From 3e96e3db065e0d618996efc1c4e6318febdf78da Mon Sep 17 00:00:00 2001
From: Astitva Aggarwal <astitvaaggarwalimportant@gmail.com>
Date: Fri, 29 Mar 2024 22:25:27 +0530
Subject: [PATCH] update BPINN_PDEinvsol_tests.jl

---
 test/BPINN_PDEinvsol_tests.jl | 1113 +--------------------------------
 1 file changed, 1 insertion(+), 1112 deletions(-)

diff --git a/test/BPINN_PDEinvsol_tests.jl b/test/BPINN_PDEinvsol_tests.jl
index 1fadc8a0a..748ff2168 100644
--- a/test/BPINN_PDEinvsol_tests.jl
+++ b/test/BPINN_PDEinvsol_tests.jl
@@ -242,1115 +242,4 @@ u_predict = pmean(sol2.ensemblesol[1])
 
 @test u_predict≈u_real atol=1.5
 @test mean(u_predict .- u_real) < 0.1
-@test sol1.estimated_de_params[1]≈param atol=param * 0.3
-
-
-
-println("Example 3: Lotka Volterra with New parameter estimation")
-@parameters t α β γ δ
-@variables x(..) y(..)
-
-Dt = Differential(t)
-eqs = [Dt(x(t))*α  ~ x(t) - β * x(t) * y(t), Dt(y(t))*γ  ~ δ * x(t) * y(t) - y(t)]
-bcs = [x(0) ~ 1.0, y(0) ~ 1.0]
-domains = [t ∈ Interval(0.0, 7.0)]
-
-# Define the parameters' values
-# params = [α => 1.0, β => 0.5, γ => 0.5, δ => 1.0]
-# p = [1.5, 1.0, 3.0, 1.0]
-
-chainl = [
-    Lux.Chain(Lux.Dense(1, 6, tanh), Lux.Dense(6, 6, tanh),Lux.Dense(6, 1)),
-    Lux.Chain(Lux.Dense(1, 6, tanh), Lux.Dense(6, 6, tanh),Lux.Dense(6, 1))
-]
-
-initl, st = Lux.setup(Random.default_rng(), chainl[1])
-initl1, st1 = Lux.setup(Random.default_rng(), chainl[2])
-
-using NeuralPDE, Lux, OrdinaryDiffEq, Distributions, Random
-
-function lotka_volterra(u, p, t)
-    # Model parameters. 
-    α, β, γ, δ = p
-    # Current state.
-    x, y = u
-
-    # Evaluate differential equations.
-    dx = (α - β * y) * x # prey
-    dy = (δ * x - γ) * y # predator
-
-    return [dx, dy]
-end
-# initial-value problem.
-u0 = [1.0, 1.0]
-# p = [2/3, 2/3, 1/3.0, 1/3.0]
-p = [1.5, 1.0, 3.0, 1.0]
-tspan = (0.0, 7.0)
-prob = ODEProblem(lotka_volterra, u0, tspan, p)
-dt = 0.01
-solution = solve(prob, Tsit5(); saveat = dt)
-
-
-# function moving_average_smoothing(data::Vector{T}, window_size::Int) where {T}
-#     smoothed_data = similar(data, T, length(data))
-
-#     for i in 1:length(data)
-#         start_idx = max(1, i - window_size)
-#         end_idx = min(length(data), i + window_size)
-#         smoothed_data[i] = mean(data[start_idx:end_idx])
-#     end
-
-#     return smoothed_data'
-# end
-
-# Extract solution
-time = solution.t
-u = hcat(solution.u...)
-time1=solution.t
-u_noisy = u .+ u .* (0.3 .* randn(size(u)))
-
-plot(time,u[1,:])
-plot!(time,u[2,:])
-scatter!(time1,u_noisy[1,:])
-scatter!(time1,u_noisy[2,:])
-
-# window_size = 5
-# smoothed_datasets = [moving_average_smoothing(u1[i, :], window_size)
-#                      for i in 1:length(solution.u[1])]
-# u2 = vcat(smoothed_datasets[1], smoothed_datasets[2])
-# Randomly select some points from the solution
-num_points = 150  # Number of points to select
-selected_indices = rand(1:size(u_noisy, 2), num_points)
-upoints = [u_noisy[:, i] for i in selected_indices]
-timepoints = [time[i] for i in selected_indices]
-temp=hcat(upoints...)
-dataset = [hcat(temp[i, :], timepoints) for i in 1:2]
-
-# plot(time,u[1,:])
-# plot!(time,u[2,:])
-
-discretization = BayesianPINN(chainl, GridTraining([0.01]), param_estim = true,
-    dataset = [dataset, nothing])
-
-@named pde_system = PDESystem(eqs,
-    bcs,
-    domains,
-    [t],
-    [x(t), y(t)],
-    [α, β, γ, δ],
-    defaults = Dict([α =>2, β => 3, γ =>3, δ =>2]))
-
-# creating dictionary for masking equations
-eqs = pde_system.eqs
-Dict_differentials = Dict()
-exps = toexpr.(eqs)
-nullobj = [recur_expression(exp, Dict_differentials) for exp in exps]
-
-sol3 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.05, 0.05],
-    priorsNNw = (0.0, 5.0),
-    saveats = [1 / 50.0],
-    # Kernel = AdvancedHMC.NUTS(0.8),
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], progress = true)
-
-# time
-# dataset
-# chainl[1](time', sol3.estimated_nn_params[1], st)[1][1,:]
-# plot!(time1, chainl[1](time1', sol3.estimated_nn_params[1], st)[1][1,:])
-# plot!(time1, chainl[2](time1', sol3.estimated_nn_params[2], st)[1][1,:])
-# plot!(time1, chainl[1](time1', sol5.estimated_nn_params[1], st)[1][1,:])
-# plot!(time1, chainl[2](time1', sol5.estimated_nn_params[2], st)[1][1,:])
-# time1 = collect(0.0:(1 / 100.0):8.0)
-
-sol4 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0),
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], progress = true
-)
-
-
-sol5_00 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.15, 0.15],
-    phystd = [0.15, 0.15], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.3, 0.3],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-sol5_0 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.05, 0.05],
-    phystd = [0.05, 0.05], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.1, 0.1],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-sol5 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.05, 0.05],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.2, 0.2],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-# 100 points(sol5_2 vs sol3)
-sol5_2 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.05, 0.05],
-    priorsNNw = (0.0, 5.0),
-    phystdnew = [0.1, 0.1],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-# 100 points(sol5_2 vs sol3)
-sol5_2_1 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.05, 0.05],
-    priorsNNw = (0.0, 5.0),
-    phystdnew = [0.08, 0.08],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-# 100 points(sol5_2 vs sol3)
-sol5_2_2 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0),
-    phystdnew = [0.2, 0.2],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-# 50 datapoint 0-5 sol5 vs sol4
-# julia> sol4.estimated_de_params
-# 4-element Vector{Particles{Float64, 234}}:
-#  0.549 ± 0.0058
-#  0.71 ± 0.0042
-#  0.408 ± 0.0063
-#  0.355 ± 0.0015
-
-# julia> sol5.estimated_de_params
-# 4-element Vector{Particles{Float64, 234}}:
-#  0.604 ± 0.0052
-#  0.702 ± 0.0034
-#  0.346 ± 0.0037
-#  0.335 ± 0.0013
-
-# 100 datapoint 0-5 sol5_2 vs sol3
-# julia> sol3.estimated_de_params
-# 4-element Vector{Particles{Float64, 234}}:
-#  0.598 ± 0.0037
-#  0.711 ± 0.0027
-#  0.399 ± 0.0032
-#  0.333 ± 0.0011
-
-# julia> sol5_2.estimated_de_params
-# 4-element Vector{Particles{Float64, 234}}:
-#  0.604 ± 0.0035
-#  0.686 ± 0.0026
-#  0.395 ± 0.0029
-#  0.328 ± 0.00095
-
-# timespan for full dataset (0-8)
-sol6 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0),
-    saveats = [1 / 50.0],
-    param = [
-        Normal(1, 2),
-        Normal(1, 1),
-        Normal(1, 2),
-        Normal(1, 1)
-    ], progress = true)
-
-sol5_3 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.3, 0.3],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(1, 2),
-        Normal(1, 1),
-        Normal(1, 2),
-        Normal(1, 1)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-sol5_4 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.2, 0.2],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(1, 2),
-        Normal(1, 1),
-        Normal(1, 2),
-        Normal(1, 1)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-sol5_5 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.05, 0.05],
-    priorsNNw = (0.0, 5.0),
-    saveats = [1 / 50.0],
-    param = [
-        Normal(1, 2),
-        Normal(1, 1),
-        Normal(1, 2),
-        Normal(1, 1)
-    ], progress = true
-)
-
-sol7 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.05, 0.05],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.3, 0.3],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(1, 2),
-        Normal(1, 1),
-        Normal(1, 2),
-        Normal(1, 1)
-    ], Dict_differentials = Dict_differentials, progress = true)
-
-sol5_5_1 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.05, 0.05],
-    priorsNNw = (0.0, 5.0),
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], progress = true
-)
-
-sol7_1 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.05, 0.05],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.3, 0.3],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true)
-    
-sol7_2 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.1, 0.1],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true)
-
-sol7_3 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.2, 0.2],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true)
- 
-sol7_4 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0), 
-    phystdnew = [0.3, 0.3],
-    saveats = [1 / 50.0],
-    param = [
-        Normal(2, 2),
-        Normal(2, 1),
-        Normal(2, 2),
-        Normal(2, 1)
-    ], Dict_differentials = Dict_differentials, progress = true)
-
-lpfun = function f(chain::Chains) # function to compute the logpdf values
-    niter, nparams, nchains = size(chain)
-    lp = zeros(niter + nchains) # resulting logpdf values
-    for i = 1:nparams
-        lp += logpdf(MvNormal(Array(chain[:,i,:])) , dataset[1][:,1]')
-        lp += logpdf(MvNormal(Array(chain[:,i,:])) , dataset[1][:,2]')
-    end
-    return lp
-end
-
-DIC, pD = dic(sol3.original.mcmc_chain, lpfun)
-DIC1, pD1 = dic(sol4.original.mcmc_chain, lpfun)
-
-size(sol3.original.mcmc_chain)
-Array(sol3.original.mcmc_chain[1,:,:])
-length(sol3.estimated_nn_params[1])
-chainl[1](time', sol3.estimated_nn_params[1], st)[1]
-
-data = [hcat(calculate_derivatives2(dataset[i][:, 2], dataset[1][:, 1]),dataset[i][:, 2]) for i in eachindex(dataset)]
-dataset[1][:,1]
-dataset[2]
-plot!(dataset[1][:,2],dataset[1][:,1])
-eqs
-sol5 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 200,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.02, 0.02],
-    priorsNNw = (0.0, 5.0),
-    saveats = [1 / 50.0],
-    # Kernel = AdvancedHMC.NUTS(0.8),
-    param = [
-        Normal(3, 2),
-        Normal(3, 2)
-        # LogNormal(1, 2),
-        # LogNormal(1, 2),
-        # LogNormal(1, 2),
-        # LogNormal(1, 2)
-    ], progress = true)
-
-# plot(time, chainl[1](time', sol2.estimated_nn_params[1], st)[1])
-# plot!(time, chainl[2](time', sol2.estimated_nn_params[2], st)[1])
-
-sol6 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 200,
-    bcstd = [0.5, 0.5],
-    phystd = [0.5, 0.5], l2std = [0.02, 0.02],
-    priorsNNw = (0.0, 5.0), phystdnew = [0.5, 0.5],
-    saveats = [1 / 50.0],
-    # Kernel = AdvancedHMC.NUTS(0.8),aa
-    param = [
-        # LogNormal(2, 3),LogNormal(2, 3),LogNormal(2, 3),LogNormal(2, 3)
-        # Normal(3, 2),
-        # Normal(4, 2),
-        Normal(3, 2),
-        Normal(3, 2)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-function calculate_derivatives2(indvar,depvar)
-    x̂, time = indvar,depvar
-    num_points = length(x̂)
-    # Initialize an array to store the derivative values.
-    derivatives = similar(x̂)
-
-    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]
-
-        derivative = (x̂[i + 1] - x̂[i - 1]) / (Δt_forward + Δt_backward)
-
-        derivatives[i] = derivative
-    end
-
-    # 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
-dataset[1]
-dataset[2]
-dataset[1][:,1]=calculate_derivatives2(dataset[1][:,2], dataset[1][:,1])
-dataset[2][:,1]=calculate_derivatives2(dataset[2][:,2], dataset[2][:,1])
-dataset[1]
-dataset[2]
-sol7 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 200,
-    bcstd = [0.5, 0.5],
-    phystd = [0.5, 0.5], l2std = [0.05, 0.05],
-    priorsNNw = (0.0, 5.0),
-    saveats = [1 / 50.0],
-    # Kernel = AdvancedHMC.NUTS(0.8),
-    param = [
-        Normal(0, 2),
-        Normal(0, 2)
-        # LogNormal(1, 2),
-        # LogNormal(1, 2),
-        # LogNormal(1, 2),
-        # LogNormal(1, 2)
-    ], progress = true)
-
-# plot(time, chainl[1](time', sol2.estimated_nn_params[1], st)[1])
-# plot!(time, chainl[2](time', sol2.estimated_nn_params[2], st)[1])
-
-sol8 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 700,
-    bcstd = [0.1, 0.1],
-    phystd = [0.1, 0.1], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 5.0), phystdnew = [0.1, 0.1],
-    saveats = [1 / 50.0],
-    # Kernel = AdvancedHMC.NUTS(0.8),aa
-    param = [
-        # LogNormal(2, 3),LogNormal(2, 3),LogNormal(2, 3),LogNormal(2, 3)
-        # Normal(3, 2),
-        # Normal(4, 2),
-        Normal(0, 2),
-        Normal(0, 2)
-    ], Dict_differentials = Dict_differentials, progress = true
-)
-
-timepoints = collect(0.0:(1 / 100.0):9.0)
-plot!(timepoints', chainl[1](timepoints', sol5_4.estimated_nn_params[1], st)[1])
-plot!(timepoints, chainl[2](timepoints', sol5_4.estimated_nn_params[2], st)[1])
-
-using Plots, StatsPlots
-plotly()
-
-plot(time, u[1, :])
-plot!(time, u[2, :])
-scatter!(time, u_noisy[1, :])
-scatter!(time, u_noisy[2, :])
-scatter!(discretization.dataset[1][1][:,2], discretization.dataset[1][1][:,1])
-scatter!(discretization.dataset[1][2][:,2], discretization.dataset[1][2][:,1])
-
-# plot28(sol4 seems better vs sol3 plots, params seems similar)
-plot!(sol3.timepoints[1]', sol3.ensemblesol[1],legend=nothing)
-plot!(sol3.timepoints[2]', sol3.ensemblesol[2])
-plot!(sol4.timepoints[1]', sol4.ensemblesol[1])
-plot!(sol4.timepoints[2]', sol4.ensemblesol[2])
-
-plot!(sol4_2.timepoints[1]', sol4_2.ensemblesol[1],legend=nothing)
-plot!(sol4_2.timepoints[2]', sol4_2.ensemblesol[2])
-plot!(sol5_2.timepoints[1]', sol5_2.ensemblesol[1],legend=nothing)
-plot!(sol5_2.timepoints[2]', sol5_2.ensemblesol[2])
-
-plot!(sol4_3.timepoints[1]', sol4_3.ensemblesol[1],legend=nothing)
-plot!(sol4_3.timepoints[2]', sol4_3.ensemblesol[2])
-plot!(sol5_3.timepoints[1]', sol5_3.ensemblesol[1])
-plot!(sol5_3.timepoints[2]', sol5_3.ensemblesol[2])
-plot!(sol5_4.timepoints[1]', sol5_4.ensemblesol[1],legend=nothing)
-plot!(sol5_4.timepoints[2]', sol5_4.ensemblesol[2])
-
-
-# plot 36 sol4 vs sol5(params sol4 better, but plots sol5 "looks" better),plot 44(sol5 better than sol6 overall)
-plot!(sol5.timepoints[1]', sol5.ensemblesol[1],legend=nothing)
-plot!(sol5.timepoints[2]', sol5.ensemblesol[2])
-plot!(sol6.timepoints[1]', sol6.ensemblesol[1])
-plot!(sol6.timepoints[2]', sol6.ensemblesol[2])
-
-# plot52 sol7 vs sol5(sol5 overall better plots, params?)
-plot!(sol7.timepoints[1]', sol7.ensemblesol[1])
-plot!(sol7.timepoints[2]', sol7.ensemblesol[2])
-
-# sol8,sol8_2,sol9,sol9_2 bad
-plot!(sol8.timepoints[1]', sol8.ensemblesol[1])
-plot!(sol8.timepoints[2]', sol8.ensemblesol[2])
-plot!(sol8_2.timepoints[1]', sol8_2.ensemblesol[1])
-plot!(sol8_2.timepoints[2]', sol8_2.ensemblesol[2])
-
-plot!(sol9.timepoints[1]', sol9.ensemblesol[1])
-plot!(sol9.timepoints[2]', sol9.ensemblesol[2])
-plot!(sol9_2.timepoints[1]', sol9_2.ensemblesol[1])
-plot!(sol9_2.timepoints[2]', sol9_2.ensemblesol[2])
-
-
-plot!(sol5_5.timepoints[1]', sol5_5.ensemblesol[1])
-plot!(sol5_5.timepoints[2]', sol5_5.ensemblesol[2],legend=nothing)
-
-plot!(sol5_5_1.timepoints[1]', sol5_5_1.ensemblesol[1])
-plot!(sol5_5_1.timepoints[2]', sol5_5_1.ensemblesol[2],legend=nothing)
-plot!(sol7_1.timepoints[1]', sol7_1.ensemblesol[1])
-plot!(sol7_1.timepoints[2]', sol7_1.ensemblesol[2])
-
-plot!(sol7_4.timepoints[1]', sol7_4.ensemblesol[1])
-plot!(sol7_4.timepoints[2]', sol7_4.ensemblesol[2])
-
-plot!(sol5_2_1.timepoints[1]', sol5_2_1.ensemblesol[1],legend=nothing)
-plot!(sol5_2_1.timepoints[2]', sol5_2_1.ensemblesol[2])
-plot!(sol5_2_2.timepoints[1]', sol5_2_2.ensemblesol[1],legend=nothing)
-plot!(sol5_2_2.timepoints[2]', sol5_2_2.ensemblesol[2])
-
-plot!(sol5_0.timepoints[1]', sol5_0.ensemblesol[1])
-plot!(sol5_0.timepoints[2]', sol5_0.ensemblesol[2],legend=nothing)
-
-plot!(sol5_00.timepoints[1]', sol5_00.ensemblesol[1])
-plot!(sol5_00.timepoints[2]', sol5_00.ensemblesol[2],legend=nothing)
-
-# test with lower number of points
-# test same calls 2 times or more
-# consider full range dataset case
-# combination of all above
-
-# run 1 100 iters
-sol5.estimated_de_params
-sol6.estimated_de_params
-
-# run 2 200 iters
-sol5.estimated_de_params
-sol6.estimated_de_params
-
-# run 2 200 iters
-sol3.estimated_de_params
-sol4.estimated_de_params
-
-# p = [2/3, 2/3, 1/3, 1/3]
-sol3.estimated_de_params
-sol4.estimated_de_params
-dataset[1]
-eqs
-α, β, γ, δ = p
-p
-#  1.0
-#  0.6666666666666666
-#  1.0
-#  0.33333333333333333
-
-1/a
-1/c
-eqs
-using StatsPlots
-plotly()
-plot(sol3.original.mcmc_chain)
-plot(sol4.original.mcmc_chain)
-
-# 4-element Vector{Particles{Float64, 34}}:
-#  1.23 ± 0.022
-#  0.858 ± 0.011
-#  3.04 ± 0.079
-#  1.03 ± 0.024
-# 4-element Vector{Particles{Float64, 34}}:
-#  1.2 ± 0.0069
-#  0.835 ± 0.006
-#  3.22 ± 0.01
-#  1.08 ± 0.0053
-# # plot(time', chainl[1](time', sol1.estimated_nn_params[1], st)[1])
-# # plot!(time, chainl[2](time', sol1.estimated_nn_params[2], st)[1])
-
-# sol3 = ahmc_bayesian_pinn_pde(pde_system,
-#     discretization;
-#     draw_samples = 500,
-#     bcstd = [0.05, 0.05],
-#     phystd = [0.005, 0.005], l2std = [0.1, 0.1],
-#     phystdnew = [0.5, 0.5],
-#     #  Kernel = AdvancedHMC.NUTS(0.8),
-#     priorsNNw = (0.0, 10.0),
-#     saveats = [1 / 50.0],
-#     param = [
-#         Normal(0.0, 2),
-#         Normal(0.0, 2),
-#         Normal(0.0, 2),
-#         Normal(0.0, 2)
-#     ],
-#     Dict_differentials = Dict_differentials, progress = true)
-
-# sol = ahmc_bayesian_pinn_pde(pde_system,
-#     discretization;
-#     draw_samples = 500,
-#     bcstd = [0.05, 0.05],
-#     phystd = [0.005, 0.005], l2std = [0.1, 0.1],
-#     priorsNNw = (0.0, 10.0),
-#     saveats = [1 / 50.0],
-#     # Kernel = AdvancedHMC.NUTS(0.8),
-#     param = [
-#         Normal(1.0, 2),
-#         Normal(1.0, 2),
-#         Normal(1.0, 2),
-#         Normal(1.0, 2)
-#     ], progress = true)
-
-# plot!(sol.timepoints[1]', sol.ensemblesol[1])
-# plot!(sol.timepoints[2]', sol.ensemblesol[2])
-
-# sol1 = ahmc_bayesian_pinn_pde(pde_system,
-#     discretization;
-#     draw_samples = 500,
-#     bcstd = [0.05, 0.05],
-#     phystd = [0.005, 0.005], l2std = [0.1, 0.1],
-#     phystdnew = [0.5, 0.5],
-#     #  Kernel = AdvancedHMC.NUTS(0.8),
-#     priorsNNw = (0.0, 10.0),
-#     saveats = [1 / 50.0],
-#     param = [
-#         Normal(1.0, 2),
-#         Normal(1.0, 2),
-#         Normal(1.0, 2),
-#         Normal(1.0, 2)
-#     ],
-#     Dict_differentials = Dict_differentials, progress = true)
-
-# plot!(sol1.timepoints[1]', sol1.ensemblesol[1])
-# plot!(sol1.timepoints[2]', sol1.ensemblesol[2])
-
-sol = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 500,
-    bcstd = [0.05, 0.05],
-    phystd = [0.005, 0.005], l2std = [0.1, 0.1],
-    priorsNNw = (0.0, 10.0),
-    saveats = [1 / 50.0],
-    # Kernel = AdvancedHMC.NUTS(0.8),
-    param = [
-        Normal(1.0, 2),
-        Normal(1.0, 2),
-        Normal(1.0, 2),
-        Normal(1.0, 2)
-    ])
-
-# plot!(sol.timepoints[1]', sol.ensemblesol[1])
-# plot!(sol.timepoints[2]', sol.ensemblesol[2])
-
-sol1 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 500,
-    bcstd = [0.05, 0.05],
-    phystd = [0.005, 0.005], l2std = [0.1, 0.1],
-    phystdnew = [0.5, 0.5],
-    #  Kernel = AdvancedHMC.NUTS(0.8),
-    priorsNNw = (0.0, 10.0),
-    saveats = [1 / 50.0],
-    param = [
-        Normal(1.0, 2),
-        Normal(1.0, 2),
-        Normal(1.0, 2),
-        Normal(1.0, 2)
-    ],
-    Dict_differentials = Dict_differentials)
-
-param = 2 * π
-ts = vec(sol1.timepoints[1])
-u_real = [analytic_sol_func1(0.0, t) for t in ts]
-u_predict = pmean(sol1.ensemblesol[1])
-
-@test u_predict≈u_real atol=1.5
-@test mean(u_predict .- u_real) < 0.1
-@test sol1.estimated_de_params[1]≈param atol=param * 0.3
-
-# points1 = []
-# for eq_arg in eq_args
-#     a = []
-#     # for each (depvar,[indvar1..]) if indvari==indvar (eq_arg)
-#     for i in eachindex(symbols_input)
-#         if symbols_input[i][2] == eq_arg
-#             # include domain points of that depvar
-#             # each loss equation take domain matrix [points..;points..]
-#             push!(a, train_sets[i][:, 2:end]')
-#         end
-#     end
-#     # vcat as new row for next equation
-#     push!(points1, vcat(a...))
-# end
-# println(points1 == points)
-
-# using NeuralPDE, Flux, Lux, ModelingToolkit, LinearAlgebra, AdvancedHMC
-# import ModelingToolkit: Interval, infimum, supremum, Distributions
-# using Plots, MonteCarloMeasurements
-
-# @parameters x, t, α
-# @variables u(..)
-# Dt = Differential(t)
-# Dx = Differential(x)
-# Dx2 = Differential(x)^2
-# Dx3 = Differential(x)^3
-# Dx4 = Differential(x)^4
-
-# # α = 1
-# β = 4
-# γ = 1
-# eq = Dt(u(x, t)) + u(x, t) * Dx(u(x, t)) + α * Dx2(u(x, t)) + β * Dx3(u(x, t)) + γ * Dx4(u(x, t)) ~ 0
-
-# u_analytic(x, t; z = -x / 2 + t) = 11 + 15 * tanh(z) - 15 * tanh(z)^2 - 15 * tanh(z)^3
-# du(x, t; z = -x / 2 + t) = 15 / 2 * (tanh(z) + 1) * (3 * tanh(z) - 1) * sech(z)^2
-
-# bcs = [u(x, 0) ~ u_analytic(x, 0),
-#     u(-10, t) ~ u_analytic(-10, t),
-#     u(10, t) ~ u_analytic(10, t),
-#     Dx(u(-10, t)) ~ du(-10, t),
-#     Dx(u(10, t)) ~ du(10, t)]
-
-# # Space and time domains
-# domains = [x ∈ Interval(-10.0, 10.0),
-#     t ∈ Interval(0.0, 1.0)]
-
-# # Discretization
-# dx = 0.4;
-# dt = 0.2;
-
-# # Function to compute analytical solution at a specific point (x, t)
-# function u_analytic_point(x, t)
-#     z = -x / 2 + t
-#     return 11 + 15 * tanh(z) - 15 * tanh(z)^2 - 15 * tanh(z)^3
-# end
-
-# # Function to generate the dataset matrix
-# function generate_dataset_matrix(domains, dx, dt)
-#     x_values = -10:dx:10
-#     t_values = 0.0:dt:1.0
-
-#     dataset = []
-
-#     for t in t_values
-#         for x in x_values
-#             u_value = u_analytic_point(x, t)
-#             push!(dataset, [u_value, x, t])
-#         end
-#     end
-
-#     return vcat([data' for data in dataset]...)
-# end
-
-# datasetpde = [generate_dataset_matrix(domains, dx, dt)]
-
-# # noise to dataset
-# noisydataset = deepcopy(datasetpde)
-# noisydataset[1][:, 1] = noisydataset[1][:, 1] .+
-#                         randn(size(noisydataset[1][:, 1])) .* 5 / 100 .*
-#                         noisydataset[1][:, 1]
-
-# # plot(datasetpde[1][:, 2], datasetpde[1][:, 1], title = "Dataset from Analytical Solution")
-# # plot!(noisydataset[1][:, 2], noisydataset[1][:, 1])
-
-# # Neural network
-# chain = Lux.Chain(Lux.Dense(2, 8, Lux.tanh),
-#     Lux.Dense(8, 8, Lux.tanh),
-#     Lux.Dense(8, 1))
-
-# discretization = NeuralPDE.BayesianPINN([chain],
-#     GridTraining([dx, dt]), param_estim = true, dataset = [noisydataset, nothing])
-
-# @named pde_system = PDESystem(eq,
-#     bcs,
-#     domains,
-#     [x, t],
-#     [u(x, t)],
-#     [α],
-#     defaults = Dict([α => 0.5]))
-
-# sol1 = ahmc_bayesian_pinn_pde(pde_system,
-#     discretization;
-#     draw_samples = 100,
-#     bcstd = [0.2, 0.2, 0.2, 0.2, 0.2],
-#     phystd = [1.0], l2std = [0.05], param = [Distributions.LogNormal(0.5, 2)],
-#     priorsNNw = (0.0, 10.0),
-#     saveats = [1 / 100.0, 1 / 100.0], progress = true)
-
-# eqs = pde_system.eqs
-# Dict_differentials = Dict()
-# exps = toexpr.(eqs)
-# nullobj = [recur_expression(exp, Dict_differentials) for exp in exps]
-
-# sol2 = ahmc_bayesian_pinn_pde(pde_system,
-#     discretization;
-#     draw_samples = 100,
-#     bcstd = [0.2, 0.2, 0.2, 0.2, 0.2],
-#     phystd = [1.0], phystdnew = [0.05], l2std = [0.05],
-#     param = [Distributions.LogNormal(0.5, 2)],
-#     priorsNNw = (0.0, 10.0),
-#     saveats = [1 / 100.0, 1 / 100.0], Dict_differentials = Dict_differentials,
-#     progress = true)
-
-# phi = discretization.phi[1]
-# xs, ts = [infimum(d.domain):dx:supremum(d.domain)
-#           for (d, dx) in zip(domains, [dx / 10, dt])]
-# u_predict = [[first(pmean(phi([x, t], sol1.estimated_nn_params[1]))) for x in xs]
-#              for t in ts]
-# u_real = [[u_analytic(x, t) for x in xs] for t in ts]
-# diff_u = [[abs(u_analytic(x, t) - first(pmean(phi([x, t], sol1.estimated_nn_params[1]))))
-#            for x in xs]
-#           for t in ts]
-
-# # p1 = plot(xs, u_predict, title = "predict")
-# # p2 = plot(xs, u_real, title = "analytic")
-# # p3 = plot(xs, diff_u, title = "error")
-# # plot(p1, p2, p3)
-
-# phi = discretization.phi[1]
-# xs, ts = [infimum(d.domain):dx:supremum(d.domain)
-#           for (d, dx) in zip(domains, [dx / 10, dt])]
-# u_predict = [[first(pmean(phi([x, t], sol2.estimated_nn_params[1]))) for x in xs]
-#              for t in ts]
-# u_real = [[u_analytic(x, t) for x in xs] for t in ts]
-# diff_u = [[abs(u_analytic(x, t) - first(pmean(phi([x, t], sol2.estimated_nn_params[1]))))
-#            for x in xs]
-#           for t in ts]
-
-# # p1 = plot(xs, u_predict, title = "predict")
-# # p2 = plot(xs, u_real, title = "analytic")
-# # p3 = plot(xs, diff_u, title = "error")
-# # plot(p1, p2, p3)
-
-@parameters t, p
-@variables u(..)
-
-Dt = Differential(t)
-eqs = Dt(u(t)) - cos(p * t) ~ 0
-bcs = [u(0) ~ 0.0]
-domains = [t ∈ Interval(0.0, 2.0)]
-
-chainl = Lux.Chain(Lux.Dense(1, 6, tanh), Lux.Dense(6, 1))
-initl, st = Lux.setup(Random.default_rng(), chainl)
-
-@named pde_system = PDESystem(eqs,
-    bcs,
-    domains,
-    [t],
-    [u(t)],
-    [p],
-    defaults = Dict([p => 4.0]))
-
-analytic_sol_func1(u0, t) = u0 + sin(2 * π * t) / (2 * π)
-timepoints = collect(0.0:(1 / 100.0):2.0)
-u1 = [analytic_sol_func1(0.0, timepoint) for timepoint in timepoints]
-u1 = u1 .+ (u1 .* 0.2) .* randn(size(u1))
-dataset = [hcat(u1, timepoints)]
-
-discretization = BayesianPINN([chainl], GridTraining([0.02]), param_estim = true,
-    dataset = [dataset, nothing])
-
-sol1 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 1500,
-    bcstd = [0.05],
-    phystd = [0.01], l2std = [0.01],
-    priorsNNw = (0.0, 1.0),
-    saveats = [1 / 50.0],
-    param = [LogNormal(4.0, 2)], progress = true)
-
-param = 2 * π
-ts = vec(sol1.timepoints[1])
-u_real = [analytic_sol_func1(0.0, t) for t in ts]
-u_predict = pmean(sol1.ensemblesol[1])
-
-@test u_predict≈u_real atol=0.1
-@test mean(u_predict .- u_real) < 0.01
-@test sol1.estimated_de_params[1]≈param atol=0.1
-sol1.estimated_de_params[1]
-
-eqs = pde_system.eqs
-Dict_differentials = Dict()
-exps = toexpr.(eqs)
-nullobj = [recur_expression(exp, Dict_differentials) for exp in exps]
-
-sol2 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 1500,
-    bcstd = [0.05],
-    phystd = [0.01], l2std = [0.02], phystdnew = [0.02],
-    priorsNNw = (0.0, 1.0),
-    saveats = [1 / 50.0],
-    param = [LogNormal(4.0, 2)],
-    Dict_differentials = Dict_differentials,
-    progress = true)
-
-param = 2 * π
-ts_2 = vec(sol2.timepoints[1])
-u_real_2 = [analytic_sol_func1(0.0, t) for t in ts]
-u_predict_2 = pmean(sol2.ensemblesol[1])
-
-@test u_predict_2≈u_real_2 atol=0.1
-@test mean(u_predict_2 .- u_real_2) < 0.01
-@test sol2.estimated_de_params[1]≈param atol=0.1
-sol2.estimated_de_params[1]
-
-plot(ts_2, u_predict_2)
-plot!(ts_2, u_real_2)
-
-@parameters t, σ_
-@variables x(..), y(..), z(..)
-Dt = Differential(t)
-eqs = [Dt(x(t)) ~ σ_ * (y(t) - x(t)),
-    Dt(y(t)) ~ x(t) * (28.0 - z(t)) - y(t),
-    Dt(z(t)) ~ x(t) * y(t) - 8 / 3 * z(t)]
-
-bcs = [x(0) ~ 1.0, y(0) ~ 0.0, z(0) ~ 0.0]
-domains = [t ∈ Interval(0.0, 1.0)]
-
-input_ = length(domains)
-n = 7
-chain = [
-    Lux.Chain(Lux.Dense(input_, n, Lux.tanh), Lux.Dense(n, n, Lux.tanh),
-        Lux.Dense(n, 1)),
-    Lux.Chain(Lux.Dense(input_, n, Lux.tanh), Lux.Dense(n, n, Lux.tanh),
-        Lux.Dense(n, 1)),
-    Lux.Chain(Lux.Dense(input_, n, Lux.tanh), Lux.Dense(n, n, Lux.tanh),
-        Lux.Dense(n, 1))
-]
-
-#Generate Data
-function lorenz!(du, u, p, t)
-    du[1] = 10.0 * (u[2] - u[1])
-    du[2] = u[1] * (28.0 - u[3]) - u[2]
-    du[3] = u[1] * u[2] - (8 / 3) * u[3]
-end
-
-u0 = [1.0; 0.0; 0.0]
-tspan = (0.0, 1.0)
-prob = ODEProblem(lorenz!, u0, tspan)
-sol = solve(prob, Tsit5(), dt = 0.01, saveat = 0.05)
-ts = sol.t
-us = hcat(sol.u...)
-us = us .+ ((0.05 .* randn(size(us))) .* us)
-ts_ = hcat(sol(ts).t...)[1, :]
-dataset = [hcat(us[i, :], ts_) for i in 1:3]
-
-discretization = BayesianPINN(chain, GridTraining([0.01]); param_estim = true,
-    dataset = [dataset, nothing])
-
-@named pde_system = PDESystem(eqs, bcs, domains,
-    [t], [x(t), y(t), z(t)], [σ_], defaults = Dict([p => 1.0 for p in [σ_]]))
-
-sol1 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 100,
-    bcstd = [0.3, 0.3, 0.3],
-    phystd = [0.1, 0.1, 0.1],
-    l2std = [1, 1, 1],
-    priorsNNw = (0.0, 1.0),
-    saveats = [0.01],
-    param = [Normal(14.0, 2)], progress = true)
-
-idealp = 10.0
-p_ = sol1.estimated_de_params[1]
-@test sum(abs, pmean(p_) - 10.00) < 0.3 * idealp[1]
-# @test sum(abs, pmean(p_[2]) - (8 / 3)) < 0.3 * idealp[2]
-
-@parameters x y
-@variables u(..)
-Dxx = Differential(x)^2
-Dyy = Differential(y)^2
-
-# 2D PDE
-eq = Dxx(u(x, y)) + Dyy(u(x, y)) ~ -sin(pi * x) * sin(pi * y)
-
-# Boundary conditions
-bcs = [u(0, y) ~ 0.0, u(1, y) ~ 0.0,
-    u(x, 0) ~ 0.0, u(x, 1) ~ 0.0]
-
-# Space and time domains
-domains = [x ∈ Interval(0.0, 1.0),
-    y ∈ Interval(0.0, 1.0)]
-
-# Neural network
-dim = 2 # number of dimensions
-chain = Lux.Chain(Lux.Dense(dim, 9, Lux.σ), Lux.Dense(9, 9, Lux.σ), Lux.Dense(9, 1))
-
-# Discretization
-dx = 0.04
-discretization = BayesianPINN([chain], GridTraining(dx), dataset = [[dataset], nothing])
-
-@named pde_system = PDESystem(eq, bcs, domains, [x, y], [u(x, y)])
-
-eqs = pde_system.eqs
-Dict_differentials = Dict()
-exps = toexpr.(eqs)
-nullobj = [recur_expression(exp, Dict_differentials) for exp in exps]
-
-sol1 = ahmc_bayesian_pinn_pde(pde_system,
-    discretization;
-    draw_samples = 5,
-    bcstd = [0.01, 0.01, 0.01, 0.01],
-    phystd = [0.005],
-    priorsNNw = (0.0, 2.0),
-    saveats = [1 / 100.0, 1 / 100.0],
-    Dict_differentials = Dict_differentials,
-    progress = true)
-
-xs = sol1.timepoints[1]
-sol1.ensemblesol[1]
-analytic_sol_func(x, y) = (sin(pi * x) * sin(pi * y)) / (2pi^2)
-
-dataset = hcat(u_real, xs')
-u_predict = pmean(sol1.ensemblesol[1])
-u_real = [analytic_sol_func(xs[:, i][1], xs[:, i][2]) for i in 1:length(xs[1, :])]
-@test u_predict≈u_real atol=0.8
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+@test sol1.estimated_de_params[1]≈param atol=param * 0.3
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