Date of Award
2023
Document Type
Open Access Dissertation
Degree Name
Doctor of Philosophy in Mechanical Engineering-Engineering Mechanics (PhD)
Administrative Home Department
Department of Mechanical Engineering-Engineering Mechanics
Advisor 1
Susanta Ghosh
Committee Member 1
Ramakrishna Tipireddy
Committee Member 2
Shiva Rudraraju
Committee Member 3
Soumik Sarkar
Abstract
Computational and data-driven models suffer from a wide range of uncertainties that impact the reliability of such models. Given the exponential proliferation of machine learning models in real-world systems, establishing a degree of confidence in their predictions becomes paramount. Reliability in predictions takes on utmost significance in domains such as autonomous driving, medical image analysis, etc., where human lives are involved, and inaccuracies in predictions could lead to disastrous outcomes. For these reasons, comprehending and quantifying uncertainties in computational and data-driven models is of utmost importance. A number of techniques have been developed to quantify uncertainties in machine learning models. Amongst these methods, the Bayesian Neural Networks (BNNs) are widely used due to their strong mathematical foundation to quantify uncertainties through their stochastic parameters. Despite their wide application, they suffer from limitations such as instability in optimization and poor approximation. This occurs due to the unboundedness property of the KL divergence used in BNNs to approximate the posterior distribution of weights. In addition, the uncertainties quantified by the BNNs are not well understood. In this work, novel loss functions are developed for BNNs using the JS divergences which are bounded and symmetric. This loss eliminates the problem of unstable optimization. In addition, rigorous theoretical analysis and empirical experiments are performed to evaluate the performance of the proposed loss functions. Further, the uncertainties quantified by the BNNs are explained by visualizing the data in a three-dimensional space through a nonlinear dimensionality reduction. Furthermore, the uncertainties are utilized to improve the performance of the BNNs on a binary classification of medical images. Calibrating the parameters of a computational model by trial and error is a challenging task due to the computational cost associated with it. The problem is further complicated if the parameter space is high dimensional and the experimental data is limited. In this work, the parameters of a fracture model are calibrated systematically through a Bayesian approach. Uncertainties in the model are quantified considering both the data and the model uncertainty. These uncertainties are provided as confidence intervals which improves the reliability of the model's prediction.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Thiagarajan, Ponkrshnan, "NOVEL BAYESIAN NEURAL NETWORKS AND UNCERTAINTY QUANTIFICATION OF COMPUTATIONAL MECHANICS MODELS", Open Access Dissertation, Michigan Technological University, 2023.
Included in
Applied Mechanics Commons, Artificial Intelligence and Robotics Commons, Biomedical Commons, Numerical Analysis and Computation Commons, Probability Commons