| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| 2d Darcy Flow | 2d Darcy Flow (test) | Test Relative Error0.65 | 51 | |
| PDE Solving | Darcy-Flow 2d (test) | Relative MSE0.0001 | 33 | |
| PDE Solving | Darcy flow (test) | Relative MSE0.0001 | 30 | |
| Operator learning | Darcy Flow 512x512 grid sub-sampled (test) | Relative L2 Error0.0065 | 28 | |
| PDE Solving | Darcy Flow 64x64 resolution | Relative L2 Error0.0561 | 27 | |
| PDE Solving | Darcy Flow 256x256 resolution | Relative L2 Error6.66 | 17 | |
| PDE Solving | Darcy Flow 128x128 resolution | Relative L2 Error6.19 | 17 | |
| PDE Solving | Darcy Flow 32x32 resolution | Relative L2 Error0.0326 | 17 | |
| PDE constrained field generation | Darcy Flow (val) | NLL-3.5 | 16 | |
| Fluid Flow Prediction | Darcy Flow 700 train and 200 test examples official FNO (test) | Relative L2 Error6.32 | 15 | |
| Inverse PDE solving | Darcy Flow | Relative Error1.3 | 13 | |
| Functional estimation | Darcy flow | RMSE0.41 | 12 | |
| Operator Learning | Darcy Flow beta = 1 (test) | RMSE0.0054 | 12 | |
| Partial Differential Equation Solving | 2-D Darcy Flow | MSE0.0002 | 12 | |
| PDE Inverse Problem | Darcy Flow Noisy | Error Rate12.34 | 12 | |
| PDE Forward Problem | Darcy Flow Noisy | L2 Relative Error3.77 | 12 | |
| Forward PDE Solving | Darcy Flow (test) | Relative H1 Error0.105 | 12 | |
| Forward PDE solving | Darcy Flow | Relative Error0.0127 | 12 | |
| PDE Solving | Darcy flow noisy observations, sigma_max^2 = 0.001 | Test Error0.0109 | 11 | |
| PDE Solving | Darcy flow noisy inputs, sigma_max^2 = 0.001 | Test Error0.0056 | 11 | |
| PDE Solving | Darcy flow clean data | Test Error0.0055 | 11 | |
| Reconstruction | Darcy Flow | PSNR38.41 | 10 | |
| Generation | Darcy Flow | Data Fidelity Deviation1.19 | 10 | |
| PDE Reconstruction | Darcy Flow 3% uniformly random measurements | Coefficient Rel L2 Error2.07 | 10 | |
| Inverse Problem | Darcy Flow 97% Sparse Observation | L2 Relative Error5.18 | 9 |