| dc.description.abstract | Inverse problems pose a significant challenge as they aim to estimate the causal factors that result in a measured response. However, the responses are often truncated, partially available, and corrupted by measurement noise, rendering the problems ill-posed, and may have multiple or no solutions. Solving such problems using regularization transforms them into a family of well-posed functions. While physics-based models are interpretable, they operate under approximations and assumptions. Data-driven models such as machine learning and deep learning have shown promise in solving mechanics-based inverse problems, but they lack robustness, convergence, and generalization when operating under partial information, compromising the interpretability and explainability of their predictions. To overcome these challenges, hybrid physics-data-driven models can be formulated by integrating prior knowledge of physical laws, expert knowledge, spatial invariances, empirically validated rules, etc., acting as a regularizing agent to select a more feasible solution space. This approach improves prediction accuracy, robustness, generalization, interpretability, and explainability of the data-driven models. In this dissertation, we propose various physics-data-driven models to solve inverse problems related to engineering mechanics by integrating prior knowledge and its representation into a data-driven pipeline at different stages. We have used these hybrid models to solve six different inverse problems, such as leakage estimation of a pressurized habitat, estimating dispersion relations of a waveguide, structural damage identification, filtering temperature effects in guided waves, material property prediction, and guided wave generation and material design.
The dissertation presents a detailed overview of inverse problems, definitions of the six inverse problems, and the motivation behind using hybrid models for their solution. Six different hybrid models, such as adaptive model calibration, physics-informed neural networks, inverse deep surrogate, deep latent variable, and unsupervised representation learning models, are formulated, and arranged on different levels of a pyramid, showing the trade-off between autonomy and explainability. All these new methods are designed with practical implementation in mind. The first model uses an adaptive real-time calibration framework to estimate the severity of leaks in a pressurized deep space habitat before they become a threat to the crew and habitat. The second model utilizes a physics-informed neural network to estimate the speed of wave propagation in a waveguide from limited experimental observations. The third model uses deep surrogate models to solve structural damage identification and material property prediction problems. The fourth model proposes a domain knowledge-based data augmentation scheme for ultrasonic guided waves-based damage identification. The fifth model uses unsupervised feature learning to solve guided waves-based structural anomaly detection and filtering the temperature effects on guided waves. The final model employs a deep latent variable model for structural anomaly detection, guided wave generation, and material design problems. Overall, the thesis demonstrates the effectiveness of hybrid models that combine prior knowledge with machine learning techniques to address a wide range of inverse problems. These models offer faster, more accurate, and more automated solutions to these problems than traditional methods. | en_US |
