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Solving partial differential equations research benchmarks – Page 3 · SOTA2 Research

Solving partial differential equations

Benchmarks

Dataset NameSOTA MethodSort

Dataset NameSOTA methodMetricTrendResultsLast Updated

3.28Percentage Improvement

3

Jun 19, 2026

28Percentage Improvement

3

Jun 19, 2026

82.08Percentage Improvement

3

Jun 19, 2026

Heat2D LongTime

-0.01Percentage Improvement

3

Jun 19, 2026

35.11Percentage Improvement

3

Jun 19, 2026

Heat2D Multiscale

94.32Percentage Improvement

3

Jun 19, 2026

Poisson3D Complex

27Percentage Improvement

3

Jun 19, 2026

PoissonBoltzmann2D

1.86Percentage Improvement

3

Jun 19, 2026

6.63Percentage Improvement

3

Jun 19, 2026

30.3Percentage Improvement

3

Jun 19, 2026

Allen-Cahn Equation vanilla PINN (test)

4.95rRMSE

3

Jun 4, 2026

Wave Equation vanilla PINN (test)

0.94rRMSE

3

Jun 4, 2026

Reaction Equation vanilla PINN (test)

5.31rRMSE

3

Jun 4, 2026

Convection Equation Eq. 11 vanilla PINN (test)

0.91rRMSE

3

Jun 4, 2026

4.38Relative L2 Error

3

May 13, 2026

Two-body Allen-Cahn equation 1MD

4,856Memory (MB)

2

Mar 26, 2026

Helmholtz equation high-frequency regime Example 2 (test)

—

—Primary metric

0

Feb 26, 2026

1D Klein-Gordon equation a=10

—

—Primary metric

0

Feb 26, 2026

1D Klein-Gordon equation a=5

—

—Primary metric

0

Feb 26, 2026

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Popular datasets

Two-body Allen-Cahn equation Heat2D Allen-Cahn equation Burgers Helmholtz

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