Physics informed by deep learning: numerical solutions of modified Korteweg-de Vries equation

DOI10.1155/2021/5569645OpenAlexW3169046500MaRDI QIDQ2244291

Yuexing Bai, Sudao Bilige, Temuer Chaolu

Publication date: 12 November 2021

Published in: Advances in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2021/5569645

Mathematics Subject Classification ID

Biology and other natural sciences (92-XX) Numerical analysis (65-XX)

Uses Software

• L-BFGS
• Chebfun

Cites Work

• On the limited memory BFGS method for large scale optimization
• Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation
• Hidden physics models: machine learning of nonlinear partial differential equations
• Abundant lump solution and interaction phenomenon of (3+1)-dimensional generalized Kadomtsev-Petviashvili equation
• Rational solutions and lump solutions to the generalized \((3+1)\)-dimensional shallow water-like equation
• An introduction to neural network methods for differential equations
• Neural network as a function approximator and its application in solving differential equations
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Ion acoustic solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili-Burgers equation in quantum plasma
• Solving high-dimensional partial differential equations using deep learning
• Unnamed Item

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