better BPINN formulation, improvements to include dataset domain points #842
Conversation
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@Vaibhavdixit02 @ChrisRackauckas this is the new PR, closed the previous one due to large number of merge conflicts after the repo was recently majorly formatted. Discussions from previous PR: #799 |
src/collocated_estim.jl
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| # if length(Tar.prob.u0) == 1 | ||
| # nnsol = [f(û[i], | ||
| # Tar.prob.p, | ||
| # t[i]) | ||
| # for i in 1:length(û[:, 1])] | ||
| # else | ||
| # nnsol = [f([û[i], u1[i]], | ||
| # Tar.prob.p, | ||
| # t[i]) | ||
| # for i in 1:length(û[:, 1])] | ||
| # end | ||
| # form of NN output matrix output dim x n | ||
| # nnsol = reduce(hcat, nnsol) | ||
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| # > Instead of dataset gradients trying NN derivatives with dataset collocation | ||
| # # convert to matrix as nnsol | ||
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these long comments should get cleaned up
src/collocated_estim.jl
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| # PDE(DU,U,P,T)=0 | ||
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| # Derivated via Central Diff | ||
| # function calculate_derivatives2(dataset) | ||
| # x̂, time = dataset | ||
| # num_points = length(x̂) | ||
| # # Initialize an array to store the derivative values. | ||
| # derivatives = similar(x̂) | ||
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| # for i in 2:(num_points - 1) | ||
| # # Calculate the first-order derivative using central differences. | ||
| # Δt_forward = time[i + 1] - time[i] | ||
| # Δt_backward = time[i] - time[i - 1] | ||
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| # derivative = (x̂[i + 1] - x̂[i - 1]) / (Δt_forward + Δt_backward) | ||
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| # derivatives[i] = derivative | ||
| # end | ||
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| # # Derivatives at the endpoints can be calculated using forward or backward differences. | ||
| # derivatives[1] = (x̂[2] - x̂[1]) / (time[2] - time[1]) | ||
| # derivatives[end] = (x̂[end] - x̂[end - 1]) / (time[end] - time[end - 1]) | ||
| # return derivatives | ||
| # end |
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initially wrote this for testing, while figuring out which kind of derivative is to be used in new loss. the above was the case where the derivative was datapoint interpolation derivatives via central diff.
src/collocated_estim.jl
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| # A1 = (prob.u0' .+ | ||
| # (prob.tspan[2] .- (dataset[end]' .+ sqrt(eps(eltype(Float64)))))' .* | ||
| # chainflux(dataset[end]' .+ sqrt(eps(eltype(Float64))))') | ||
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| # A2 = (prob.u0' .+ | ||
| # (prob.tspan[2] .- (dataset[end]'))' .* | ||
| # chainflux(dataset[end]')') | ||
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| A1 = chainflux(dataset[end]' .+ sqrt(eps(eltype(dataset[end][1])))) | ||
| A2 = chainflux(dataset[end]') | ||
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| gradients = (A2 .- A1) ./ sqrt(eps(eltype(dataset[end][1]))) |
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You shouldn't use this for gradients?
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not anymore, i wrote this for it to work for a specific case, normally the same is done using the derivative function NNodederi in the BPINN ode solver.
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There's a lot of random stuff together in here. Break this apart into simple one thing PRs and lets merge those. |
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@AstitvaAggarwal do you think you can make this into multiple smaller PRs as Chri suggested above? |
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Yes, will do |
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@ChrisRackauckas @Vaibhavdixit02 I've seperated the code into two PRs. one for the better ode solver and this for the PDE solver. |
Checklist
contributor guidelines, in particular the SciML Style Guide and
COLPRAC.
Additional context
will add docs and more tests separately