Abstract
AbstractSolving general non-linear partial differential equations (PDE) precisely and efficiently has been a long-lasting challenge in the field of scientific computing. Based on the deep learning framework for solving non-linear PDEs physics-informed neural networks (PINN), we introduce an adaptive collocation strategy into the PINN method to improve the effectiveness and robustness of this algorithm when selecting the initial data to be trained. Instead of merely training the neural network once, multi-step discrete time models are considered when predicting the long time behaviour of solutions of the Allen-Cahn equation. Numerical results concerning solutions of the Allen-Cahn equation are presented, which demonstrate that this approach can improve the robustness of original neural networks approximation.KeywordsDeep learningAdaptive collocationDiscrete time modelsPhysics informed neural networksAllen-Cahn equation
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
