Deep Adaptive Basis Galerkin Method for High-Dimensional Evolution Equations With Oscillatory Solutions

Keyphrases

• Evolution Equations 100%
• Deep Neural Network 100%
• Galerkin Method 100%
• Oscillatory Solution 100%
• Adaptive Base 100%
• Space Variables 66%
• Loss Function 66%
• Time Variable 66%
• Numerical Examples 33%
• Allen-Cahn Equation 33%
• High-dimensional Space 33%
• Error Bound 33%
• Product Basis 33%
• Spectral Galerkin Method 33%
• Linear Parabolic Equations 33%
• Function Type 33%
• Tensor Product 33%
• True Solution 33%
• Solution Error 33%
• Deep Neural Network Algorithm 33%
• Deep Least-square Method 33%
• Linear System of Differential Equations 33%
• Linear Hyperbolic Equation 33%
• Barra 33%

Mathematics

• Evolution Equation 100%
• Deep Neural Network 100%
• Loss Function 50%
• Numerical Example 25%
• Dimensional Space 25%
• Tensor 25%
• Linear System 25%
• Parabolic 25%
• Basis Function 25%
• Error Bound 25%
• Positive Constant 25%
• Posteriori 25%
• True Solution 25%
• System Of Differential Equations 25%
• Least Squares Method 25%