Accelerating Data Generation for Nonlinear temporal PDEs via homologous perturbation in solution space

Recent advancements in data-driven deep learning methods, particularly neural operators, are making significant strides in solving nonlinear temporal partial differential equations (PDEs). This is crucial because these methods traditionally rely on generating large quantities of solution pairs through conventional numerical techniques, which can be time-consuming. By accelerating this data generation process, researchers can enhance the efficiency and effectiveness of training models, ultimately leading to faster and more accurate solutions in various scientific and engineering applications.