Forward PDE solving on Poisson
0.038Relative L2 ErrorDi-BiLPS
Evaluation Results
| Method | Links | |||
|---|---|---|---|---|
| Di-BiLPS2026.05 | 0.038 | — | 19.69 | |
| DiffPDE2026.05 | 0.045 | — | 255.37 | |
| Spatio-Temporal MeanFlowSolver Category=Ours2026.05 | 0.18 | — | — | |
| FNOSolver Category=Neural operator2026.05 | 0.23 | — | — | |
| DiffusionPDESolver Category=Generative PDE2026.05 | 0.76 | — | — | |
| FNO2026.05 | 1.009 | — | — | |
| PINO2026.05 | 1.071 | — | — | |
| PINNs2026.05 | 1.281 | — | — | |
| HQNNParameter value (λ)=12026.06 | 1.45 | — | — | |
| DeepONet2026.05 | 1.555 | — | — | |
| PINOSolver Category=Neural operator2026.05 | 1.58 | — | — | |
| Rectified FlowSolver Category=Generative PDE2026.05 | 1.58 | — | — | |
| PINNParameter value (λ)=52026.06 | 1.66 | — | — | |
| HQNNParameter value (λ)=62026.06 | 1.76 | — | — | |
| PINNParameter value (λ)=62026.06 | 2.81 | — | — | |
| PI-HPQNNParameter value (λ)=62026.06 | 3.05 | — | — | |
| HQNNParameter value (λ)=52026.06 | 3.18 | — | — | |
| PI-HPQNNParameter value (λ)=12026.06 | 3.28 | — | — | |
| FPINNParameter value (λ)=52026.06 | 4.61 | — | — | |
| DeepONetSolver Category=Neural operator2026.05 | 5.46 | — | — | |
| PI-HPQNNParameter value (λ)=52026.06 | 6.11 | — | — | |
| FPINNParameter value (λ)=62026.06 | 9 | — | — | |
| FPINNParameter value (λ)=12026.06 | 9.4 | — | — | |
| PINNParameter value (λ)=12026.06 | 9.59 | — | — | |
| PBFMSolver Category=Generative PDE2026.05 | 28.56 | — | — | |
| PINNSolver Category=Physics-informed coordinate-based2026.05 | 32.01 | — | — | |
| I-PINNSolver Category=Physics-informed coordinate-based2026.05 | 54.64 | — | — | |
| DeepONetObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | — | 155.5 | — | |
| DiffusionPDEObservation mode=Sparse (5/128 points)2024.06 | — | 4.5 | — | |
| DiffusionPDEnumber of steps=1000, number of observations=5002026.05 | — | 0.1532 | — | |
| FM4PDEnumber of steps=1000, number of observations=5002026.05 | — | 0.0302 | — | |
| FNOObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | — | 100.9 | — | |
| PINNsObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | — | 128.1 | — | |
| PINOObservation mode=Sparse (5/128 points), Training setup=Full observation2024.06 | — | 107.1 | — |