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Papers Benchmarks Datasets Tasks

PDE solving research benchmarks – Page 10 · SOTA2 Research

PDE solving

Benchmarks

Dataset NameSOTA MethodSort

Dataset NameSOTA methodMetricTrendResultsLast Updated

anisotropic ridge advect 128 (test)

1.37L2 Error

4

Apr 29, 2026

Advection equation

1.15Relative L2 Error

4

Apr 20, 2026

Adv-React (test)

4.1Relative L2 Error

4

Apr 14, 2026

Neutron Diff (test)

4.6Relative L2 Error

4

Apr 14, 2026

React-Diff (test)

2.1Relative L2 Error

4

Apr 14, 2026

Conv-Diff (test)

10.7Relative L2 Error

4

Apr 14, 2026

0Relative L2 Error

4

Apr 7, 2026

WaveBench helmholtz_anisotropic

0.046VRMSE

4

Mar 6, 2026

0.12Test Error

4

Feb 26, 2026

Inviscid Burgers (test)

0Relative L2 Error

4

Feb 26, 2026

Helmholtz Equation sigma_obs=0.5 (val)

0.023Residual Error

4

Feb 26, 2026

Helmholtz Equation sigma_obs=0.1 (val)

0.024Residual

4

Feb 26, 2026

Helmholtz Equation sigma_obs=0.05 (val)

0.024Residual Error

4

Feb 26, 2026

Helmholtz Equation sigma_obs=0 (val)

0.025Residual

4

Feb 26, 2026

PDEBench Diffusion-Sorption (1D) (test)

0.002nRMSE

4

Feb 26, 2026

PDEBench Burgers (1D) (test)

0.31nRMSE

4

Feb 26, 2026

PDEBench Advection (1D) (test)

0.008nRMSE

4

Feb 26, 2026

PDEBench Burgers (test)

0.003nRMSE

4

Feb 26, 2026

Darcy Flow NAS-Bench-360

0.5Full-pipeline Runtime (GPU hours)

4

Feb 26, 2026

3D Navier-Stokes flow

FNO (with 2-step loss)

0.17Error (t=40)

4

Feb 26, 2026

Multi-scale PDE

1L2 Relative Error

3

Jul 3, 2026

1.53Relative L2 Error

3

Jul 3, 2026

Navier–Stokes PDE

1.13Relative L2 Error

3

Jul 3, 2026

0.045PSRE

3

Jun 23, 2026

15.3PSRE

3

Jun 23, 2026

Page 10 of 13

Popular datasets

PDEBench Darcy Flow Darcy Navier-Stokes Poisson

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