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Darcy Flow

Benchmarks

Task NameDataset NameSOTA ResultTrend
2d Darcy Flow2d Darcy Flow (test)
Test Relative Error0.65
51
PDE SolvingDarcy-Flow 2d (test)
Relative MSE0.0001
33
PDE SolvingDarcy flow (test)
Relative MSE0.0001
30
Operator learningDarcy Flow 512x512 grid sub-sampled (test)
Relative L2 Error0.0065
28
PDE SolvingDarcy Flow 64x64 resolution
Relative L2 Error0.0561
27
PDE SolvingDarcy Flow 256x256 resolution
Relative L2 Error6.66
17
PDE SolvingDarcy Flow 128x128 resolution
Relative L2 Error6.19
17
PDE SolvingDarcy Flow 32x32 resolution
Relative L2 Error0.0326
17
PDE constrained field generationDarcy Flow (val)
NLL-3.5
16
Fluid Flow PredictionDarcy Flow 700 train and 200 test examples official FNO (test)
Relative L2 Error6.32
15
Inverse PDE solvingDarcy Flow
Relative Error1.3
13
Functional estimationDarcy flow
RMSE0.41
12
Operator LearningDarcy Flow beta = 1 (test)
RMSE0.0054
12
Partial Differential Equation Solving2-D Darcy Flow
MSE0.0002
12
PDE Inverse ProblemDarcy Flow Noisy
Error Rate12.34
12
PDE Forward ProblemDarcy Flow Noisy
L2 Relative Error3.77
12
Forward PDE SolvingDarcy Flow (test)
Relative H1 Error0.105
12
Forward PDE solvingDarcy Flow
Relative Error0.0127
12
PDE SolvingDarcy flow noisy observations, sigma_max^2 = 0.001
Test Error0.0109
11
PDE SolvingDarcy flow noisy inputs, sigma_max^2 = 0.001
Test Error0.0056
11
PDE SolvingDarcy flow clean data
Test Error0.0055
11
ReconstructionDarcy Flow
PSNR38.41
10
GenerationDarcy Flow
Data Fidelity Deviation1.19
10
PDE ReconstructionDarcy Flow 3% uniformly random measurements
Coefficient Rel L2 Error2.07
10
Inverse ProblemDarcy Flow 97% Sparse Observation
L2 Relative Error5.18
9
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