Numerical dispersion suppression in the two-dimensional acoustic wave equation using PETSc and an improved Pix2Pix algorithm

Abstract

This work addresses the suppression of numerical dispersion in the solution of the two-dimensional acoustic wave equation using the Portable, Extensible Toolkit for Scientific Computation (PETSc) in combination with an improved Pix2Pix algorithm. The proposed approach begins with the numerical solution of the wave equation via a Finite Difference Method (FDM) solver implemented with PETSc, enabling efficient parallel computation. Coarse-grid simulations, which inherently exhibit numerical dispersion, are generated and compared against reference solutions obtained from refined-grid simulations. The coarse-grid data are used as inputs and the refined-grid solutions as target outputs for training a conditional Generative Adversarial Network (cGAN) based on an enhanced Pix2Pix architecture. Several parameter configurations are investigated to determine the optimal training setup, including learning rate, number of epochs, and certainty coefficients for both the L1 and Sobel loss terms. The trained model is then applied to different velocity models to assess its generalization capabilities. Performance evaluation is conducted by computing the Normalized Root Mean Square Error (NRMSE) between the cGAN-predicted fields and the reference solutions. The results demonstrate that the improved Pix2Pix model can significantly reduce numerical dispersion effects, producing wavefields that closely match the accuracy of high-resolution simulations while retaining the lower computational cost of coarse-grid calculations.