Uncertainty Quantification

The low-rank covariance factorization B^T B automatically enforces positive semidefiniteness without eigenvalue clipping or Gram-Schmidt steps. The Gaussian residual law assumed by MNO cannot represent heavy tails, jumps, or multimodal terminal distributions. MNO's diagonal variance consistency loss does not penalize off-diagonal covariance entries, resulting in worse full-covariance recovery than Neural SPDE despite better mean accuracy. MNO fills a niche for one-shot terminal marginal moments at operator speed that existing approaches cannot fill without significant computational overhead.