mixle.doe.propagate module

Forward uncertainty propagation: push an input distribution through a model to output statistics.

Given input uncertainty (a Gaussian or a sampler) and a model f, report the induced uncertainty on the output – mean, standard deviation, and quantiles. Monte Carlo is general; the unscented transform propagates the first two moments with 2d+1 deterministic sigma points (exact for a linear model, a good cheap approximation for mild nonlinearity). The back half of the UQ loop, after sensitivity.

propagate(func, mean, cov=None, *, n=10000, method='montecarlo', quantiles=(0.05, 0.5, 0.95), seed=0)[source]

Propagate a Gaussian input N(mean, cov) through func to output statistics.

Parameters:

  • func (Callable[[ndarray], ndarray]) – a vectorized model f(X) -> y mapping (m, d) inputs to (m,) (or (m, k)) outputs.

  • mean (ndarray) – length-d input mean. cov: (d, d) input covariance (defaults to identity).

  • n (int) – Monte Carlo sample size (ignored by the unscented method).

  • method (str) – 'montecarlo' (sample + summarize, gives quantiles) or 'unscented' (sigma-point moment propagation, mean + std only). Looked up through the propagator registry.

  • quantiles (tuple[float, ...]) – output quantiles to report (Monte Carlo only).

  • cov (ndarray | None)

  • seed (int)

Returns:

{'mean', 'std', 'quantiles' (mc only), 'samples' (mc only)}.

Return type:

dict[str, Any]

register_propagator(name)[source]

Decorator registering a propagation method under name for propagate().

The decorated callable receives (func, mean, cov, *, n, quantiles, seed) (mean/cov already coerced to float arrays) and returns the output-statistics dict.

Parameters:

name (str)

Return type:

Callable[[Callable[[…], dict[str, Any]]], Callable[[…], dict[str, Any]]]

unscented_transform(func, mean, cov, *, alpha=1e-3, beta=2.0, kappa=0.0)[source]

Propagate (mean, cov) through func with the unscented (sigma-point) transform.

Returns the output (mean, covariance). Exact for an affine func; for a nonlinear one it captures the mean and covariance to second order with only 2d+1 evaluations.

Parameters:
Return type:

tuple[ndarray, ndarray]