Physics informed neural networks to solve forward and inverse fluid flow and heat transfer problems

Aliakbari, Maryam (2023) Physics informed neural networks to solve forward and inverse fluid flow and heat transfer problems. Doctoral thesis, Northern Arizona University.

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Abstract

This dissertation proposes novel approaches to address challenges in solving fluid flow and transport problems in heterogeneous systems using deep learning methods.The first approach is a multi-fidelity modeling approach that combines data generated by a low-fidelity computational fluid dynamics (CFD) solution strategy and data-free physics- informed neural networks (PINN) to obtain improved accuracy. High-fidelity models of multiphysics fluid flow processes are often computationally expensive. On the other hand, less accurate low-fidelity models could be efficiently executed to provide an approximation to the solution. Multi-fidelity approaches combine high-fidelity and low-fidelity data and/or models to obtain a desirable balance between computational efficiency and accuracy. In the proposed approach, transfer learning based on low-fidelity CFD data is used to initial- ize PINN, which is then used to obtain the final results without any high-fidelity training data. Several partial differential equations are solved to predict velocity and temperature in different fluid flow, heat transfer, and porous media transport problems. The proposed approach significantly improves the accuracy of low-fidelity CFD data and also improves the convergence speed and accuracy of PINN. The second approach is an ensemble PINN (ePINN) method that is proposed to solve the uniqueness issue of inverse problems. In inverse modeling, measurement data are used to estimate unknown parameters that vary in space. However, due to the spatial variability of these unknown parameters in heterogeneous systems (e.g., permeability or diffusivity), the inverse problem is ill-posed and infinite solutions are possible. PINN has become a popular approach for solving inverse problems but is sensitive to hyperparameters and can produce unrealistic patterns. The ePINN approach uses an ensemble of parallel neural networks that are initialized with a meaningful pattern of the unknown parameter. These parallel networks provide a basis that is fed into a main neural network that is trained using PINN. It is shown that an appropriately selected set of patterns can guide PINN in producing more realistic results that are relevant to the problem of interest. The proposed ePINN approach increases the accuracy in inverse problems and mitigates the challenges associated with non-uniqueness. The third approach is a novel method called ensemble deep operator neural network (eDeepONet), which is designed to solve the solution operators of partial differential equa- tions (PDEs) using deep neural networks. eDeepONet involves training multiple sub-DeepONets on smaller subsets of the dataset, which are then combined in a fully connected neural network to predict the final solution. eDeepONet reduces the complexity of the training process, improves convergence, and provides more accurate solutions compared to the tra- ditional DeepONet approach. Additionally, eDeepONet is designed to handle parametric PDE equations and does not require explicit knowledge of the PDE equation or its bound- ary conditions, making it more flexible and applicable in a wider range of applications. The effectiveness of eDeepONet in enhancing prediction accuracy and improving convergence is demonstrated on a 2D diffusion problem. Overall, the proposed approaches demonstrate the potential of deep learning methods in solving challenging fluid flow and transport problems in homogeneous and heterogeneous systems. The multi-fidelity approach improves the accuracy of low-fidelity data and reduces computational cost. The ePINN approach mitigates the challenges associated with non- uniqueness in inverse problems. The eDeepONet approach reduces the complexity of the training process, improves convergence, and provides more accurate solutions for PDEs. These advances in deep learning methods have the potential to revolutionize our ability to model and predict fluid flow and transport in a wide range of applications.

Item Type:	Thesis (Doctoral)
Publisher’s Statement:	© Copyright is held by the author. Digital access to this material is made possible by the Cline Library, Northern Arizona University. Further transmission, reproduction or presentation of protected items is prohibited except with permission of the author.
Keywords:	computational fluid dynamics; deep learning; Deep Operator Neural Networks; Multi-fidelity modeling; Partial differential equations; physics informed neural network
Subjects:	Q Science > QC Physics
NAU Depositing Author Academic Status:	Student
Department/Unit:	Graduate College > Theses and Dissertations College of the Environment, Forestry, and Natural Sciences > Physics and Astronomy
Date Deposited:	01 Aug 2023 21:28
Last Modified:	01 Aug 2023 21:28
URI:	https://openknowledge.nau.edu/id/eprint/6078

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