Efficient Finite Element Solution Methods formed from Artificial Neural Networks for Solving Complex Fluid Dynamics Problems

  • Chen, Boyang (Imperial College London)
  • Heaney, Claire E (Imperial College London)
  • Pain, Christopher C (Imperial College London)

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Recently, a huge effort has been made to develop highly efficient libraries to perform Artificial Intelligence (AI) related computation on different computing architectures capable of running on CPUs, GPUs and AI computers [1]. This has not only made the algorithms based on these libraries highly efficient and portable between different architectures [2], but also has substantially simplified the implementation of numerical approaches to solve Partial Differential Equations (PDEs) [3]. In this way, prototyping and developing highly efficient and architecture-agnostic algorithms has become the norm in the field due to the ubiquity of these libraries. In this work, we present a novel AI-based methodology to bring the power of AI software and hardware into the field of Computational Fluid Dynamics (CFD) and simplify the development of CFD software. Convolutional and graph neural networks are formed by the most popular AI libraries, Pytorch and TensorFlow, in order to solve the incompressible flow equations on structured and unstructured mesh through a finite element discretisation and a rapid multi-grid solution method. The presented AI high-fidelity solver is applied to predict complex fluid dynamics such as flow past a bluff body and two-dimensional Kolmogorov flow, and carry out the simulation of air flow within the South Kensington area in London. The results are validated with previous studies and indicate that the methodology can solve all those problems using repurposed AI libraries in an efficient way, and presents a new avenue to explore in the development of numerical methods to undertake CFD simulations.