Basir, Shamsulhaq
(2023)
Scientific Machine Learning for Transport Phenomena in Thermal and Fluid Sciences.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Physics-informed neural networks (PINNs) have become popular as part of the rapidly expanding deep learning field in recent years. However, their origins date back to the early 1990s, when neural networks were adopted as meshless numerical methods to solve partial differential equations (PDEs). PINNs incorporate equations of known physics into the objective function as a regularization term, necessitating hyperparameter tuning to ensure convergence. Lack of a validation dataset or a priori knowledge of the solution can make PINNs impractical. Moreover, learning inverse PDE problems with noisy data can be difficult since it can lead to overfitting noise or underfitting high-fidelity data. To overcome these obstacles, this dissertation introduces physics and equality constrained artificial neural networks (PECANNs) as a deep learning framework for forward and inverse PDE problems. The backbone of this framework is a constrained optimization formulation that embeds governing equations along any available data in a principled fashion using an adaptive augmented Lagrangian method. Additionally, the framework is extended to learn the solution of large-scale PDE problems through a novel Schwarz-type domain decomposition method with a generalized Robin-type interface condition. The efficacy and versatility of the PECANN approach are demonstrated by solving several challenging forward and inverse PDE problems that arise in thermal and fluid sciences.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
13 June 2023 |
| Date Type: |
Publication |
| Defense Date: |
31 March 2023 |
| Approval Date: |
13 June 2023 |
| Submission Date: |
11 April 2023 |
| Access Restriction: |
1 year -- Restrict access to University of Pittsburgh for a period of 1 year. |
| Number of Pages: |
130 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Swanson School of Engineering > Mechanical Engineering and Materials Science |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Augmented Lagrangian method, Constrained optimization, Deep learning, Inverse problems, domain decomposition methods, adaptive robin interface condition |
| Date Deposited: |
13 Jun 2023 14:16 |
| Last Modified: |
13 Jun 2024 05:15 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/44401 |
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