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Explore the challenges and advancements in applying machine learning to fluid mechanics simulations in this comprehensive lecture. Delve into the complexities of fluid mechanics simulations, understanding why they are computationally expensive due to the wide range of interacting time and length scales. Examine various approaches developed by the speaker's research group to address these challenges, including the use of physics-based feature spaces and convolutional neural networks (CNNs) for mapping 2D to 3D turbulence simulations. Learn about their recent attempts to utilize Optimal Transport for simulation interpolation, and gain insights into the difficulties encountered, particularly regarding boundary conditions and solution representation. Discover the successes and failures in this cutting-edge field, providing a balanced view of the current state of fluid-mechanics-informed machine learning.
