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Function Approximation research benchmarks · SOTA2 Research

Function Approximation

Benchmarks

Dataset NameSOTA MethodSort

Dataset NameSOTA methodMetricTrendResultsLast Updated

Function F2(xi)

0MSE

49

Jun 25, 2026

Two-dimensional function Equation 34

0L_inf Error

40

May 29, 2026

Bratley Sum D=250

0.001Relative MSE

40

Apr 1, 2026

Bratley Sum D=100

0Relative MSE

40

Apr 1, 2026

Padé[K/3]-rKAN

0MSE

33

Feb 26, 2026

Bratley Sum D=500

0.002Relative MSE

30

Apr 1, 2026

hierarchical Tanh-KAN

15Runtime

27

Jun 4, 2026

Bratley Sum D=750

0.001Relative MSE

20

Apr 1, 2026

Oscillatory Function Equation 23 (test)

0Error (d=1)

14

Jun 4, 2026

Function Approximation [np, 6, 1]

0.005Time (sec/iter)

14

Feb 26, 2026

ModP (x, 4) over [0, 29]

0MAE

12

Feb 26, 2026

0RMSE

10

Apr 30, 2026

0.039RMSE

10

Apr 30, 2026

Bratley Sum D=2000

4.012Relative MSE

10

Apr 1, 2026

Bratley Sum D=1000

0.002Relative MSE

10

Apr 1, 2026

1D multiscale function

2.86L(θ) Error

8

Jun 16, 2026

1.07Relative L2 Error

7

May 22, 2026

1.37Relative L2 Error

7

May 22, 2026

0.012Rel. L2 Error

7

May 22, 2026

3.04Relative L2 Error

7

May 22, 2026

Negative Entropy (test)

0Tsolve (s)

7

Feb 26, 2026

Negative Logarithm (Neg. Log) (test)

0Solve Time (s)

7

Feb 26, 2026

Eq. (23) Dimension 2

hierarchical RBF-KAN

40.3Runtime

6

Jun 4, 2026

Besov space B^s_{q,r}([0, 1]^d)

Yarotsky and Zhevnerchuk

2Approximation Error

6

Jun 1, 2026

Functions on low-dimensional manifolds

Gurevych et al.

1Depth

6

May 12, 2026

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

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