Reinforcement Learning to Refine FEM Meshes for Acoustic Problems

Abstract

Numerical methods are central to modern engineering and the Finite Element Method (FEM) specifically is used in a variety of domains and for countless applications. One of the main challenges of using FEM lies in the choice of parameters to generate the mesh. This is particularly the case in acoustics. Indeed, for the phenomena to be correctly modelled, the mesh parameters must be chosen in concordance with the frequency range of interest. So far, the choices regarding the mesh are mostly guided by past experience or widely accepted guidelines (for instance 7–10 points per wavelength when using quadratic elements). In this contribution, we explore the use of reinforcement learning to construct and refine a FEM mesh. This technique implies that the machine is learning how to complete a given task based solely on the so-called state of the environment (including a measure of the error on the result). The key aspect of this research is to challenge the traditional guidelines used for acoustic problems by letting a machine explore and converge without human intervention. The overall strategy will be introduced and demonstrated on simple problems, the results compared with pre-existing recommendations and the challenges ahead will be briefly presented.