4848
4949rbf (x) = exp .(- (x .^ 2 ))
5050
51- chain = Lux. Chain (
52- Lux. Dense (2 , 5 , rbf), Lux. Dense (5 , 5 , rbf), Lux. Dense (5 , 5 , rbf),
53- Lux. Dense (5 , 2 ))
51+ chain = multi_layer_feed_forward (2 , 2 , width = 5 , initial_scaling_factor = 1 )
5452ude_sys = lotka_ude (chain)
5553
56- sys = mtkcompile (ude_sys, allow_symbolic = true )
54+ sys = mtkcompile (ude_sys)
55+
56+ @test length (equations (sys)) == 2
5757
5858prob = ODEProblem {true, SciMLBase.FullSpecialize} (sys, [], (0 , 5.0 ))
5959
6060model_true = mtkcompile (lotka_true ())
6161prob_true = ODEProblem {true, SciMLBase.FullSpecialize} (model_true, [], (0 , 5.0 ))
62- sol_ref = solve (prob_true, Vern9 (), abstol = 1e-12 , reltol = 1e-12 )
62+ sol_ref = solve (prob_true, Vern9 (), abstol = 1e-8 , reltol = 1e-8 )
6363
6464ts = range (0 , 5.0 , length = 21 )
6565data = reduce (hcat, sol_ref (ts, idxs = [model_true. x, model_true. y]). u)
@@ -70,10 +70,9 @@ get_vars = getu(sys, [sys.x, sys.y])
7070set_x = setsym_oop (sys, sys. nn. p)
7171
7272function loss (x, (prob, sol_ref, get_vars, data, ts, set_x))
73- # new_u0, new_p = set_x(prob, 1, x)
7473 new_u0, new_p = set_x (prob, x)
7574 new_prob = remake (prob, p = new_p, u0 = new_u0)
76- new_sol = solve (new_prob, Vern9 (), abstol = 1e-10 , reltol = 1e-8 , saveat = ts)
75+ new_sol = solve (new_prob, Vern9 (), abstol = 1e-8 , reltol = 1e-8 , saveat = ts)
7776
7877 if SciMLBase. successful_retcode (new_sol)
7978 mean (abs2 .(reduce (hcat, get_vars (new_sol)) .- data))
@@ -106,30 +105,32 @@ op = OptimizationProblem(of, x0, ps)
106105# oh = []
107106
108107# plot_cb = (opt_state, loss) -> begin
108+ # opt_state.iter % 500 ≠ 0 && return false
109109# @info "step $(opt_state.iter), loss: $loss"
110110# push!(oh, opt_state)
111111# new_p = SciMLStructures.replace(Tunable(), prob.p, opt_state.u)
112112# new_prob = remake(prob, p = new_p)
113- # sol = solve(new_prob, Rodas4() )
113+ # sol = solve(new_prob, Vern9(), abstol = 1e-8, reltol = 1e-8 )
114114# display(plot(sol))
115115# false
116116# end
117117
118- res = solve (op, Adam (), maxiters = 10000 ) # , callback = plot_cb)
118+ res = solve (op, Adam (1e-3 ), maxiters = 25_000 , callback = plot_cb)
119119
120120display (res. stats)
121- @test res. objective < 1
121+ @test res. objective < 1e-4
122+
123+ u0, p = set_x (prob, res. u)
124+ res_prob = remake (prob; u0, p)
125+ res_sol = solve (res_prob, Vern9 (), abstol = 1e-8 , reltol = 1e-8 , saveat = ts)
122126
123- res_p = set_x (prob, res. u)
124- res_prob = remake (prob, p = res_p)
125- res_sol = solve (res_prob, Vern9 ())
127+ @test SciMLBase. successful_retcode (res_sol)
128+ @test mean (abs2 .(reduce (hcat, get_vars (res_sol)) .- data)) ≈ res. objective
126129
127130# using Plots
128131# plot(sol_ref, idxs = [model_true.x, model_true.y])
129132# plot!(res_sol, idxs = [sys.x, sys.y])
130133
131- @test SciMLBase. successful_retcode (res_sol)
132-
133134function lotka_ude2 ()
134135 @variables t x (t)= 3.1 y (t)= 1.5 pred (t)[1 : 2 ]
135136 @parameters α= 1.3 [tunable = false ] δ= 1.8 [tunable = false ]
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