Solving PDEs on unknown manifolds with machine learning

Keyphrases

• Machine Learning 100%
• Neural Network 100%
• PDE 100%
• Hypothesis Space 100%
• Loss Function 66%
• Algebraic Equation 66%
• Diffusion Maps 66%
• Global Minimizer 66%
• Elliptic PDE 66%
• Numerical Examples 33%
• Interpolation Method 33%
• Rough Surface 33%
• Nonconvex 33%
• Numerical Methods 33%
• Computational Framework 33%
• Supervised Learning 33%
• Minimization Problem 33%
• Training Data 33%
• Consistent Estimator 33%
• Consistent Solution 33%
• Cloud-based 33%
• Meshless 33%
• Graph Laplacian 33%
• Asymptotic Expansion 33%
• Regression Problem 33%
• Least Squares Regression 33%
• Learning Task 33%
• Point Cloud 33%
• Elliptic Differential Operator 33%
• Empirical Risk Minimization 33%
• Generalization Error 33%
• Training Error 33%
• Map Learning 33%
• Large Width 33%
• Well-posed 33%
• PDE Solutions 33%
• Gradient Descent 33%
• Deep Learning 33%
• Machine Learning Theory 33%
• PDE Solvers 33%
• Higher Codimension 33%
• Two-layer Neural Network 33%

Mathematics

• Manifold 100%
• Partial Differential Equation 100%
• Neural Network 66%
• Algebraic Equation 33%
• Loss Function 33%
• Global Minimizer 33%
• Numerical Example 16%
• Matrix (Mathematics) 16%
• Differential Operator 16%
• Minimization Problem 16%
• Least Square 16%
• Square Regression 16%
• Consistent Estimator 16%
• Data Point 16%
• Graph Laplacian 16%
• Asymptotic Expansion 16%
• Empirical Risk Minimization 16%
• Training Data 16%
• Learning Task 16%
• Deep Learning Method 16%
• Mathematical Method 16%
• Boundary Condition 16%