Neural Preconditioner: Learning Preconditioners for Conjugate Gradient PDE Solvers
Our Method is inherently a numerical solver that can produce arbitrary accuracy. Here we demonstrate how our method win over end-to-end learning method in terms of accuracy.
Poisson2D-Ours/GT (as Inviscid Navier-Stokes)
Top subfigure visualizes the horizontal fluid flow over time
Bottom subfigure visualizes the vertical fluid flow over time
poisson2d-2.mp4Ours / Numerical Solver Simulation
Boundary Condition,
Obstacle: the inner circle and most of the top and bottom edges of the rectangle
Influx: most of the left edge and small fraction of the bottom edge
Outflus: most of the right edges and small fraction of the right edge
MGN / End-to-end Neural Network Simulation
Heat2D-Ours/GT
Boundary Condition: Black points on the boundary of the geometry are the dirichlet boundary
heat.mp4Ours / Numerical Solver Simulation
MGN / End-to-end Neural Network Simulation
Wave2D
Boundary Condition: continuous set of points on the outer boundary of the circular plate shape
wave.mp4Ours / Numerical Solver Simulation
mgn.mp4