Physics-Informed Deep Learning for Computational Fluid Dynamics

The integration of physics and deep learning, known as physics-informed deep learning, has recently emerged in scientific computing and demonstrates significant potential in addressing the challenges of our time. Among various disciplines, computational fluid dynamics often faces limitations in the numerical modeling of complex fluid flow and particularly benefits from advances in physics-informed deep learning. However, understanding the applicability and limitations of this interdisciplinary field raises various questions, constituting an ongoing area of research. This thesis investigates several aspects of physics-informed deep learning for computational fluid dynamics. Encompassing topics ranging from chemical kinetics tabulation to the simulation of dynamical systems, the investigations involve several studies on how to leverage physical knowledge in the design of deep learning applications. Additionally, a critical aspect of these inquiries involves evaluating both the advantages and limitations inherent in this approach. With a particular focus on physics-informed neural networks, the study further explores the role of physical systems and differential equations in the optimization complexity of deep learning models. Throughout this document, the thesis addresses various research questions and holds relevance for individuals interested in applying physics-informed deep learning in scientific computing. With a focus on unraveling the interconnections between physics and deep learning, reading this document can help in developing deep learning approaches for computational fluid dynamics, understanding the associated difficulties, and finding the remedies to overcome them.