Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach

Mathematics

• Neural Networks 89%
• Higher Dimensions 87%
• Eigenvalue Problem 82%
• High-dimensional 77%
• Parameter Optimization 65%
• Forward-backward Stochastic Differential Equations 64%
• Feynman-Kac Formula 63%
• Fokker-Planck 59%
• Eigenvalues and Eigenfunctions 55%
• Fixed Point Problem 51%
• Nonlinear Operator 50%
• Loss Function 48%
• Approximation 48%
• Operator 44%
• Semilinear 44%
• Eigenfunctions 41%
• Differential operator 39%
• Semigroup 35%
• Fixed point 33%
• Numerical Examples 29%

Physics & Astronomy

• eigenvalues 81%
• operators 67%
• eigenvectors 55%
• differential operators 41%
• approximation 33%
• differential equations 25%
• optimization 20%

Engineering & Materials Science

• Eigenvalues and eigenfunctions 100%
• Deep neural networks 92%
• Differential equations 42%
• Neural networks 28%