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Allen-Cahn

Benchmarks

Task NameDataset NameSOTA ResultTrend
PDE RolloutAllen-Cahn 3D
Relative L2 Error (t=50)4.1246
24
Solving PDEAllen-Cahn
Relative Error0.0001
21
Forward PDE SolvingAllen–Cahn 10K-epoch
Relative L2 Error1.19
16
Learning PDE Solution OperatorsAllen-Cahn 1D
Mean L2 Relative Error0.05
12
Solving Time-Dependent PDEsAllen-Cahn
Relative L2 Error0
12
Solving Partial Differential EquationsAllen-Cahn continuous parameter space (test)
Memory (MB)1,328
10
Learning PDE solution operators1D Allen-Cahn
Training Time (s)1.09
7
Operator LearningAllen-Cahn (test)
Mean Relative L2 Error0.0042
6
Solving Partial Differential EquationsAllen-Cahn
Total Parameters27,937
6
Partial Differential Equation SolvingAllen–Cahn
Total Training Time (min)20.05
6
Operator LearningAllen–Cahn
Max GPU Memory Usage (GB)6.87
6
Inverse PDE Problem SolvingAllen-Cahn-2D
Success Rate100
6
PDE solvingAllen-Cahn
Inference Time (s)1.33
6
Spatiotemporal PDE SolvingAllen-Cahn
MSE0.0088
6
PDE SolvingAllen-Cahn (test)
Relative L1 Error (Final Time)1.03
6
Solving nonlinear PDEAllen-Cahn (test)
MSE0
6
Solving Allen-Cahn EquationAllen–Cahn (train)
Residual MSE1.54
5
PDE controlAllen-Cahn 20D
Evaluation Time119.8
5
PDE controlAllen-Cahn 10D
Evaluation Cost66.29
5
PDE dynamics predictionAllen-Cahn 1D (test)
Relative Prediction Error (5-step)0.0055
4
PDE dynamics predictionAllen-Cahn 2D (test)
5-Step Relative Prediction Error0.37
3
PDE Inverse ProblemAllen-Cahn-2D (full)
SR100
3
Solving high-dimensional inseparable PDEsAllen-Cahn 100KD
Error0.0543
3
Solving high-dimensional inseparable PDEsAllen-Cahn 10KD
Error0.0001
3
Solving high-dimensional inseparable PDEsAllen-Cahn 1KD
Error0.0526
3
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