On Residual Minimization for PDEs: Failure of PINN, Modified Equation, and Implicit Bias.
Tao LuoQixuan ZhouPublished in: CoRR (2023)
Keyphrases
- numerical solution
- partial differential equations
- fourth order
- objective function
- numerical methods
- eikonal equation
- image denoising
- root cause
- variance reduction
- finite difference
- failure prediction
- level set
- data sets
- minimization problems
- success or failure
- component failures
- euler lagrange
- boundary value problem
- regularization term
- total variation
- image restoration
- trade off
- image processing
- genetic algorithm