Darcy
Benchmarks
| Task Name | Dataset Name | SOTA Result | Trend | |
|---|---|---|---|---|
| PDE Solving | Darcy | Relative L2 Error0.0042 | 46 | |
| PDE Solving | Darcy Regular Grid (test) | Relative L2 Error0.0042 | 41 | |
| Operator Learning | Darcy Regular Grid (test) | Relative L2 Error0.0057 | 15 | |
| PDE Solving | Darcy (test) | Relative Error0.72 | 11 | |
| Inverse PDE solving | Darcy | Relative L2 Error1.02 | 10 | |
| Fluid flow prediction | Darcy 256^2 zero-shot resolution transfer 4x | Relative L2 Error4.59 | 10 | |
| Fluid flow prediction | Darcy 128^2 zero-shot resolution transfer 2x | Relative L2 Error4.03 | 10 | |
| Spatial super-resolution | Darcy spatial super-resolution (test) | NRMSE0.0583 | 9 | |
| Forward PDE solving | Darcy | Relative L2 Error0.25 | 9 | |
| PDE Rollout Prediction | Darcy trajectory set (test) | Rollout Relative H1 Error0.0165 | 8 | |
| PDE Solving | Darcy N_train=100 (OOD) | Normalized L2 Error0.57 | 8 | |
| PDE Solving | Darcy N_train=100 (ID) | Normalized L2 Error0.56 | 8 | |
| Regression | Darcy Synthetic (test) | NRMSE0.0167 | 8 | |
| Scaling-law extrapolation | Darcy high-D (holdout) | RMSE (log space)0.17 | 6 | |
| Scaling-law extrapolation | Darcy high-C (holdout) | RMSE (log space)0.168 | 6 | |
| Deep Operator Learning | Darcy | Relative L2 Error1.12 | 6 | |
| Functional Mapping | Darcy Synthetic | MNLL-4.13 | 6 | |
| Posterior Sampling | Darcy | Time per Sample (s)1.05 | 6 | |
| Neural surrogate modeling | Darcy | NMAE1.6 | 5 | |
| Inverse Problem | Darcy (test) | Relative Error2.41 | 5 | |
| Forward Problem | Darcy (test) | RE3.1 | 5 | |
| PDE Solving | Darcy zero-shot 241 x 241 (test) | Relative L2 Error2.44 | 5 | |
| PDE Solving | Darcy zero-shot 211 x 211 (test) | Relative L2 Error0.0229 | 5 | |
| PDE Solving | Darcy zero-shot 141 x 141 (test) | Relative L2 Error0.0214 | 5 | |
| PDE Solving | Darcy zero-shot 85 x 85 (test) | Relative L2 Error0.0192 | 5 |
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