Neural-PDE-solver/diff_adv_gpu.jl at master · collinwarner/Neural-PDE-solver · GitHub

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using OrdinaryDiffEq, Flux, DiffEqFlux, DiffEqOperators,  LinearAlgebra,  Plots, Sundials, CuArrays

function Neural_PDE()

    datasize = 10#30 #number of timepoints in the interval
    N =50  #number of steps in z in the interval
    tspan = (0.0f0,0.15f0) #start and end time with better precision
    t = range(tspan[1], tspan[2], length = datasize) #time range
    #Finite Difference Method PDE -> ODE
    dz = 1/(N) #step size in z
    d = ones(N-2) #diagnol5
    dl = ones(N-3) #super/lower diagonal
    zv = zeros(N-2) #zero diagonal used to extend D* for boundary condtions


    #D1 first order discritization of ∂_z
    D1= diagm(-1 => -dl, 0 => d)
    D1_B = hcat(zv, D1, zv)
    D1_B[1,1] = -1 #
    #D1_B = cu((1/dz)*D1_B)
    D1_B = cu((1/dz)*D1_B)


    #D2 discritization of ∂_zz
    D2 = diagm(-1=>dl, 0=>-2*d, 1 => dl)
    κ = 0.05
    D2_B = hcat(zv, D2, zv) #add space for the boundary conditions space for "ghost nodes"
    #we only solve for the interior space steps
    D2_B[1,1] = D2_B[end, end] = 1
print("nut")


    D2_B = cu((κ/(dz^2)).*D2_B) #add the constant κ as the equation requires and finish the discritization

    #D2_B = cu((κ/(dz^2)).*D2_B) #add the constant κ as the equation requires and finish the discritization


    #Boundary Conditons matrix QQ? need to figure this out

    Q= Matrix{Int64}(I, N-2, N-2)
    #QQ= cu(vcat(zeros(1,N-2), Q, zeros(1,N-2)))
    QQ= cu(vcat(zeros(1,N-2), Q, zeros(1,N-2)))


    #Initial Conditions
    zs = (1:N) * dz
    z = zs[2:N-1]
    f0 = z -> z#exp(-200*(z-0.75)^2)
    u0 = f0.(zs)
    #plot(zs, u0)

    #get true solution

    x = u0[2:N-1] |> gpu
    r = zeros(N-2)
    #r = cu([0;r;0])
    r = [0;r;0]

    firstp =D1_B,D2_B,QQ,similar(r),r,similar(r)
    #p =D2_B,QQ,similar(r),r,similar(r)

    function ode_i(du, u, p, t)


        D1_B, D2_B, QQ, tmp, r, tmp2 = p
        Φ = cos.(sin.(u.^3) .+ sin.(cos.(u.^2)))

        #Φ = CUDAnative.cos.(CUDAnative.sin.(u.^3) .+ CUDAnative.sin.(CUDAnative.cos.(u.^2)))

        du .= D1_B*(QQ*Φ) + D2_B*(QQ*u)
    end

    generate_data = ODEProblem(ode_i, x,tspan, firstp)
    true_sol = solve(generate_data, Tsit5(), saveat=t, abstol = 1e-8, reltol = 1e-8)


    training_data = cu(collect(true_sol))


    u0 = param(x) #|>gpu
    #tspan = (0.0f0,25.0f0)

    ann = Chain(Dense(N,50,tanh), Dense(50,N-2)) |>gpu

    p1 = Flux.data(DiffEqFlux.destructure(ann))
    p2 = vec(D2_B)
    p3 = vec(QQ)
    p4 = param([p1;p2;p3])
    ps = Flux.params(p4,u0)

    function dudt_(u::TrackedArray,p,t)

        Flux.Tracker.collect(DiffEqFlux.restructure(ann, p[1:length(p1)])(reshape(p[length(p1)+1+length(p2):end], size(QQ))*u) + reshape(p[length(p1)+1:length(p1)+length(p2)], size(D2_B))*(reshape(p[length(p1)+1+length(p2):end], size(QQ))*u))


    end
    function dudt_(u::AbstractArray,p,t)

        Flux.data(DiffEqFlux.restructure(ann, p[1:length(p1)])(reshape(p[length(p1)+1+length(p2):end], size(QQ))*u)) + reshape(p[length(p1)+1:length(p1)+length(p2)], size(D2_B))*(reshape(p[length(p1)+1+length(p2):end], size(QQ))*u)

    end
    prob = ODEProblem{false}(dudt_,u0,tspan,p4)
    diffeq_adjoint(p4,prob,Tsit5(),u0=u0, saveat = t)#,abstol=1e-8,reltol=1e-8)

    predict_adjoint()  =   diffeq_adjoint(p4,prob,Tsit5(),u0=u0, saveat = t)#,abstol=1e-8,reltol=1e-8)


    loss_adjoint()  = sum(abs2, training_data - predict_adjoint()) #super slow dev the package, watch chris's video, inside the layer do something
    loss_adjoint()

    data = Iterators.repeated((), 100)
    opt = ADAM(0.1)

    pre_pts=zeros(datasize)

    cb = function ()
        display(loss_adjoint())
        cur_pred = collect(Flux.data(predict_adjoint()))
        pl = scatter(t,true_sol[end,:],label="data", legend =:bottomright)

        scatter!(pl,t,cur_pred[end,:],label="prediction")
        display(plot(pl))
    end

    lyrs = Flux.params(p4)
    Flux.train!(loss_adjoint, lyrs, data, opt)#, cb = cb)
    while(loss_adjoint()>0.01)
        Flux.train!(loss_adjoint, lyrs, data, opt)#, cb = cb)
    end
    cb()
    new_tf = 0.15f0

    for i in 1:8

        new_tf += 0.05f0
        tspan = (0.0f0,new_tf) #start and end time with better precision
        t = range(tspan[1], tspan[2], length = datasize) #time range


        generate_data = ODEProblem(ode_i, x,tspan, firstp)
        true_sol = solve(generate_data, Tsit5(), saveat=t)
        training_data = cu(collect(true_sol))


        prob = ODEProblem{false}(dudt_,u0,tspan,p4)
        diffeq_adjoint(p4,prob,Tsit5(),u0=u0, saveat = t)#,abstol=1e-8,reltol=1e-8)


        lyrs = Flux.params(p4)
        Flux.train!(loss_adjoint, lyrs, data, opt)#, cb = cb)
        while(loss_adjoint()>0.01)
            Flux.train!(loss_adjoint, lyrs, data, opt)#, cb = cb)
        end
        cb()

        #cur_pred = collect(Flux.data(predict_adjoint()))
        #pl = scatter(t,true_sol[end,:],label="data", legend =:bottomright)

        #scatter!(pl,t,cur_pred[end,:],label="prediction")
        #display(plot(pl))

    end
end#

Neural_PDE()