Scientific deep learning for efficient modeling and uncertainty quantification in engineering systems

Computation-intensive problems are becoming increasingly common in the analysis and design of engineering systems. On the one hand, many science and engineering problems require repetitive simulation runs of a model with different input values. Examples of these problems include design optimization, model calibration, sensitivity analysis, what-if analysis, and design space exploration. In many real-world problems, obtaining a reliable outcome requires a large number of these simulations, typically for a partial differential equation, which can be limited by the available computational resources. On the other hand, reliable analysis of the response of engineering systems often requires taking into account the inherent uncertainties in the system and quantifying the impact of these uncertainties on the quantities of interest. Conducting uncertainty quantification with Monte Carlo methods are often infeasible because of the need to execute a large number of forward model evaluations to achieve converged distributions or statistics. For systems characterized by numerous input parameters, the response calculation is particularly challenging as one also has to deal with the curse of dimensionality, which is the exponential increase in the volume of the input space, as the number of parameters increases linearly. The overarching objective of this dissertation is to take a step toward addressing these computational challenges and contribute to the promotion of efficient computational analysis, design, and control of engineering systems. This is achieved by developing deep learning solutions that are particularly tailored for these systems and can account for various uncertainties in their behaviors. In particular, and in moving toward this objective, we introduce various deep learning approaches for efficient modeling, metamodeling, and forward and inverse uncertainty quantification in engineering systems. In the first part of the dissertation, we introduce deep learning methods for efficient supervised, semi-supervised, and unsupervised modeling and metamodeling in engineering systems. The backbone of the unsupervised learning task in these tools is the physics-informed neural networks which are a new class of deep neural networks that are trained to satisfy the governing laws of physics described in the form of partial differential equations. In the second part of the dissertation, we introduce a variant of physics-informed neural networks for solving high-dimensional random differential equations (forward uncertainty quantification), and also the adaptive physics-informed neural networks for efficient and accurate parameter estimation and model calibration. A variety of engineering applications are considered to verify the accuracy and efficiency of the proposed methods.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Nabian, Mohammad Amin

Contributors dc:contributor

• Meidani, Hadi
• Sowers, Richard B
• Spencer, Billie F
• Yan, Jinhui

• deep neural networks
• deep learning
• machine learning
• scientific deep learning
• physics-informed neural networks
• differential equations
• physics-based simulations
• surrogates
• metamodels
• data-driven
• predictive modeling
• design optimization
• regularization
• Bayesian
• Markov chain Monte Carlo
• uncertainty quantification

Statement dc:rights

• Copyright 2020 Mohammad Amin Nabian

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/109317

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/109317