Estimation of the Computational Efficiency of Parallel Implementation of the Algorithm for Modeling a Location Source Based on an Ensemble of Physico-Informed Neural Networks

The paper presents a parallel implementation of an algorithm for modeling a single dislocation source based on an ensemble of physics‑informed neural networks (Physics‑Informed Neural Networks, PINN). The task of approximating the Berlage pulse, which describes the displacement of a dislocation source under rock deformation, is considered; this is a key element in the study of high‑frequency geoacoustic emission arising during the failure of geomaterials under the influence of mechanical stresses. A method for decomposing the time domain into an arbitrary number of subdomains (\( n=1,\dots,8 \)) is proposed, each of which is trained on a separate computational process. To combine the predictions of the subdomains, the MultiDomainPINN ensemble architecture is used, which ensures smooth coordination of solutions at the boundaries of the overlapping regions. The quality of the approximation is assessed using statistical metrics: mean squared error (MSE), root mean squared error (RMSE), normalized root mean square error (NRMSE), coefficient of determination (\( R^2 \)), and maximum absolute error, which allows for a quantitative comparison of the PINN solution with the analytical Berlage impulse. To quantitatively assess the computational efficiency of the parallel implementation, TAECO metrics are used, which allow for evaluating the algorithm’s efficiency. The assessment was carried out at the inference stage of trained models for parameters that were not involved in the training, by comparing them with successive runs of the 4th‑order Rosenbrock method. MultiDomainPINN provides high performance, with a 70--76‑fold speedup compared to the Rosenbrock method while maintaining comparable accuracy (MSE at the level of \( 10^{-10} \)—\( 10^{-8} \)). The developed software is scalable and can be adapted for a wide range of tasks related to modeling seismic signals and wave processes, including machine learning tasks in geophysics, seismology, and solid mechanics.