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Reduced-order modeling (ROM) of fluid flows has been an active area of research for several decades. The huge computational cost of direct numerical simulations has motivated researchers to develop more efficient alternative methods, such as ROMs and other surrogate models. Similar to many application areas, such as computer vision and language modeling, machine learning and data-driven methods have played an important role in the development of novel models for fluid dynamics. The transformer is one of the state-of-the-art deep learning architectures that has made several breakthroughs in many application areas of artificial intelligence in recent years, including but not limited to natural language processing, image processing, and video processing. In this work, we investigate the capability of this architecture in learning the dynamics of fluid flows in a ROM framework. We use a convolutional autoencoder as a dimensionality reduction mechanism and train a transformer model to learn the system's dynamics in the encoded state space. The model shows competitive results even for turbulent datasets. 

Meshing is a critical, but user-intensive process necessary for stable and accurate simulations in computational fluid dynamics (CFD). Mesh generation is often a bottleneck in CFD pipelines. Adaptive meshing techniques allow the mesh to be updated automatically to produce an accurate solution for the problem at hand. Existing classical techniques for adaptive meshing require either additional functionality out of solvers, many training simulations, or both. Current machine learning techniques often require substantial computational cost for training data generation, and are restricted in scope to the training data flow regime. Mesh Deep Q Network (MeshDQN) is developed as a general purpose deep reinforcement learning framework to iteratively coarsen meshes while preserving target property calculation. A graph neural network based deep Q network is used to select mesh vertices for removal and solution interpolation is used to bypass expensive simulations at each step in the improvement process. MeshDQN requires a single simulation prior to mesh coarsening, while making no assumptions about flow regime, mesh type, or solver, only requiring the ability to modify meshes directly in a CFD pipeline. MeshDQN successfully improves meshes for two 2D airfoils.