Deep Learning and Uncertainty Quantification: Methodologies and Applications / Yibo Yang.

Format:

Book

Thesis/Dissertation

Author/Creator:

Yang, Yibo, author.

Contributor:

University of Pennsylvania. Mechanical Engineering and Applied Mechanics, degree granting institution.

Language:

English

Subjects (All):

Computational physics.

Applied mathematics.

Mechanical Engineering and Applied Mechanics--Penn dissertations.

Penn dissertations--Mechanical Engineering and Applied Mechanics.

Local Subjects:

Computational physics.

Applied mathematics.

Mechanical Engineering and Applied Mechanics--Penn dissertations.

Penn dissertations--Mechanical Engineering and Applied Mechanics.

Physical Description:

1 online resource (260 pages)

Distribution:

Ann Arbor : ProQuest Dissertations & Theses, 2022

Contained In:

Dissertations Abstracts International 84-02B.

Place of Publication:

[Philadelphia, Pennsylvania] : University of Pennsylvania, 2022.

Language Note:

English

Summary:

Uncertainty quantification is a recent emerging interdisciplinary area that leverages the power of statistical methods, machine learning models, numerical methods and data-driven approach to provide reliable inference for quantities of interest in natural science and engineering problems. In practice, the sources of uncertainty come from different aspects such as: aleatoric uncertainty where the uncertainty comes from the observations or is due to the stochastic nature of the problem; epistemic uncertainty where the uncertainty comes from inaccurate mathematical models, computational methods or model parametrization. Cope with the above different types of uncertainty, a successful and scalable model for uncertainty quantification requires prior knowledge in the problem, careful design of mathematical models, cautious selection of computational tools, etc. The fast growth in deep learning, probabilistic methods and the large volume of data available across different research areas enable researchers to take advantage of these recent advances to propose novel methodologies to solve scientific problems where uncertainty quantification plays important roles. The objective of this dissertation is to address the existing gaps and propose new methodologies for uncertainty quantification with deep learning methods and demonstrate their power in engineering applications.On the methodology side, we first present a generative adversarial framework to model aleatoric uncertainty in stochastic systems. Secondly, we leverage the proposed generative model with recent advances in physics-informed deep learning to learn the uncertainty propagation in solutions of partial differential equations. Thirdly, we introduce a simple and effective approach for posterior uncertainty quantification for learning nonlinear operators. Fourthly, we consider inverse problems of physical systems on identifying unknown forms and parameters in dynamical systems via observed noisy data.On the application side, we first propose an importance sampling approach for sequential decision making. Second, we propose a physics-informed neural network method to quantify the epistemic uncertainty in cardiac activation mapping modeling and conduct active learning. Third, we present an anto-encoder based framework for data augmentation and generation for data that is expensive to obtain such as single-cell RNA sequencing.

Notes:

Source: Dissertations Abstracts International, Volume: 84-02, Section: B.

Advisors: Perdikaris, Paris; Committee members: Purohit, Prashant K.; Chaudhari, Pratik.

Department: Mechanical Engineering and Applied Mechanics.

Ph.D. University of Pennsylvania 2022.

Local Notes:

School code: 0175

ISBN:

9798837503399

Access Restriction:

Restricted for use by site license.