About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909444091150336 |
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| author | Es'kin, Vasiliy A. Malkhanov, Alexey O. Smorkalov, Mikhail E. |
| author_facet | Es'kin, Vasiliy A. Malkhanov, Alexey O. Smorkalov, Mikhail E. |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20851 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks Es'kin, Vasiliy A. Malkhanov, Alexey O. Smorkalov, Mikhail E. Numerical Analysis Artificial Intelligence Machine Learning Computational Physics 68T07 (Primary) 65Z05, 65M99 (Secondary) I.2.1; I.2.7; J.2 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). |
| title | About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks |
| topic | Numerical Analysis Artificial Intelligence Machine Learning Computational Physics 68T07 (Primary) 65Z05, 65M99 (Secondary) I.2.1; I.2.7; J.2 |
| url | https://arxiv.org/abs/2412.20851 |