Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven Approach
Physics-informed neural networks (PINNs) have emerged as a promising approach for simulating nonlinear physical systems, particularly in the field of fluid dynamics and turbulence modelling. Traditional turbulence models often rely on simplifying assumptions or closed numerical models, which simplif...
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MDPI AG
2024-11-01
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| author | William Fox Bharath Sharma Jianhua Chen Marco Castellani Daniel M. Espino |
| author_facet | William Fox Bharath Sharma Jianhua Chen Marco Castellani Daniel M. Espino |
| author_sort | William Fox |
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| description | Physics-informed neural networks (PINNs) have emerged as a promising approach for simulating nonlinear physical systems, particularly in the field of fluid dynamics and turbulence modelling. Traditional turbulence models often rely on simplifying assumptions or closed numerical models, which simplify the flow, leading to inaccurate flow predictions or long solve times. This study examines solver constraints in a PINNs solver, aiming to generate an understanding of an optimal PINNs solver with reduced constraints compared with the numerically closed models used in traditional computational fluid dynamics (CFD). PINNs were implemented in a periodic hill flow case and compared with a simple data-driven approach to neural network modelling to show the limitations of a data-driven model on a small dataset (as is common in engineering design). A standard full equation PINNs model with predicted first-order stress terms was compared against reduced-boundary models and reduced-order models, with different levels of assumptions made about the flow to monitor the effect on the flow field predictions. The results in all cases showed good agreement against direct numerical simulation (DNS) data, with only boundary conditions provided for training as in numerical modelling. The efficacy of reduced-order models was shown using a continuity only model to accurately predict the flow fields within 0.147 and 2.6 percentage errors for streamwise and transverse velocities, respectively, and a modified mixing length model was used to show the effect of poor assumptions on the model, including poor convergence at the flow boundaries, despite a reduced solve time compared with a numerically closed equation set. The results agree with contemporary literature, indicating that physics-informed neural networks are a significant improvement in solve time compared with a data-driven approach, with a novel proposition of numerically derived unclosed equation sets being a good representation of a turbulent system. In conclusion, it is shown that numerically unclosed systems can be efficiently solved using reduced-order equation sets, potentially leading to a reduced compute requirement compared with traditional solver methods. |
| format | Article |
| id | doaj-art-89cc2fa8a4c2495e8a6e499adde80884 |
| institution | OA Journals |
| issn | 2311-5521 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Fluids |
| spelling | doaj-art-89cc2fa8a4c2495e8a6e499adde808842025-08-20T02:00:45ZengMDPI AGFluids2311-55212024-11-0191227910.3390/fluids9120279Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven ApproachWilliam Fox0Bharath Sharma1Jianhua Chen2Marco Castellani3Daniel M. Espino4Department of Mechanical Engineering, University of Birmingham, Birmingham B15 2TT, UKDepartment of Mechanical Engineering, University of Birmingham, Birmingham B15 2TT, UKDepartment of Mechanical Engineering, University of Birmingham, Birmingham B15 2TT, UKDepartment of Mechanical Engineering, University of Birmingham, Birmingham B15 2TT, UKDepartment of Mechanical Engineering, University of Birmingham, Birmingham B15 2TT, UKPhysics-informed neural networks (PINNs) have emerged as a promising approach for simulating nonlinear physical systems, particularly in the field of fluid dynamics and turbulence modelling. Traditional turbulence models often rely on simplifying assumptions or closed numerical models, which simplify the flow, leading to inaccurate flow predictions or long solve times. This study examines solver constraints in a PINNs solver, aiming to generate an understanding of an optimal PINNs solver with reduced constraints compared with the numerically closed models used in traditional computational fluid dynamics (CFD). PINNs were implemented in a periodic hill flow case and compared with a simple data-driven approach to neural network modelling to show the limitations of a data-driven model on a small dataset (as is common in engineering design). A standard full equation PINNs model with predicted first-order stress terms was compared against reduced-boundary models and reduced-order models, with different levels of assumptions made about the flow to monitor the effect on the flow field predictions. The results in all cases showed good agreement against direct numerical simulation (DNS) data, with only boundary conditions provided for training as in numerical modelling. The efficacy of reduced-order models was shown using a continuity only model to accurately predict the flow fields within 0.147 and 2.6 percentage errors for streamwise and transverse velocities, respectively, and a modified mixing length model was used to show the effect of poor assumptions on the model, including poor convergence at the flow boundaries, despite a reduced solve time compared with a numerically closed equation set. The results agree with contemporary literature, indicating that physics-informed neural networks are a significant improvement in solve time compared with a data-driven approach, with a novel proposition of numerically derived unclosed equation sets being a good representation of a turbulent system. In conclusion, it is shown that numerically unclosed systems can be efficiently solved using reduced-order equation sets, potentially leading to a reduced compute requirement compared with traditional solver methods.https://www.mdpi.com/2311-5521/9/12/279data-driven modelflow predictionsnumerically closedperiodic hillphysics-informed neural networkturbulence modelling |
| spellingShingle | William Fox Bharath Sharma Jianhua Chen Marco Castellani Daniel M. Espino Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven Approach Fluids data-driven model flow predictions numerically closed periodic hill physics-informed neural network turbulence modelling |
| title | Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven Approach |
| title_full | Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven Approach |
| title_fullStr | Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven Approach |
| title_full_unstemmed | Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven Approach |
| title_short | Optimising Physics-Informed Neural Network Solvers for Turbulence Modelling: A Study on Solver Constraints Against a Data-Driven Approach |
| title_sort | optimising physics informed neural network solvers for turbulence modelling a study on solver constraints against a data driven approach |
| topic | data-driven model flow predictions numerically closed periodic hill physics-informed neural network turbulence modelling |
| url | https://www.mdpi.com/2311-5521/9/12/279 |
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