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Spinachboul update function #457

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Spinachboul update function #457

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07c0131
Improved GEKPLS Function
Spinachboul Dec 21, 2023
4358bee
Update Improvedgekpls.md
Spinachboul Dec 21, 2023
ef4c12b
Update Improvedgekpls.md
Spinachboul Dec 21, 2023
da68799
Update pages.jl
Spinachboul Dec 21, 2023
2e519c9
Update tensor_prod.md
Spinachboul Dec 28, 2023
c546840
Update docs/src/tensor_prod.md
Spinachboul Dec 31, 2023
dc946d4
Update pages.jl
Spinachboul Dec 31, 2023
63a72d3
Update tensor_prod.md
Spinachboul Jan 4, 2024
670ecc7
Update tensor_prod.md
Spinachboul Jan 4, 2024
02aabfb
Update Improvedgekpls.md
Spinachboul Jan 4, 2024
fa8164a
Delete docs/src/Improvedgekpls.md
Spinachboul Jan 4, 2024
688fee1
Update tensor_prod.md
Spinachboul Jan 5, 2024
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4 changes: 2 additions & 2 deletions docs/src/tensor_prod.md
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@@ -1,6 +1,5 @@
# Tensor product function
The tensor product function is defined as:
``f(x) = \prod_{i=1}^d \cos(a\pi x_i)``
The tensor product function is defined as: ```\[ f(x) = ∏ᵢ=₁ᵈ cos(aπxᵢ) \]```
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But this isn't correct. This is one example of a tensor product.

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Yes, that is true. Maybe we specifically say it is one of the possible forms. I think this was taken from https://smt.readthedocs.io/en/latest/_src_docs/problems/tensorproduct.html

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@Spinachboul Spinachboul Jan 4, 2024 •
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Well, @ChrisRackauckas and @sathvikbhagavan
Should we properly define the tensor product function like this:
equation

Or just stating this example would be fine??

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Yes that would do it. But do we have an actual issue that is being solved here?

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As the benchmarks need some cleanup, I think we can startoff with this PR to clean up the tensor product benchmark? Although I am not sure why would we need a surrogate for computing tensor product 😅

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@sathvikbhagavan
I think there would be a couple of factors as to why surrogates could be used to compute tensor product:

  • Computational Complexity would be decreased
  • Efficient memory handling
  • Normalization of products of tensors which provide numerical stability

This PR #457 only consists of changing the example of tensor product into a more readable form up till now, but I would also work towards explaining the mathematical concepts behind surrogate models in my draft PR as we discussed earlier.


Let's import Surrogates and Plots:
```@example tensor
Expand Down Expand Up @@ -38,3 +37,4 @@ plot!(xs,f.(xs), label="True function", legend=:top)
plot!(xs, loba_1.(xs), label="Lobachevsky", legend=:top)
plot!(xs, krig.(xs), label="Kriging", legend=:top)
```