CorleoneOED

CorleoneOED designs controls and measurement schedules for local parameter estimation in differential-equation models. It augments a Corleone ShootingLayer with state sensitivities and Fisher information. “Local” means information is computed at nominal physical parameter values, rather than averaged over an unknown parameter distribution.

Start with the example below, then follow a complete executable tutorial:

• Continuous Lotka–Volterra design: optimize fishing and two measurement densities.
• Multiple experiments: combine independent schedules and a global prior.
• Discrete compartmental design: allocate relaxed weights to candidate sampling events.

The formulation defines what is computed; the design guide explains parameter storage, shooting, vectorization, constraints, and priors. Numerical scope covers SVD reduction, DAE assumptions, and verified AD behavior. Exact signatures and return values live in the API reference.

A first mixed design

This example needs CorleoneOED, LuxCore, Random, and OrdinaryDiffEqTsit5. It does not need Optimization or ComponentArrays. The model is $\dot x=\theta x$ at $\theta=-2$; the nominal rate is fixed, while all measurement weights start at one.

using CorleoneOED, LuxCore, Random, OrdinaryDiffEqTsit5

problem = ODEProblem((x, p, t) -> p[1] .* x, [1.0], (0.0, 1.0), [-2.0];
    abstol=1e-10, reltol=1e-10)
design = OEDLayer(problem, Tsit5(); params=[1], measurements=(
    ContinuousMeasurement(:density, [0.0, 0.5, 1.0], (x, p, t) -> x[1]),
    DiscreteMeasurement(:sample, [0.0, 0.5, 1.0], (x, p, t) -> x[1]),
))
ps, st = LuxCore.setup(Xoshiro(1), design)
trajectory, next_st = design(nothing, ps, st)
F = fisher_information(design, trajectory)
budgets = sampling_sums(design, trajectory)
@assert size(F) == (1, 1) && only(F) > 0
@assert budgets ≈ [1.0, 3.0]
(; information=only(F), budgets)

(information = 0.0759587313963171, budgets = [1.0, 3.0])

The continuous grid makes two density intervals, not three parameter values: its endpoints are boundaries. The discrete grid specifies three actual observations, including both endpoints. Selecting params=[1] estimates information about p[1]; it does not make p[1] a tunable design variable.

For comparison, the exact information here is $(2-26e^{-4})/64 + e^{-2}/4 + e^{-4}$. The first term is continuous information; the initial discrete observation has zero state sensitivity.

reference = (2 - 26exp(-4))/64 + exp(-2)/4 + exp(-4)
@assert isapprox(only(F), reference; rtol=1e-7)
sampling_sums(design, nothing, ps, st) # the same budgets, without an ODE solve

2-element Vector{Float64}:
 1.0
 3.0

The returned trajectory retains its parameter and state containers by reference. Re-solve after changing them when you need saved states and parameter queries to represent the same experiment; see ownership and histories.

Next: solve a constrained design

The tutorials add ComponentArrays for packing, Optimization/OptimizationMOI and Ipopt for the continuous optimizer, and CairoMakie for plots. Their random seeds, solver settings, reconstruction, termination checks, and budget checks are part of the executable sources. An integer mask is demonstrated separately from the continuous relaxation.

For a checkout, follow the documentation build instructions. Scientific references and software provenance are listed separately.