Towards Optimally Weighted Physics-Informed Neural Networks in Ocean Modelling

de Wolff, Taco; Carrillo, Hugo; Martí, Luis; Sanchez-Pi, Nayat

doi:10.48550/arxiv.2106.08747

Cited by 7 publications

(8 citation statements)

References 10 publications

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“…For the PINN model, all parameters were found either manually or through a grid search [21,30]. The RK4 model usually does not require any sophisticated parameter search; usually, a larger grid size is used to approximate the derivatives and a smaller CFL number is used to ensure the stability is sufficient.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…This research considers a transient gas flow in pipelines using symmetry-enhanced Physics-Informed Neural Networks, with manual selection of the necessary hyperparameters using a weighted loss function [30]. The PINN leverages the continuous Lie symmetry information inherent in PDEs, wherein the invariant surface conditions (ISCs) induced by these symmetries are integrated into the PINN's loss function [31].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Applications of Symmetry-Enhanced Physics-Informed Neural Networks in High-Pressure Gas Flow Simulations in Pipelines

Alpar,

Faizulin,

Tokmukhamedova

et al. 2024

Symmetry

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This article presents a detailed examination of the methodology and modeling tools utilized to analyze gas flows in pipelines, rooted in the fundamental principles of gas dynamics. The methodology integrates numerical simulations with modern neural network techniques, particularly focusing on the PINN utilizing the continuous symmetry data inherent in PDEs, which is called the symmetry-enhanced Physics-Informed Neural Network. This innovative approach combines artificial neural networks (ANNs) integrating physical equations, which provide enhanced efficiency and accuracy when modeling various complex processes related to physics with a symmetric and asymmetric nature. The presented mathematical model, based on the system of Euler equations, has been carefully implemented using Python language. Verification with analytical solutions ensures the accuracy and reliability of the computations. In this research, a comparative and comprehensive analysis was carried out comparing the outcomes obtained using the symmetry-enhanced PINN method and those from conventional computational fluid dynamics (CFD) approaches. The analysis highlighted the advantages of the symmetry-enhanced PINN method, which produced smoother pressure and velocity fluctuation profiles while reducing the computation time, demonstrating its capacity as a revolutionary modeling tool. The estimated results derived from this study are of paramount importance for ensuring ongoing energy supply reliability and can also be used to create predictive models related to gas behavior in pipelines. The application of modeling techniques for gas flow simulations has the potential to improve the integrity of our energy infrastructure and utilization of gas resources, contributing to advancing our understanding of symmetry principles in nature. However, it is crucial to emphasize that the effectiveness of such models relies on continuous monitoring and frequent updates to ensure alignment with real-world conditions. This research not only contributes to a deeper understanding of compressible gas flows but also underscores the crucial role of advanced modeling methodologies in the sustainable management of gas resources for both current and future generations. The numerical data covered the physics of the process related to the modeling of high-pressure gas flows in pipelines with regard to density, velocity and pressure, where the PINN model was able to outperform the classical CFD method for velocity by 170% and for pressure by 360%, based on L∞ values.

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Section: Computational Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Applications of Symmetry-Enhanced Physics-Informed Neural Networks in High-Pressure Gas Flow Simulations in Pipelines

Alpar,

Faizulin,

Tokmukhamedova

et al. 2024

Symmetry

View full text Add to dashboard Cite

show abstract

“…This research considers a transient gas flow in pipelines using Physics-Informed Neural Networks, with manual selection of the necessary hyperparameters using a weighted loss function [28]. In addition to that, evaluation of the PINN model performance, the following problems will be solved for demonstrating the effectiveness of the method: Burgers Equation [29,30], Viscous Burgers Equation [30,31] and Euler's Equations of gas dynamics [32,33], where the main focus will be on the compressible flow problem.…”

Section: Introductionmentioning

confidence: 99%

Application Weighted Physics-Informed Neural Networks to High-Pressure Gas Flows Simulation in Pipelines

Alpar,

Faizulin,

Tokmukhamedova

et al. 2024

Preprint

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This article presents a detailed examination of the methodology and modeling tools utilized to analyze gas flow in pipelines, rooted in the fundamental principles of gas dynamics. The methodology integrates numerical simulations with modern neural network techniques, particularly focusing on the Physics-Informed Neural Network (PINN) method. This innovative approach combines artificial neural networks (ANNs) with physical equations, offering a more efficient and accurate way to model various complex processes and phenomena. The proposed mathematical model, based on the Euler equation, has been meticulously implemented using the Python language. Verification with analytical solutions ensures the accuracy and reliability of the computations. In the research, a comprehensive comparative analysis was conducted between results obtained using the PINN method and those from conventional Computational Fluid Dynamics (CFD) approaches. The analysis highlighted the advantages of the PINN method, which produced smoother pressure and velocity fluctuation profiles while reducing computation time, demonstrating its potential as a transformative modeling tool. The data derived from this study are of paramount importance for ensuring ongoing energy supply reliability and can also be used to create predictive models related to gas behavior in pipelines. The application of modeling techniques for gas flow simulation has the potential to revolutionize the integrity of our energy infrastructure and utilization of gas resources. However, it is crucial to emphasize that the effectiveness of such models relies on continuous monitoring and frequent updates to ensure alignment with real-world conditions. This research not only contributes to a deeper understanding of compressible gas flows but also underscores the crucial role of advanced modeling methodologies in the sustainable management of gas resources for both current and future generations.

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“…Furthermore, increasing the resolution of collocation points within the boundary layer does not lead to a resolution of PINN training issues. While PINN has been successfully applied to various advection-diffusion transport problems, including boundary layers, through optimal weighting of loss terms and a focus on low Peclet numbers [8,9,10,11,12,13,14], it has remained elusive in handling thin boundary layers with vanishing viscosity/diffusivity, presenting a significant challenge for PINN.…”

Section: Introductionmentioning

confidence: 99%

Exploring Physics-Informed Neural Networks for Solving Boundary Layer Problems

Pratama,

Gunawan

2023

JFMA

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In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN) to tackle boundary layer problems. We here examine four different cases of boundary layers of second-order ODE: a linear ODEwith constant coefficients, a nonlinear ODE with homogeneous boundary conditions, an ODE with non-constant coefficients, and an ODE featuring multiple boundary layers. We adapt the line of PINN technique for handling those problems, and our results show that the accuracy of the resulted solutions depends on how we choose the most reliable and robust activation functions when designing the architecture of the PINN. Beside that, through our explorations, we aim to improve our understanding on how the PINN technique works better for boundary layer problems. Especially, the use of the SiLU (Sigmoid-Weighted Linear Unit) activation function in PINN has proven to be particularly remarkable in handling our boundary layer problems.

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Towards Optimally Weighted Physics-Informed Neural Networks in Ocean Modelling

Cited by 7 publications

References 10 publications

Applications of Symmetry-Enhanced Physics-Informed Neural Networks in High-Pressure Gas Flow Simulations in Pipelines

Applications of Symmetry-Enhanced Physics-Informed Neural Networks in High-Pressure Gas Flow Simulations in Pipelines

Application Weighted Physics-Informed Neural Networks to High-Pressure Gas Flows Simulation in Pipelines

Exploring Physics-Informed Neural Networks for Solving Boundary Layer Problems

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