DOI: https://doi.org/10.14710/jfma.v6i2.20084

EXPLORING PHYSICS-INFORMED NEURAL NETWORKS FOR SOLVING BOUNDARY LAYER PROBLEMS

Muchamad Harry Yudha Pratama  -  Mathematics Master Study Program, Institut Teknologi Bandung, Indonesia
*Agus Yodi Gunawan  -  Industrial and Financial Mathematics Research Group, , Indonesia

How to cite (IEEE): M. H. Y. Pratama, and A. Y. Gunawan, "EXPLORING PHYSICS-INFORMED NEURAL NETWORKS FOR SOLVING BOUNDARY LAYER PROBLEMS," Journal of Fundamental Mathematics and Applications (JFMA), vol. 6, no. 2, pp. 101-116, Nov. 2023. https://doi.org/10.14710/jfma.v6i2.20084
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Abstract

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 ODE
with 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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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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