About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks

• URL: http://arxiv.org/abs/2412.20851v1
• Date: Mon, 30 Dec 2024 10:42:28 GMT
• Title: About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks
• Authors: Vasiliy A. Es'kin, Alexey O. Malkhanov, Mikhail E. Smorkalov,
• Abstract summary: A rectified sigmoid activation function has been proposed to solve physical problems described by the ODE with neural networks.<n> Numerical experiments demonstrate the superiority of neural networks with a rectified sigmoid function over neural networks with a sigmoid function.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The article is devoted to the study of neural networks with one hidden layer and a modified activation function for solving physical problems. A rectified sigmoid activation function has been proposed to solve physical problems described by the ODE with neural networks. Algorithms for physics-informed data-driven initialization of a neural network and a neuron-by-neuron gradient-free fitting method have been presented for the neural network with this activation function. Numerical experiments demonstrate the superiority of neural networks with a rectified sigmoid function over neural networks with a sigmoid function in the accuracy of solving physical problems (harmonic oscillator, relativistic slingshot, and Lorentz system).

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