A comprehensive study of numerical methods and physico-informed neural networks for modeling coupled Berlage oscillators. Modern information technologies and IT education

The paper provides a comparative analysis of the effectiveness of numerical methods and a neural network approach for solving a system of coupled linear ordinary differential equations of the second order, modeling the processes of geoacoustic emission in rocks. The research covers embedded numerical methods (LSODA, BDF, Radau), a specialized implementation of the Rosenbrock method of the 4th order of accuracy, as well as a physically informed neural network (PINN) with residual connections and normalization. The system of equations describes two coupled Berlage oscillators with variable coefficients characterizing the generation of high-frequency geoacoustic pulses. All algorithms have been implemented with parallel computing support to ensure high performance. A comparison of methods in terms of accuracy (root mean square, maximum and relative errors), computational efficiency and stability in the Python programming language using the PyTorch and scikit-learn libraries for implementing a neural network approach has been carried out. It is shown that the developed integrated approach makes it possible to effectively solve systems of equations for the class of problems under consideration. The neural network approach provides accuracy comparable to numerical methods. The proposed complex can be successfully applied both in fundamental research of geoacoustic processes and in practical tasks of monitoring the condition of rocks.

Sergienko D.F., Parovik R.I. A comprehensive study of numerical methods and physico-informed neural networks for modeling coupled Berlage oscillators. Modern information technologies and IT education. 2025. Vol. 21, No. 4. ISSN:2411-1473.