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Added updated environment, updated new functions #134

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Added updated environment, updated new functions #134

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36 changes: 7 additions & 29 deletions 12_ultima_continued/12_ultima_continued.jl
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
### A Pluto.jl notebook ###
# v0.12.21
# v0.14.2

using Markdown
using InteractiveUtils
Expand Down Expand Up @@ -295,33 +295,13 @@ begin

# Create a Basis
@variables u[1:2]
# Lots of polynomials
polys = Operation[1]

for i ∈ 1:5
push!(polys, u[1]^i)
push!(polys, u[2]^i)
for j ∈ i:5
if i != j
push!(polys, (u[1]^i)*(u[2]^j))
push!(polys, u[2]^i*u[1]^i)
end
end
end
# Polynomial and sin based

end

# ╔═╡ d58d6d84-544e-11eb-17b8-91723456fc15
begin
# And some other stuff
h = [cos.(u)...; sin.(u)...; polys...]
basis = Basis(h, u)
b_ = [polynomial_basis(u, 5); sin.(u)]

h
end

# ╔═╡ 5a6dcdc8-5451-11eb-2a2f-cbc4f35844c0
basis
basis = Basis(b_, u)

end;

# ╔═╡ 23be1198-5451-11eb-07b7-e76b21ff565a
md"So, as you can see above, we just created a **Function Space** of 29 dimensions. That space include *every* possible [linear combination](https://en.wikipedia.org/wiki/Linear_combination#:~:text=From%20Wikipedia%2C%20the%20free%20encyclopedia,a%20and%20b%20are%20constants) of each dimension. And we are going to ask to SINDy to give us the simplest function that shows the same Input-Output behaviour the Neural Network just learned.
Expand Down Expand Up @@ -382,7 +362,7 @@ unknown_eq = ODEFunction(unknown_sys)
# Just the equations
b = Basis((u, p, t)->unknown_eq(u, [1.; 1.], t), u)

# Retune for better parameters -> we could also use DiffEqFlux or other parameter estimation tools here.
# Retune for better parameters
Ψf = SINDy(Xₙ[:, 2:end], L̂[:, 2:end], b, STRRidge(0.01), maxiter = 100, convergence_error = 1e-18)
end

Expand Down Expand Up @@ -432,8 +412,6 @@ md"""### References
# ╠═03e26dea-5449-11eb-38dc-957ea73db154
# ╟─58a1294c-544c-11eb-27ca-8512bc3d5461
# ╠═b38b9410-544e-11eb-220b-5746f897b5f4
# ╠═d58d6d84-544e-11eb-17b8-91723456fc15
# ╠═5a6dcdc8-5451-11eb-2a2f-cbc4f35844c0
# ╟─23be1198-5451-11eb-07b7-e76b21ff565a
# ╠═9de34578-5452-11eb-14cb-d5d1cdb91e63
# ╠═6fc293fa-5453-11eb-0965-e917ffac7340
Expand Down
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