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Papers Benchmarks Datasets Tasks

PDE solving research benchmarks – Page 6 · SOTA2 Research

PDE solving

Benchmarks

Dataset NameSOTA MethodSort

Dataset NameSOTA methodMetricTrendResultsLast Updated

Reaction-Diffusion (train)

0Error

7

May 18, 2026

Reaction-Diffusion (val)

0Error

7

May 18, 2026

Viscous-Burgers (train)

0Error

7

May 18, 2026

Viscous-Burgers (val)

0Error

7

May 18, 2026

Laplace (train)

0Error

7

May 18, 2026

0Error

7

May 18, 2026

Poisson (train)

0Error

7

May 18, 2026

0Error

7

May 18, 2026

two-body Allen-Cahn equation 10K D

512.38Speed (it/s)

7

Mar 26, 2026

two-body Allen-Cahn equation 1K D

1,200Speed (it/s)

7

Mar 26, 2026

two-body Allen-Cahn equation 100 D

2,100Speed (it/s)

7

Mar 26, 2026

Burgers' (test)

4.27Relative Error

7

Apr 14, 2026

Diffusion-Reaction Point-wise (test)

0.008Rel L2 Error

7

Feb 26, 2026

Convection-Diffusion-Reaction (C-D-R) PDE Gaussian distribution N(pi, (pi/2)^2) initial condition (general cases)

0.009Absolute Error

7

Feb 26, 2026

Reaction-Diffusion (Reac.-Diff.) PDE general cases Gaussian distribution N(pi, (pi/2)^2) initial condition

0.025Absolute Error

7

Feb 26, 2026

Convection-Diffusion (Conv.-Diff.) PDE Gaussian distribution N(pi, (pi/2)^2) initial condition (general cases)

0.033Abs. Error

7

Feb 26, 2026

Reaction PDE Gaussian distribution N(pi, (pi/2)^2) initial condition (general cases)

0.003Abs. Err.

7

Feb 26, 2026

Diffusion PDE Gaussian distribution N(pi, (pi/2)^2) initial condition (general cases)

0.08Abs. Err.

7

Feb 26, 2026

Convection PDE general cases Gaussian distribution N(pi, (pi/2)^2) initial condition

0.004Absolute Error

7

Feb 26, 2026

PINNacle v1 (test)

0.015Burgers 1D (C) Error

6

Jun 4, 2026

0.013Error (1D Burgers, C)

6

Jun 4, 2026

2D Darcy flow triangular notch domain

0.64Relative L2 Error

6

Jun 1, 2026

2D Poisson Equation (beta1=3.0, beta2=2.0) analytical solution (test)

0eLoss

6

May 20, 2026

Charged particles in electric field

0.004L2 Error

6

May 4, 2026

Transport through flow field

0.012L2 Error

6

May 4, 2026

Page 6 of 13

Popular datasets

PDEBench Darcy Flow Darcy Navier-Stokes Poisson

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