Trajectories and reset samples

ShootingLayer returns (trajectory, next_st). A Trajectory contains saved state samples and access to the parameters used for prediction. It does not interpolate or integrate between those samples.

Saved grids and both sides of a reset

Continuous handoffs appear once in trajectory.t. A scheduled interior reset retains both the incoming endpoint and outgoing start, even if their values are equal. reset_indices points to the outgoing samples. The immediately preceding samples contain the incoming values.

using Corleone, LuxCore, OrdinaryDiffEqTsit5, Random

problem = ODEProblem((x, p, t) -> [p[1]], [0.0], (0.0, 3.0), [1.0])
layer = ShootingLayer(problem, Tsit5(),
    Tunable(1; kind = Val(:variable), default = [0.5, 1.5]) => [1.0, 2.0],
    Constant(1) => nothing)
ps, st = LuxCore.setup(MersenneTwister(42), layer)
trajectory, next_st = layer(nothing, ps, st)
(; times = trajectory.t, outgoing_indices = trajectory.reset_indices)

(times = [0.0, 1.0, 1.0, 2.0, 2.0, 3.0], outgoing_indices = [3, 5])

The saved times are [0, 1, 1, 2, 2, 3]. The two states at time 1 are the incoming value of approximately 1 and the assigned value 0.5:

k = first(trajectory.reset_indices)
round.([trajectory.u[k - 1][1], trajectory.u[k][1]]; digits = 6)

2-element Vector{Float64}:
 1.0
 0.5

trajectory.residuals stores state matching residual vectors per integration segment start. Their entries are compressed to the active tunable variables; they are not a matrix indexed by every state and saved time. Use shooting_constraints for the complete optimizer residual vector, including any inserted-parameter equalities:

residuals = shooting_constraints(trajectory)
round.(residuals; digits = 6)

2-element Vector{Float64}:
 -0.5
  0.0

The shooting formulation defines the residual sign. The plotting API draws reset segments without a continuous line across each jump and can show variable matching residuals.

Symbolic state and parameter queries

For an ordinary numerical problem, the generated state and parameter names are :u₁, :u₂, … and :p₁, :p₂, …. Problems with a symbolic container retain its original symbols and indices.

The last query is from SymbolicIndexingInterface. Parameters are piecewise constant and right-continuous, and their history grid can differ from the state sample grid. Do not combine the two histories by assuming matching column indices.

Timed numerical expressions such as :(u₁(1.0)) select the post-reset state by default. A callback can inspect either saved side explicitly. Bare signal names inside expressions denote their full series on the saved grid; a plain Symbol objective selector denotes the terminal value. See expression evaluation.

Internal solver saving options, including saveat, can add state samples. Integration stops need not each be saved. Read the actual trajectory.t and trajectory.u together rather than reconstructing a saved grid from control switches or segment endpoints.

Ownership and differentiation

The trajectory retains the layer, supplied parameters, and returned Lux state by reference. Its numerical state arrays are shared with the segment solutions. Parameter histories are evaluated on demand through the retained parameter layer; there is no detached parameter-history copy.

Consequently, changing a parameter buffer changes later parameter queries, but does not recompute saved state values. Run the layer again for a trajectory consistent with changed parameters. Avoid mutating retained numerical data between a forward evaluation and its pullback.

Symbolic metadata is shared through symbolic_container(trajectory), which returns the layer's ControlSymbolCache. Query control and quadrature subsets on that wrapper; see symbolic bookkeeping.

Differentiation is validated for numerical values on fixed time grids. It does not establish derivatives through changing reset times, grid topology, or event schedules. Backend and sensitivity requirements are documented in automatic differentiation.