Comparison of numerical methods and neural network approaches for simulating high-frequency geoacoustic emission from a single dislocation source

We present a comparative analysis of numerical methods (4th-order Rosenbrock, Radau, BDF, and LSODA from the SciPy library) and the Physics-Informed Neural Networks (PINN) approach for solving a mathematical model of high-frequency geoacoustic emission from a single dislocation source using Python. Parallel implementation of the Rosenbrock method on eight processors significantly improved its performance. We compared the methods in terms of accuracy, computational cost, and stability. The results show that the PINN approach, with an architecture specifically designed for mathematical physics problems, achieves accuracy comparable to the manually implemented Rosenbrock method. In addition, PINNs offer advantages such as simplified problem parameterization and a global approximation of the solution, ensuring smoothness and avoiding the numerical dispersion typical of grid-based methods.