Hybrid physics-data driven models for the solution of mechanics based inverse problems

includes bibliographical reference and index

PhD; 2023; Aerospace engineering

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.