Burgers' Equation
Benchmarks
TaskDatasetSOTA resultTrendResults
Burgers' Equation Shift Trajectory Manifold
1.16Relative Test Error
140
1d Burgers' equation (test)
0.008Relative Error
85
Burgers' Equation various resolutions (val)
0.002Relative L2 Error
36
Burgers' equation Case 3.3
0MSE
32
Burgers' Equation E1
0MSE
28
Burgers' equation viscosity ν = 0.02
0Relative L2 Error
20
Burgers' equation
0L2 Relative Error
18
Burgers' Equation (test)
0.002Max Relative L2 Error
11
Burgers' equation (test)
0.075RMSE
10
Burgers' equation nu=0.01
0.114RMSE
10
Burgers equation (test)
4.19L2 Error
9
Burgers' equation multiple-source dataset 1000 data per case
1Discovered PDE Structure
8
Burgers' equation multiple-source 100 data per case
1PDE Structure Match
8
Burgers’ equation n = 32 (test)
0Relative L2 Error
8
Burgers' Equation PDE (Noise Levels: 0%, 1%, 10% (large))
0.754RMSE (0% Noise)
8
Burgers Equation
2.18Wall-clock Time (CPU)
6
one-dimensional Burgers' equation
0.049Relative L2 Error (EL2)
6
Burgers’ equation (0.2% Noise)
0MSE
5
Burgers equation periodic boundary conditions spectral-1024 reference (T=4)
0Relative L2 Error
5
Burgers equation periodic boundary conditions spectral-1024 reference (T=3)
0Relative L2 Error
5
Burgers equation periodic boundary conditions spectral-1024 reference (T=2)
0Relative L2 Error
5
Burgers equation periodic boundary conditions spectral-1024 reference (T=1)
0Relative L2 Error
5
Burgers' Equation (Boundary Condition)
0.32Reconstruction Error (RE)
5
Burgers Equation (test)
0.006RMSE
5
Burgers equation 5% noise
1.78Relative Viscosity Error
4