| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| 2d Darcy Flow | 2d Darcy Flow (test) | Test Relative Error0.65 | 51 | |
| Operator learning | Darcy Flow 512x512 grid sub-sampled (test) | Relative L2 Error0.0065 | 28 | |
| PDE constrained field generation | Darcy Flow (val) | NLL-3.5 | 16 | |
| PDE Solving | Darcy-Flow 2d (test) | Relative MSE0.0162 | 15 | |
| 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 | |
| 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 | |
| PDE Reconstruction | Darcy Flow 3% uniformly random measurements | Coefficient Rel L2 Error2.07 | 10 | |
| Forward PDE solving | Darcy Flow | Relative Error0.49 | 10 | |
| Inverse Problem | Darcy Flow 97% Sparse Observation | L2 Relative Error5.18 | 9 | |
| Forward Simulation | Darcy Flow 97% Sparse Observation | L2 Relative Error0.0249 | 9 | |
| Inverse PDE solving | Darcy Flow Full Observation | L2 Relative Error0.021 | 9 | |
| Forward PDE solving | Darcy Flow Full Observation | L2 Relative Error1.05 | 9 | |
| Forward PDE Solving | Darcy Flow (test) | Relative H1 Error0.105 | 9 | |
| PDE Solving | Darcy Flow | Relative L2 Error0.79 | 9 | |
| Solving Darcy Flow | Darcy flow noisy observations, sigma_y_max^2 = 0.001 (test) | Test Error0.0109 | 8 | |
| Solving Darcy Flow | Darcy flow noisy inputs, sigma_x_max^2 = 0.001 (test) | Test Error0.0056 | 8 | |
| Solving Darcy Flow | Darcy flow clean (test) | Test Error0.0055 | 8 | |
| Generative Modeling | Darcy flow 1024 samples (test) | Relative Error0.022 | 7 | |
| Operator Learning | Darcy Flow RPB (Out) | Rel. Median L1 Error0.5 | 7 | |
| Operator Learning | Darcy Flow RPB (In) | Relative Median L1 Error0.38 | 7 | |
| Inverse PDE Inference | Darcy Flow 64x64 (test) | Relative L2 Error1.1 | 6 |