components like beams and plates by augmenting partial differential equations (PDEs) with neural networks. Using limited measurement data, NeuralSI is ideal for SHM applications where the exact state of a structure is often unknown. The model can extrapolate to both standard and extreme conditions using identified structural parameters. Compared to data-driven neural networks and other physics-informed neural networks (PINN), NeuralSI reduces interpolation and extrapolation errors in displacement distribution by two orders of magnitude.Building on this approach, the research expands to broader systems governed by parameterized PDEs, which are critical in modeling various physical, industrial, and environmental phenomena. These systems often have unknown or unpredictable parameters that traditional methods struggle to estimate due to real-world complexities like multiphysics interactions and limited data. NeuroFieldID is introduced to estimate unknown field parameters from sparse observations by modeling them as functions of space or state variables using neural networks. Applied to several physical and biomedical problems, NeuroFieldID achieves a 100 times reduction in parameter estimation errors and a 10 times reduction in peak dynamic response errors, greatly enhancing the accuracy and efficiency of complex physics modeling.
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