A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions

With the advantages of fast calculating speed and high precision, physics-informed neural network method opens up a new approach for numerically solving nonlinear partial differential equations. Based on conserved quantities, we devise two-stage PINN which is tailored to nature equations by introducing features physical systems into networks. Its remarkable advantage lies in that it can impose constraints from global perspective. In stage one, original applied. two, additionally introduce measurement quantities mean squared error loss train This utilized simulate abundant localized wave solutions integrable We mainly study Sawada-Kotera equation as well coupled equations: classical Boussinesq-Burgers acquire data-driven soliton molecule, M-shape double-peak soliton, plateau interaction solution, etc. Numerical results illustrate dynamic behaviors these be reproduced remarkably improve prediction accuracy enhance ability generalization compared method.