Improving Boundary Layer Predictions Using Parametric Physics-Aware Neural Networks

Gomes, Antônio Tadeu A.; Silva, Larissa Miguez da; Valentin, Frédéric

doi:10.1007/978-3-031-23821-5_7

Communications in Computer and Information Science

2022

DOI: 10.1007/978-3-031-23821-5_7

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Improving Boundary Layer Predictions Using Parametric Physics-Aware Neural Networks

Antônio Tadeu A. Gomes

Larissa Miguez da Silva²,

Frédéric Valentin³

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2024

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On Loss Functionals for Physics-Informed Neural Networks for Steady-State Convection-Dominated Convection-Diffusion Problems

Frerichs-Mihov,

Henning,

John

2024

Commun. Appl. Math. Comput.

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Solutions of convection-dominated convection-diffusion problems usually possess layers, which are regions where the solution has a steep gradient. It is well known that many classical numerical discretization techniques face difficulties when approximating the solution to these problems. In recent years, physics-informed neural networks (PINNs) for approximating the solution to (initial-)boundary value problems ((I)BVPs) received a lot of interest. This paper studies various loss functionals for PINNs that are especially designed for convection-dominated convection-diffusion problems and that are novel in the context of PINNs. They are numerically compared to the vanilla and an hp-variational loss functional from the literature based on two steady-state benchmark problems whose solutions possess different types of layers. We observe that the best novel loss functionals reduce the $$L^2(\varOmega )$$ L 2 ( Ω ) error by 17.3% for the first and 5.5% for the second problem compared to the methods from the literature.

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On Loss Functionals for Physics-Informed Neural Networks for Steady-State Convection-Dominated Convection-Diffusion Problems

Frerichs-Mihov,

Henning,

John

2024

Commun. Appl. Math. Comput.

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show abstract

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Improving Boundary Layer Predictions Using Parametric Physics-Aware Neural Networks

Cited by 1 publication

References 18 publications

On Loss Functionals for Physics-Informed Neural Networks for Steady-State Convection-Dominated Convection-Diffusion Problems

On Loss Functionals for Physics-Informed Neural Networks for Steady-State Convection-Dominated Convection-Diffusion Problems

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