KANs example#20
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bwdGitHub
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| A Kolmogorov\-Arnold neural network (KAN) is a type of neural network inspired by the Kolmogorov\-Arnold representation theorem \[[1](#M_050a)\]. It approximates multivariate functions using structured function compositions with fewer parameters. KANs are general\-purpose function approximators. This example uses a KAN to represent a physics\-informed neural network (PINN). A physics\-informed neural network is a neural network that incorporates physical laws into its structure and training process \[[2](#M_050a)\]. For example, you can train a PINN by incorporating the definition of a partial differential equation (PDE) that defines a physical system in the loss function. | ||
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| This example trains a Chebyshev\-based KAN \[[3](#M_050a)\] that outputs the PDE solution $u(x,y)$ of the Helmholtz equation given the input $(x,y)$. |
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The references 2 and 3 are mixed up - 2 is Chebyshev KANs and 3 is PINNs
bwdGitHub
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Apr 27, 2026
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| # Define Chebyshev KAN Layer | ||
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| The original KAN architecture in \[[1](#M_050a)\] uses B‑splines as the edge basis functions. There are several variants of the KAN architecture. This example uses a Chebyshev‑KAN variant, which was shown to perform well in a recent comparative study \[[2](#M_050a)\]. |
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The reference 2 should be 4 here
bwdGitHub
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Apr 27, 2026
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| % Evaluate alpha for residual-based attention. | ||
| res = solverState.AdditionalLossFunctionOutputs{1}; | ||
| alpha = (1-eta).*alpha + eta.*(res./max(res)); |
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res should be abs(res) here (equation (3) here)
bwdGitHub
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Apr 27, 2026
| numOut = sz(1); | ||
| numIn = sz(2); | ||
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| weights = randn(numOut,sz(2),"single") / numIn; |
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sz(2) can be numIn here.
bwdGitHub
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Apr 27, 2026
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May need to call the file README.md for it to render on GitHub directly. The top level readme could list this example too.
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Apr 27, 2026
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Adding Chebyshev basis KANs example