test/minibatch: use Float64 for time, state, and parameters

The minibatch test was using `Float32` for `u0`, `tspan`, and the
network parameters (via the default `Lux.setup` eltype). It is a test
of the minibatching loop, not of Float32 throughput, and the Float32
choice exposes a fragile codepath in `SciMLSensitivity`'s
`InterpolatingAdjoint` checkpoint re-solve:

  1. The sub-checkpoint forward re-solve seeds its initial `dt` with
     `abs(cpsol_t[end] - cpsol_t[end - 1])` from the previous
     re-solve.
  2. With `Float32` time, an adaptive Tsit5 step that lands one ulp
     past `interval[2]` is followed by a tiny "correction" step back
     to `interval[2]`, leaving the last two `cpsol_t` entries 1 ulp
     apart (~1.2e-7).
  3. That ulp value becomes the `dt` for the next re-solve over an
     interval ~0.052 wide. The Tsit5 controller, given that
     microscopic seed, ends up emitting a `cpsol` whose time vector
     has only the start point.
  4. On the iteration after that, `cpsol_t[end - 1]` becomes
     `cpsol_t[0]` and the test errors out with
     `BoundsError: attempt to access 1-element Vector at index [0]`.

`Float64` has ~1e-16 epsilon, so the same ulp-collision pattern
produces a `dt` far below any abstol/reltol the controller cares
about and the feedback loop never amplifies into a 1-point cpsol.
The test passes against the unmodified, registered SciMLSensitivity
v7.103.0 with the Float64 change alone, no upstream patch needed.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>

Author: ChrisRackauckas

test/minibatch.jl

@@ -24,17 +24,17 @@ function callback(state, l) #callback function to observe training
     return l < 1.0e-2
 end
 
-u0 = Float32[200.0]
+u0 = [200.0]
 datasize = 30
-tspan = (0.0f0, 1.5f0)
+tspan = (0.0, 1.5)
 
 t = range(tspan[1], tspan[2], length = datasize)
 true_prob = ODEProblem(true_sol, u0, tspan)
 ode_data = Array(solve(true_prob, Tsit5(), saveat = t))
 
 ann = Lux.Chain(Lux.Dense(1, 8, tanh), Lux.Dense(8, 1, tanh))
 pp, st = Lux.setup(rng, ann)
-pp = ComponentArray(pp)
+pp = ComponentArray{Float64}(pp)
 
 prob = ODEProblem{false}(dudt_, u0, tspan, pp)