Analytical Confidence Boundaries for Non-Gaussian Uncertainty in Perturbed Spacecraft Dynamics

What the math gives to ML

The paper provides a constructive method for propagating non-Gaussian uncertainty by extracting third- and fourth-order moments analytically, avoiding Monte Carlo and dense tensor contractions. Its most transferable asset is the use of directional moment projections, such as E[u^2 v] and E[u^4], which directly encode skewness, bending, and tail elongation in a task-relevant local frame. In neural networks, the same mechanism can produce cheap non-Gaussian predictive uncertainty summaries from a polynomial, sigma-point, or local Taylor representation of the network output. A strong first application is an uncertainty-aware predictor whose confidence region is parameterized by directional skewness and kurtosis rather than forced to be Gaussian.