Using AI libraries for Incompressible Computational Fluid Dynamics
Boyang Chen Claire E. Heaney Christopher C. Pain
Recently, there has been a huge effort focused on developing highly efficient
open source libraries to perform Artificial Intelligence (AI) related
computations on different computer architectures (for example, CPUs, GPUs and
new AI processors). This has not only made the algorithms based on these
libraries highly efficient and portable between different architectures, but
also has substantially simplified the entry barrier to develop methods using
AI. Here, we present a novel methodology to bring the power of both AI software
and hardware into the field of numerical modelling by repurposing AI methods,
such as Convolutional Neural Networks (CNNs), for the standard operations
required in the field of the numerical solution of Partial Differential
Equations (PDEs). The aim of this work is to bring the high performance,
architecture agnosticism and ease of use into the field of the numerical
solution of PDEs. We use the proposed methodology to solve the
advection-diffusion equation, the non-linear Burgers equation and
incompressible flow past a bluff body. For the latter, a convolutional neural
network is used as a multigrid solver in order to enforce the incompressibility
constraint. We show that the presented methodology can solve all these problems
using repurposed AI libraries in an efficient way, and presents a new avenue to
explore in the development of methods to solve PDEs and Computational Fluid
Dynamics problems with implicit methods.