Physics Informed Neural Networks in Solving Coefficient Inverse Problems

Title	Physics Informed Neural Networks in Solving Coefficient Inverse Problems
Authors	E. B. Kuznetsov¹, S. S. Leonov^{1, 2} ¹Moscow Aviation Institute (National Research University) ²Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)
Annotation	The paper considers the process of constructing a semi-empirical recurrent neural network belonging to the class of physics informed neural networks. The authors propose an approach to building a semi-empirical network architecture using implicit Runge-Kutta family schemes, which allows to obtain an analytical functional expression equivalent to a pre-trained recurrent neural network. The proposed approach was tested on a linear, weakly rigid initial problem with one scalar parameter.
Keywords	semi-empirical recurrent neural networks, physics informed neural networks, identification, coefficient inverse problem, ordinary differential equations, initial problem.
Citation	Kuznetsov E. B., Leonov S. S. ''Physics Informed Neural Networks in Solving Coefficient Inverse Problems'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 109-114. Available at: https://conf.svmo.ru/files/2026/papers/paper85.pdf. - Date of access: 25.09.2026.