- author = "Elham Kianiharchegani",
- title = "Data-Driven Exploration of Coarse-Grained Equations: Harnessing Machine Learning",
- school = "The University of Western Ontario",
- year = "2023",
- address = "Canada",
- month = "21 " # aug,
- keywords = "genetic algorithms, genetic programming, GPlearn, Machine learning, Neurons, Physics, Partial differential equations, Neural networks, ANN, Coauthorship, Clustering, Fluid mechanics, Ordinary differential equations, ODEs, AI, Mathematics, Mechanics, 0605: Physics, 0346: Mechanics, 0405: Mathematics, 0204: Fluid mechanics, 0800: Artificial intelligence",
- ISBN = "97983-8102-412-8",
- language = "English",
-
URL = "
https://ir.lib.uwo.ca/etd/9530",
-
URL = "https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=12359&context=etd",
-
URL = "https://www.proquest.com/dissertations-theses/data-driven-exploration-coarse-grained-equations/docview/2901810389/se-2",
- size = "231 pages",
-
abstract = "In scientific research, understanding and modeling
physical systems often involves working with complex
equations called Partial Differential Equations (PDEs).
These equations are essential for describing the
relationships between variables and their derivatives,
allowing us to analyze a wide range of phenomena, from
fluid dynamics to quantum mechanics. Traditionally, the
discovery of PDEs relied on mathematical derivations
and expert knowledge. However, the advent of
data-driven approaches and machine learning (ML)
techniques has transformed this process. By harnessing
ML techniques and data analysis methods, data-driven
approaches have revolutionized the task of uncovering
complex equations that describe physical systems. The
primary goal in this thesis is to develop methodologies
that can automatically extract simplified equations by
training models using available data. ML algorithms
have the ability to learn underlying patterns and
relationships within the data, making it possible to
extract simplified equations that capture the essential
behavior of the system. This study considers three
distinct learning categories: black-box, gray-box, and
white-box learning.
The initial phase of the research focuses on black-box learning, where no prior information about the equations is available. Three different neural network architectures are explored: multi-layer perceptron (MLP), convolutional neural network (CNN), and a hybrid architecture combining CNN and long short-term memory (CNN-LSTM). These neural networks are applied to uncover the non-linear equations of motion associated with phase-field models, which include both non-conserved and conserved order parameters.
The second architecture explored in this study addresses explicit equation discovery in gray-box learning scenarios, where a portion of the equation is unknown. The framework employs eXtended Physics-Informed Neural Networks (X-PINNs) and incorporates domain decomposition in space to uncover a segment of the widely-known Allen-Cahn equation. Specifically, the Laplacian part of the equation is assumed to be known, while the objective is to discover the non-linear component of the equation. Moreover, symbolic regression techniques are applied to deduce the precise mathematical expression for the unknown segment of the equation.
Furthermore, the final part of the thesis focuses on white-box learning, aiming to uncover equations that offer a detailed understanding of the studied system. Specifically, a coarse parametric ordinary differential equation (ODE) is introduced to accurately capture the spreading radius behavior of Calcium-magnesium-aluminosilicate (CMAS) droplets. Through the use of the Physics-Informed Neural Network (PINN) framework, the parameters of this ODE are determined, facilitating precise estimation. The architecture is employed to discover the unknown parameters of the equation, assuming that all terms of the ODE are known. This approach significantly improves our comprehension of the spreading dynamics associated with CMAS droplets",
-
notes = "Copyright - Database copyright ProQuest LLC; ProQuest
does not claim copyright in the individual underlying
works; Last updated - 2025-02-03
Supervisor: Mikko Karttunen",
