HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations

Keyphrases

• Homotopy 100%
• Multiple Solutions 100%
• Physics-informed Neural Networks 100%
• Neural Network 36%
• Loss Function 18%
• Track Parameters 18%
• Training Process 18%
• Numerical Examples 9%
• Numerical Methods 9%
• Machine Learning 9%
• Network Process 9%
• Reaction-diffusion Equations 9%
• Nonlinear Differential Equations 9%
• Neural Network Training 9%
• Nontrivial Solutions 9%
• Neural Network Structure 9%
• Polynomial Systems 9%
• Isolated Root 9%
• Homotopy Function 9%
• Condition Function 9%
• Homotopy Continuation Method 9%
• Initialization Method 9%
• Heart Shape 9%
• Fully Convolutional Neural Network 9%
• Deep Learning Framework 9%
• Polynomial Roots 9%

Mathematics

• Differential Equation 100%
• Homotopy 100%
• Neural Network 100%
• Multiple Solution 100%
• Loss Function 11%
• Polynomial 5%
• Numerical Example 5%
• Approximates 5%
• nonlinear differential equation 5%
• Minimizes 5%
• Reaction-Diffusion System 5%
• Diffusion Equation 5%
• Trivial Solution 5%
• Continuation Method 5%
• Boundary Condition 5%

Chemical Engineering

• Learning System 5%