3 papers
math.NA2025
Physics-informed neural networks and neural operators for a study of EUV electromagnetic wave diffraction from a lithography mask
Vasiliy A. Es'kin, Egor V. Ivanov
Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from a mask are presen…
math.NA2024
About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks
Vasiliy A. Es'kin, Alexey O. Malkhanov, Mikhail E. Smorkalov
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 functi…
math.NA2024
Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?
Vasiliy A. Es'kin, Alexey O. Malkhanov, Mikhail E. Smorkalov
The article discusses the development of various methods and techniques for initializing and training neural networks with a single hidden layer, as well as training a separable ph…