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Papers Benchmarks Datasets Tasks

Function Approximation research benchmarks – Page 2 · SOTA2 Research

Function Approximation

Benchmarks

Dataset NameSOTA MethodSort

Dataset NameSOTA methodMetricTrendResultsLast Updated

KAN Paper Toy Functions 4D composite

1.38Mean MSE

6

Mar 31, 2026

KAN Paper Toy Functions 10D sum

0Mean Squared Error (MSE)

6

Mar 31, 2026

KAN Paper Toy Functions (x · y)

0Mean Squared Error (MSE)

6

Mar 31, 2026

KAN Paper Toy Functions e^x sin(y) + y^2

0.043Mean MSE

6

Mar 31, 2026

KAN Paper Toy Functions J0 Bessel

0Mean Squared Error (MSE)

6

Mar 31, 2026

spectral-bias (fine grids)

0.019RMSE

5

Apr 30, 2026

piece-wise fine grids

0.007RMSE

5

Apr 30, 2026

sqrt fine grids

0RMSE

5

Apr 30, 2026

double exponential fine grids

0RMSE

5

Apr 30, 2026

0RMSE

5

Apr 30, 2026

sin-low fine grids

0RMSE

5

Apr 30, 2026

0.001RMSE

5

Apr 30, 2026

0.002RMSE

5

Apr 30, 2026

0RMSE

5

Apr 30, 2026

double exponential

0RMSE

5

Apr 30, 2026

0RMSE

5

Apr 30, 2026

0RMSE

5

Apr 30, 2026

2.481RMSE

5

Feb 26, 2026

f1 1D oscillatory function (test)

1.73Test MSE

4

Jun 25, 2026

Polynomial function approximation

SLFNs with fixed weights

1.033Max Error

4

Jun 5, 2026

Eq. (23) Dimension 3

hierarchical RBF-KAN

44.8Runtime

4

Jun 4, 2026

Synthetic Fourier Series Benchmark Omega_2 = {11, 11.2, 13} (test)

100Success Rate

4

May 18, 2026

Sobolev space W^{n, infinity}([0, 1]^D) on cube partition

EUAF (Theorem 2.1)

1Norm Type

4

Jun 16, 2026

2.361RMSE

4

Feb 26, 2026

1.641RMSE

4

Feb 26, 2026

Page 2 of 4

Popular datasets

Feynman Function Bratley Sum KAN Paper Toy Functions Eq. (23)Sin

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