Solving the discretised multiphase flow equations with interface capturing on structured grids using machine learning libraries

Boyang Chen; Claire E. Heaney; Jefferson L.M.A. Gomes; Omar K. Matar; Christopher C. Pain

doi:10.1016/j.cma.2024.116974

Solving the discretised multiphase flow equations with interface capturing on structured grids using machine learning libraries

Boyang Chen, Claire E. Heaney, Jefferson L.M.A. Gomes^* (Corresponding Author), Omar K. Matar, Christopher C. Pain

^*Corresponding author for this work

Imperial College London

Research output: Contribution to journal › Article › peer-review

Abstract

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network whose weights are determined by the numerical method, rather than by training, and hence, we refer to this approach as Neural Networks for PDEs (NN4PDEs). To solve the discretised multiphase flow equations, a multigrid solver is implemented through a convolutional neural network with a U-Net architecture. Immiscible two-phase flow is modelled by the 3D incompressible Navier–Stokes equations with surface tension and advection of a volume fraction field, which describes the interface between the fluids. A new compressive algebraic volume-of-fluids method is introduced, based on a residual formulation using Petrov–Galerkin for accuracy and designed with NN4PDEs in mind. High-order finite-element based schemes are chosen to model a collapsing water column and a rising bubble. Results compare well with experimental data and other numerical results from the literature, demonstrating that, for the first time, finite element discretisations of multiphase flows can be solved using an approach based on (untrained) convolutional neural networks. A benefit of expressing numerical discretisations as neural networks is that the code can run, without modification, on CPUs, GPUs or the latest accelerators designed especially to run AI codes.

Original language	English
Article number	116974
Number of pages	27
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	426
Early online date	17 Apr 2024
DOIs	https://doi.org/10.1016/j.cma.2024.116974 https://doi.org/10.1016/j.cma.2024.116974
Publication status	E-pub ahead of print - 17 Apr 2024

Bibliographical note

The authors would like to acknowledge the following EPSRC grants: the PREMIERE programme grant, “AI to enhance manufacturing, energy, and healthcare” (EP/T000414/1); ECO-AI, “Enabling CO capture and storage using AI” (EP/Y005732/1); MUFFINS, “MUltiphase Flow-induced Fluid-flexible structure InteractioN in Subsea” (EP/P033180/1); WavE-Suite, “New Generation Modelling Suite for the Survivability of Wave Energy Convertors in Marine Environments” (EP/V040235/1); INHALE, “Health assessment across biological length scales” (EP/T003189/1); AI-Respire, “AI for personalised respiratory health and pollution” (EP/Y018680/1); RELIANT, “Risk EvaLuatIon fAst iNtelligent Tool for COVID19” (EP/V036777/1); and CO-TRACE, “COvid-19 Transmission Risk Assessment Case Studies — education Establishments” (EP/W001411/1). Also, the authors acknowledge the Innovate UK grant D-XPERT, “AI-Powered Total Building Management System“ (TS/Y020324/1). Support from Imperial-X’s Eric and Wendy Schmidt Centre for AI in Science (a Schmidt Futures program) is gratefully acknowledged. The authors state that, for the purpose of open access, a Creative Commons Attribution (CC BY) license will be applied to any Author Accepted Manuscript version relating to this article.

Data Availability Statement

The code used to generate these results can be found at the following github repository: https://github.com/bc1chen/AI4PDE.

Keywords

Artificial Intelligence
Partial differential equations
Convolutional neural networks
U-Net
Graphics Processing Units
Finite Element Method

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Cite this

Chen, B., Heaney, C. E., Gomes, J. L. M. A., Matar, O. K., & Pain, C. C. (2024). Solving the discretised multiphase flow equations with interface capturing on structured grids using machine learning libraries. Computer Methods in Applied Mechanics and Engineering, 426, Article 116974. Advance online publication. https://doi.org/10.1016/j.cma.2024.116974, https://doi.org/10.1016/j.cma.2024.116974

Solving the discretised multiphase flow equations with interface capturing on structured grids using machine learning libraries. / Chen, Boyang; Heaney, Claire E.; Gomes, Jefferson L.M.A. (Corresponding Author) et al.
In: Computer Methods in Applied Mechanics and Engineering, Vol. 426, 116974, 01.06.2024.

Research output: Contribution to journal › Article › peer-review

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abstract = "This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network whose weights are determined by the numerical method, rather than by training, and hence, we refer to this approach as Neural Networks for PDEs (NN4PDEs). To solve the discretised multiphase flow equations, a multigrid solver is implemented through a convolutional neural network with a U-Net architecture. Immiscible two-phase flow is modelled by the 3D incompressible Navier–Stokes equations with surface tension and advection of a volume fraction field, which describes the interface between the fluids. A new compressive algebraic volume-of-fluids method is introduced, based on a residual formulation using Petrov–Galerkin for accuracy and designed with NN4PDEs in mind. High-order finite-element based schemes are chosen to model a collapsing water column and a rising bubble. Results compare well with experimental data and other numerical results from the literature, demonstrating that, for the first time, finite element discretisations of multiphase flows can be solved using an approach based on (untrained) convolutional neural networks. A benefit of expressing numerical discretisations as neural networks is that the code can run, without modification, on CPUs, GPUs or the latest accelerators designed especially to run AI codes.",

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note = "The authors would like to acknowledge the following EPSRC grants: the PREMIERE programme grant, “AI to enhance manufacturing, energy, and healthcare” (EP/T000414/1); ECO-AI, “Enabling CO capture and storage using AI” (EP/Y005732/1); MUFFINS, “MUltiphase Flow-induced Fluid-flexible structure InteractioN in Subsea” (EP/P033180/1); WavE-Suite, “New Generation Modelling Suite for the Survivability of Wave Energy Convertors in Marine Environments” (EP/V040235/1); INHALE, “Health assessment across biological length scales” (EP/T003189/1); AI-Respire, “AI for personalised respiratory health and pollution” (EP/Y018680/1); RELIANT, “Risk EvaLuatIon fAst iNtelligent Tool for COVID19” (EP/V036777/1); and CO-TRACE, “COvid-19 Transmission Risk Assessment Case Studies — education Establishments” (EP/W001411/1). Also, the authors acknowledge the Innovate UK grant D-XPERT, “AI-Powered Total Building Management System“ (TS/Y020324/1). Support from Imperial-X{\textquoteright}s Eric and Wendy Schmidt Centre for AI in Science (a Schmidt Futures program) is gratefully acknowledged. The authors state that, for the purpose of open access, a Creative Commons Attribution (CC BY) license will be applied to any Author Accepted Manuscript version relating to this article.",

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Solving the discretised multiphase flow equations with interface capturing on structured grids using machine learning libraries

Abstract

Bibliographical note

Data Availability Statement

Keywords

Access to Document

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