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Papers Benchmarks Datasets Tasks

PDE solving research benchmarks – Page 9 · SOTA2 Research

PDE solving

Benchmarks

Dataset NameSOTA MethodSort

Dataset NameSOTA methodMetricTrendResultsLast Updated

Heat 100D (test)

0.004MSE

5

Feb 26, 2026

0.019MSE

5

Feb 26, 2026

PDEBench Navier Stokes (1D)

0.05nRMSE

5

Feb 26, 2026

PDEBench Diffusion Reaction (2D)

0.817nRMSE

5

Feb 26, 2026

PDEBench Shallow Water (2D)

0.005nRMSE

5

Feb 26, 2026

PDEBench Diffusion Sorption (1D)

0.002nRMSE

5

Feb 26, 2026

PDEBench Burgers 1D

0.011nRMSE

5

Feb 26, 2026

PDEBench Advection (1D)

0.003nRMSE

5

Feb 26, 2026

DIFFUSION PDE nc=36

38.94Solve Time (ms)

5

Feb 26, 2026

Darcy zero-shot 241 x 241 (test)

2.44Relative L2 Error

5

Feb 26, 2026

Darcy zero-shot 211 x 211 (test)

0.023Relative L2 Error

5

Feb 26, 2026

Darcy zero-shot 141 x 141 (test)

0.021Relative L2 Error

5

Feb 26, 2026

Darcy zero-shot 85 x 85 (test)

0.019Relative L2 Error

5

Feb 26, 2026

Darcy zero-shot 61 x 61 (test)

0.018Relative L2 Error

5

Feb 26, 2026

1.62Relative L2 Error

4

Jul 3, 2026

Keller-Segel blow-up (val)

0.188Relative L2 Error

4

Jun 19, 2026

3D Thermal Analysis Domain

98.42Accuracy (σ=0.0)

4

Jun 9, 2026

2D Thermal Analysis Domain

99.16Accuracy (σ=0.0)

4

Jun 9, 2026

1D Thermal Analysis Domain

99.72Accuracy (σ=0.0)

4

Jun 9, 2026

Mean Escape Time PDE

0.174Relative L2 Error

4

Jun 2, 2026

Poisson-Gauss PG-2

2.66Relative L2 Error

4

May 22, 2026

0.078L2 Relative Error

4

May 18, 2026

6.1L2 Relative Error

4

May 18, 2026

1Relative L2 Error

4

May 12, 2026

1Relative L2 Error

4

May 12, 2026

Page 9 of 13

Popular datasets

PDEBench Darcy Flow Darcy Navier-Stokes Poisson

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