add example for mix of flux and torch layers with diffeq; currently fails

Author: rejuvyesh

Diff for: examples/diffeqflux/simple_mix_node.jl

@@ -0,0 +1,64 @@
+using DiffEqFlux
+using OrdinaryDiffEq
+using Optimisers
+using Flux
+
+using PyCall
+using PyCallChainRules.Torch: TorchModuleWrapper, torch
+
+u0 = Float32[2.; 0.]
+datasize = 30
+tspan = (0.0f0, 1.5f0)
+
+function trueODEfunc(du,u,p,t)
+    true_A = [-0.1 2.0; -2.0 -0.1]
+    du .= ((u.^3)'true_A)'
+end
+t = range(tspan[1],tspan[2],length=datasize)
+prob = ODEProblem(trueODEfunc,u0,tspan)
+ode_data = Array(solve(prob,Tsit5(),saveat=t))
+
+torch_module = torch.nn.Sequential(
+    torch.nn.Linear(2, 50), torch.nn.Tanh(),
+    torch.nn.Linear(50, 2), torch.nn.Tanh(),
+)
+# Mix of Flux layers and Torch layers
+jlmod = Chain(Dense(2, 2, tanh), TorchModuleWrapper(torch_module), Dense(2, 2,))
+p, re = Optimisers.destructure(jlmod)
+
+dudt(u, p, t) = re(p)(u)
+prob = ODEProblem(dudt, u0, tspan)
+
+function predict_n_ode(p)
+    Array(solve(prob,Tsit5(),u0=u0,p=p,saveat=t))
+end
+  
+function loss_n_ode(p)
+    pred = predict_n_ode(p)
+    loss = sum(abs2,ode_data .- pred)
+    loss
+end
+
+loss_n_ode(p) 
+
+data = Iterators.repeated((), 1000)
+
+
+@info "before" loss_n_ode(p)
+
+function train(p;nsteps=100)
+    opt = Optimisers.ADAM(0.01)
+    state = Optimisers.setup(opt, p)
+
+    for i in 1:nsteps
+        gs, = Flux.gradient(p) do ps
+            loss_n_ode(ps)
+        end
+        state, p = Optimisers.update(state, p, gs)
+    end
+    return p
+end
+
+newp = train(p)
+
+@info "after" loss_n_ode(newp)