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Evaluation of Physics-informed Neural Network Solution Accuracy and Efficiency for Modelling Aortic Transvalvular Blood Flow.
Thesis (MEng)--Stellenbosch University, 2024.
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| Format: | Thesis |
| Language: | en_ZA en_ZA |
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Stellenbosch : Stellenbosch University
2024
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| _version_ | 1867613925856509952 |
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| access_status_str | Open Access |
| author | Du Toit, Jacques Francois |
| author2 | Laubscher, Ryno |
| author_browse | Du Toit, Jacques Francois Laubscher, Ryno |
| author_facet | Laubscher, Ryno Du Toit, Jacques Francois |
| author_sort | Du Toit, Jacques Francois |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MEng)--Stellenbosch University, 2024. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/130347 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA en_ZA |
| last_indexed | 2026-06-10T12:43:54.041Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/130347 Evaluation of Physics-informed Neural Network Solution Accuracy and Efficiency for Modelling Aortic Transvalvular Blood Flow. Du Toit, Jacques Francois Laubscher, Ryno Stellenbosch University. Faculty of Engineering. Dept. of Mechanical and Mechatronic Engineering. Aortic valve stenosis Deep learning Physics-informed neural networks Computational fluid dynamics Aortic valve -- Stenosis Deep learning (Machine learning) Neural networks (Computer science) Computational fluid dynamics UCTD Thesis (MEng)--Stellenbosch University, 2024. ENGLISH ABSTRACT: Finite volume method (FVM) based solvers for many-query-type problems like simulation-based design suffer from the curse of dimensionality. They also incur a prohibitive computational cost when solving inverse problems that incorporate measurement data to characterize incomplete physical systems. Recently a new partial differential equation (PDE) solver called the physics-informed neural network (PINN) has been gaining in popularity and is posed to address some of these shortcomings of the FVM. The PINN method shows great potential, but many challenges remain to be addressed. These challenges include poor convergence of the optimization procedure and poor solution accuracy when applying the PINN method to turbulent flow problems in the forward mode. In this work, a configuration tuning study was performed to evaluate various published methods of improving the PINN method. This study culminated in a tuned PINN implementation that improved the normalized mean absolute percentage error (NMAPE) on a forward mode problem from 50.9 % to 3.55 %. The tuned PINN was tested on the forward mode problem of simulating steady, incompressible transvalvular blood flow through stenotic aortic valves. The inverse mode problem of recovering the full pressure field of a stenotic aortic valve with an unknown inlet boundary condition given sparse, noisy measurement data of the velocity field was also solved. Solution accuracies as low as 1.65 % NMAPE were achieved without noise in the data but an exponential increase in error was observed as the noise amplitude increased. The simulation of turbulent flow using a mixing length turbulence model was also assessed. It was found that the PINN method converged to a qualitatively accurate solution, but that the quantitative accuracy was highly variable. In the forward and inverse modes, the lowest solution error reached was 42.4 % NMAPE, and 16.0 % NMAPE respectively. AFRIKAANSE OPSOMMING: Oplossingsalgoritmes wat gebaseer is op die eindige volume metode (EVM) vir probleme wat baie funksie evaluerings vereis, soos simulasiegebaseerde ontwerp, ly aan die vloek van dimensionaliteit. Hierdie metodes het ook ’n ontoelaatbare berekeningstyd wanneer dit gebruik word om inverse probleme op te los waar metingsdata gebruik word om ’n onvolledige fisiese stelsel te karakteriseer (Teenoor voorwaartse probleme waar die sisteem en grenskondisies volledig gedefinieër is). Onlangs het ’n nuwe gedeeltelike differensiaalvergelyking oplosser toegeneem in populariteit wat belyn is om die tekortkominge van die EVM gebaseerde metodes aan te spreek. Die metode word die fisikaingeligde neurale netwerk (FINN) genoem. Die FINN metode toon groot potensiaal, maar daar is nog baie uitdagings wat aangespreek moet word. Hierdie uitdagings sluit in swak konvergensie van die optimeringsprosedure en swak oplossingsakkuraatheid wanneer die FINN metode toegepas word op voorwaartse turbulente vloei probleme. In hierdie werk is ’n opstellingstudie uitgevoer om verskeie gepubliseerde metodes te evalueer wat die FINN metode verbeter. Hierdie studie het gelei tot ’n gestemde FINN implementasie wat die genoriv https://scholar.sun.ac.za UITTREKSEL v maliseerde gemiddelde absolute persentasie fout (GGAPF) op ’n voorwaartse probleem van 50.9 % tot 3.55 % verbeter het. Die gekose voorwaartse probleem was die simulasie van bloedvloei deur ’n stenotiese aortaklep. ’n Inverse weergawe van die probleem was ook opgelos. Die probleem was om ’n volledige drukveld van ’n stenotiese aortaklep af te lei sonder ’n bekende inlaatsnelheidsgrenskondisie. Dit was moontlik deur gebruik te maak van ’n beperkte hoeveelheid versteurde metingsdata van die snelheidsveld. ’n Oplossingsakkuraatheid van 1.65 % GGAPF was bereik met geen geraas in die data nie, maar ’n eksponensiele toename in fout was waargeneem soos die geraasamplitude toegeneem het. Die simulasie van turbulente vloei met behulp van ’n mengingslengte turbulensiemodel is ook geassesseer. Daar is bevind dat die FINN metode konvergeer na ’n kwalitatief akkurate oplossing, maar dat die kwantitatiewe akkuraatheid hoogs wisselvallig was. In die voorwaartse en inverse modusse was die laagste oplossingsfoute 42.4 % GGAPF en 16.0 % GGAPF onderskeidelik. Masters 2024-02-26T11:54:47Z 2024-04-26T14:18:10Z 2024-02-26T11:54:47Z 2024-04-26T14:18:10Z 2024-02 Thesis https://scholar.sun.ac.za/handle/10019.1/130347 en_ZA en_ZA Stellenbosch University xvii, 102 pages : illustrations. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Aortic valve stenosis Deep learning Physics-informed neural networks Computational fluid dynamics Aortic valve -- Stenosis Deep learning (Machine learning) Neural networks (Computer science) Computational fluid dynamics UCTD Du Toit, Jacques Francois Evaluation of Physics-informed Neural Network Solution Accuracy and Efficiency for Modelling Aortic Transvalvular Blood Flow. |
| title | Evaluation of Physics-informed Neural Network Solution Accuracy and Efficiency for Modelling Aortic Transvalvular Blood Flow. |
| title_full | Evaluation of Physics-informed Neural Network Solution Accuracy and Efficiency for Modelling Aortic Transvalvular Blood Flow. |
| title_fullStr | Evaluation of Physics-informed Neural Network Solution Accuracy and Efficiency for Modelling Aortic Transvalvular Blood Flow. |
| title_full_unstemmed | Evaluation of Physics-informed Neural Network Solution Accuracy and Efficiency for Modelling Aortic Transvalvular Blood Flow. |
| title_short | Evaluation of Physics-informed Neural Network Solution Accuracy and Efficiency for Modelling Aortic Transvalvular Blood Flow. |
| title_sort | evaluation of physics informed neural network solution accuracy and efficiency for modelling aortic transvalvular blood flow |
| topic | Aortic valve stenosis Deep learning Physics-informed neural networks Computational fluid dynamics Aortic valve -- Stenosis Deep learning (Machine learning) Neural networks (Computer science) Computational fluid dynamics UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/130347 |
| work_keys_str_mv | AT dutoitjacquesfrancois evaluationofphysicsinformedneuralnetworksolutionaccuracyandefficiencyformodellingaortictransvalvularbloodflow |