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Neural PDE Solving research benchmarks · SOTA2 Research

Neural PDE Solving

Benchmarks

Dataset NameSOTA MethodSort

Dataset NameSOTA methodMetricTrendResultsLast Updated

17.6MSE

10

Mar 4, 2026

Complex Obstacles

0MSE

10

Mar 4, 2026

FitzHugh-Nagumo

0MSE

10

Mar 4, 2026

Gray–Scott Eq. Forward 2D (test)

1.44Mean Error

7

Jun 11, 2026

Poisson Eq. L-shape domain 2D (test)

0.02Test Error

6

Feb 26, 2026

Poisson Eq. Mixed BC 2D (test)

0Test Error

6

Feb 26, 2026

Burgers equation periodic boundary conditions spectral-1024 reference (T=4)

0Relative L2 Error

5

Mar 4, 2026

Burgers equation periodic boundary conditions spectral-1024 reference (T=3)

0Relative L2 Error

5

Mar 4, 2026

Burgers equation periodic boundary conditions spectral-1024 reference (T=2)

0Relative L2 Error

5

Mar 4, 2026

Burgers equation periodic boundary conditions spectral-1024 reference (T=1)

0Relative L2 Error

5

Mar 4, 2026

Incompressible Navier-Stokes Eq. Inverse 2D (test)

0.19Test Error

5

Feb 26, 2026

Incompressible Navier-Stokes Eq. Forward 2D (test)

0.123Test Error

5

Feb 26, 2026

Gray–Scott Eq. (Inverse) 2D (test)

0.192Test Error

5

Feb 26, 2026

WaveBench 15Hz acoustic time-harmonic Helmholtz equation

0.046VRMSE

4

Mar 6, 2026

2D Poisson equation

Rigorous Error Certification for Neural PDE Solvers

0Boundary Error Bound

1

Mar 20, 2026

1D Burgers Equation

PINN (Certified via ∂-CROWN)

0.124Residual Bound

1

Mar 20, 2026

Popular datasets

Burgers' Equation Poisson Eq.Gray–Scott Eq.Incompressible Navier-Stokes Eq.FitzHugh-Nagumo

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