PDEBench fluid evolution
Neural surrogates that roll out PDE solutions with less error (placeholder)
| Route | nRMSE | Improved | 1D advection | 1D Burgers | 1D diffusion–reaction | 2D Darcy flow | 2D shallow water | 2D reaction–diffusion | 2D compressible NS | 3D compressible NS |
|---|---|---|---|---|---|---|---|---|---|---|
| Baseline · FNO | 0.091 | 0.128 | 0.148 | 0.0965 | 0.0584 | 0.125 | 0.0177 | 0.118 | 0.0363 | |
| pushforward-training | 0.0684 | 8 / 8 | 0.0989 | 0.138 | 0.0701 | 0.0407 | 0.107 | -0.0243 | 0.112 | 0.00408 |
| conservation-projection | 0.0798 | 5 / 8 | 0.133 | 0.136 | 0.0813 | 0.0708 | 0.111 | -0.0248 | 0.122 | 0.0096 |
| spectral-filter | 0.0822 | 4 / 8 | 0.0993 | 0.152 | 0.0991 | 0.0413 | 0.133 | -0.0212 | 0.109 | 0.0451 |
| unet-multiscale | 0.0851 | 6 / 8 | 0.127 | 0.133 | 0.092 | 0.0664 | 0.132 | 0.00169 | 0.109 | 0.0194 |