autodidakt
Menu
← Research

PDEBench: Faster Advection and Burgers Solvers

Faster solvers for 1D Linear Advection and 1D Viscous Burgers

PDEBench

1D linear advection

uₜ + βuₓ = 0

Reference vs discovered solver

The pinned PDEBench solution to the one-dimensional linear advection equation across the selected space and time coordinates.
The best discovered advection solver output for the same initial condition, advection speed, spatial grid, and output times.
ReferenceDiscovered solver

Move your pointer or drag on touch.

field value
-0.2030+1.181
Trajectory error
0.0002%
RMSE
1.48e-6
Maximum |error|
5.28e-6
Fidelity ratio
0.991×
Speedup vs reference
2.24×

PDEBench

1D viscous Burgers

uₜ + uuₓ = νuₓₓ

Reference vs discovered solver

The recorded PDEBench solution to the one-dimensional viscous Burgers equation across the matched space and time coordinates.
The rank-one discovered Burgers solver output for the same initial condition, viscosity, spatial coordinates, and recorded times as the PDEBench reference.
ReferenceDiscovered solver

Move your pointer or drag on touch.

field value · shared scale
-0.2830+0.935
Selected trajectory error
0.00007%
RMSE
2.80e-7
Maximum |error|
1.70e-6
Fidelity ratio
≈1.000×
Speedup vs reference
1.66×