Ph.D. Defense

Weiming Ding

(Advisor: Prof. Yang)

Machine Learning-Based Surrogate Model for High-Fidelity Computational Analysis of Complex Flow Dynamics

Monday, April 21

9:30 a.m

Montgomery Knight Building, Room 317

Online: Click here to join the meeting

Abstract
Partial differential equations (PDEs) are fundamental mathematical tools for modeling physical systems in science and engineering. Among them, conservation laws form a critical class that describe the evolution of conserved physical quantities such as mass, momentum, and energy. These laws govern complex phenomena in fluid dynamics, combustion, turbulence, and multiphase flows, disciplines where analytical solutions are rarely available. As a result, high-fidelity numerical simulations, supported by high-performance computing, are commonly used to solve these equations with fine spatial and temporal resolution. These simulations provide valuable insights into system behavior and have become indispensable tools in both scientific research and engineering design. Such simulations, however, are computationally expensive and thus become impractical for tasks involving iterative evaluations, such as design optimization, uncertainty quantification, or parametric studies.

To address these challenges, surrogate models have been developed to accelerate high-fidelity simulations by integrating engineering physics, data science, and machine learning. A variety of surrogate modeling approaches have emerged, including data-fit models, reduced-order models (ROMs), and hierarchical (multi-fidelity) models. While these approaches have shown promise in specific applications, significant limitations remain that hinder their broader adoption. These include high data requirements, limited generalization to unseen scenarios, and inadequate enforcement of physical laws.

This thesis aims to overcome these challenges by developing advanced surrogate modeling techniques that are accurate, efficient, and highly generalizable, with an emphasis on aerospace applications.

First, to manage high-dimensional spatiotemporal data, a non-intrusive reduced-order model known as common kernel-smoothed proper orthogonal decomposition (CKSPOD) is developed to emulate flow dynamics in swirl injectors with varying geometries. CKSPOD is extensively evaluated against LES and other POD-based ROMs, demonstrating strong physical coherence and outstanding performance. The framework captures complex turbulent flow characteristics with a speedup of nearly 6,000 times compared with LES-based simulations.

Second, a novel surrogate modeling technique—Neural Network with Local Converging Inputs (NNLCI)—is introduced to efficiently resolve nonlinear flow behavior with modest computational demands. To extend NNLCI to unstructured data, a powerful and flexible interpolation technique is incorporated. The framework is validated on two-dimensional inviscid supersonic flows in channels with varying bump geometries and positions. The NNLCI model accurately captures flowfield structures and dynamics, including regions with highly nonlinear shock interactions, achieving a speedup of more than two orders of magnitude.

To enhance NNLCI’s flexibility and reduce reliance on paired low-fidelity inputs, a variational autoencoder (VAE) is integrated into the framework. The resulting VAE-NNLCI model requires only a single low-fidelity input and generates an artificial converging pair that retains both case-specific and global physical features. This approach is tested on canonical one- and two-dimensional Euler problems and demonstrates improved robustness and accuracy over the standard NNLCI.

Finally, a comprehensive benchmark study compares NNLCI with state-of-the-art neural network-based PDE solvers, including physics-informed neural networks (PINNs) and neural operators. These models are evaluated on various hyperbolic conservation law problems, where sharp transitions in flow are critical for assessing model performance and robustness. Results show that NNLCI consistently achieves superior accuracy, efficiency, and generalizability. The study provides practical guidance for model selection in scientific machine learning applications.

Committee

• Prof. Vigor Yang – School of Aerospace Engineering (advisor)
• Prof. Yingjie Liu – School of Mathematics (co-advisor)
• Prof. Timothy Lieuwen – School of Aerospace Engineering
• Prof. Joseph Oefelein – School of Aerospace Engineering
• Prof. Graeme J. Kennedy – School of Aerospace Engineering