From cb38081253883370e99372f99528e12ae42e0832 Mon Sep 17 00:00:00 2001 From: Timo Betcke Date: Wed, 19 Feb 2025 14:47:59 +0000 Subject: [PATCH] Added Peira --- phd_projects/entries/peiro.qmd | 81 ++++++++++++++++++++++++++++++++++ 1 file changed, 81 insertions(+) create mode 100644 phd_projects/entries/peiro.qmd diff --git a/phd_projects/entries/peiro.qmd b/phd_projects/entries/peiro.qmd new file mode 100644 index 0000000..991d955 --- /dev/null +++ b/phd_projects/entries/peiro.qmd @@ -0,0 +1,81 @@ +--- +title: "Reinforcement Learning for Full-Hexahedral Mesh Generation" + +department: "Aeronautics" + +date: "10/02/2024" +author: + name: "Prof Joaquim Peiro and Dr Mashy Green (UCL ARC)" + affiliation: "Imperial" +institution: "Imperial" +--- +## Project Description + +Machine learning and its inherent ability for pattern matching is proposed as +an alternative to current state-of-the-art trial-and-error methods of hexahedral +mesh generation that could potentially overcome their limitations and lead to its +ultimate, yet unfulfilled, goal: a fully automatic full-hexahedral meshing tool. + +### Existing background work + + Mesh generation is the scaffolding that supports modelling and simulation: an +accurate and efficient simulation requires a high-quality mesh that appropriately +captures the complex geometrical and physical features of the problem, whilst +ensuring the stability of the numerical method employed for such simulation. +Hexahedral elements are the preferred choice for the majority of applications +in finite element analysis because their better approximation and stability prop- +erties when compared with their tetrahedral counterparts. However, the lack of +automatic, robust and reliable mesh generators of full hexahedral meshes means +that mixed or full tetrahedral meshes must be used for discretizing complex ge- +ometries. Current methods for generating complex, unstructured all-hexahedral +meshes are heuristic and often require extensive user input form accumulated +experience and time-consuming trial-and-error procedures. +We will adopt state-of-the-art machine learning methods for deep reinforce- +ment learning, such as Monte Carlo tree searching and its derivatives, that have +demonstrated their ability to cope with the demands of ‘learning’ what it takes +to win complex games such as chess or go, to identify winning strategies for +the full-hexahedral mesh generation game. Despite recent interest in using ma- +chine learning techniques for mesh generation, novelty here lies on viewing mesh +generation as a ‘game’. These techniques will be used to perform and assess mesh topological mesh +operations or ‘moves’. We will consider two main types of such operations: +hexahedral-to-hexahedral operations aiming at improving overall mesh quality, +and polyhedral-to-hexahedral operations to increase the percentage of converted +hexahedra and their mesh quality. The idea of assimilating mesh generation to +a game is new. + +### Main objectives of the project + +In the absence of a theoretically based holistic approach to full-hexahedral mesh +generation, we seek to investigate machine learning techniques for improving +the performance of state-of-the-art procedures for the topological modification +of full-hexahedral or hex-dominant meshes with a view to achieve high-quality +full-hexahedral meshes. +The idea behind the proposed methodology is to view topological mesh modi- +fication operations as ‘moves’ of a game with the aim of achieving full-hexahedral +meshes of optimal a priori mesh quality. +The main objectives of the work are: + +1. To implement and train state-of-the-art machine learning methods based +on deep reinforcement learning to ‘play’ the mesh generation ‘game’. +2. To identify the optimal ‘rules of the game’, or suitable criteria of a priori +mesh quality. +3. To select a suitable set of ‘game moves’, or topological mesh modifications, +and assess their performance according to the rules of the game. +4. To investigate the possibility of incorporating ‘sacrificial moves’ for im- +proved performance, wherein a ‘move’ that gives initially lower quality +in the short term ultimately results in a much higher-quality mesh after +many ‘moves’. + +### Details of Software/Data Deliverables + +This work will lead to the development of a robust full-hexahedral meshing ca- +pability of interest to both academia and industry. The capability will integrate: + +1. A software implementation of a library for mesh modification operations: +hexahedra-to-hexahedra and polyhedra-to-hexahedra. The library will be +stand-alone and callable by existing mesh generators such as NekMesh, +a general open-source high-order mesh generator under the Nektar++ +spectral/hp element framework. +2. Use of state-of-the-art software for machine learning, such as Tensorflow +or pyTorch, for the development of the reinforcement learning of the ‘hex- +ahedral meshing game.