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.mp4

Ours / 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.mp4

Ours / 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.mp4

Ours / Numerical Solver Simulation

mgn.mp4

MGN / End-to-end Neural Network Simulation

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