Module uncertainty 

Uncertainty propagation in ODE solutions.

This module provides tools for propagating parameter uncertainties through ODE solutions. Given an ODE system:

dy/dt = f(t, y, p),  y(t0) = y0

where the parameters p have associated uncertainties sigma_p, this module computes uncertainty bands on the solution trajectory y(t).

Two modes are supported:

• Trajectory (GUM): First-order Taylor propagation via forward sensitivity equations. At each time t: sigma_y_j(t)^2 = sum_k (dy_j/dp_k)^2 * sigma_p_k^2

• Monte Carlo: Sample parameters from distributions, solve N times, compute mean and standard deviation of the ensemble.

Composability

The main entry point solve_with_uncertainty is generic over the solver:

solve_with_uncertainty::<DoPri5, f64>(...) // explicit solver
solve_with_uncertainty::<Radau5, f64>(...) // stiff solver
solve_with_uncertainty::<Tsit5, f64>(...)  // explicit, FSAL

Any solver implementing the Solver<S> trait works without modification. For automatic solver selection on a single problem (without uncertainty quantification), see crate::auto_solve / crate::auto_solve_with_hints.

Author: Moussa Leblouba Date: 9 February 2026 Modified: 2 May 2026

Structs

UncertainParam

A parameter with uncertainty.

UncertainSolverResult

ODE result with uncertainty bands.

Enums

UncertaintyMode

Uncertainty propagation mode.

Functions

solve_monte_carlo

Solve an ODE with uncertainty propagation using Monte Carlo sampling.

solve_trajectory

Solve an ODE with uncertainty propagation using first-order Taylor (GUM) via forward sensitivity equations.

solve_with_uncertainty

Solve an ODE with uncertainty propagation.