Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization

ArXi:2605.15806v1 Announce Type: new Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends. Recovering this structure typically requires Monte Carlo rollouts or grafted generative models, both of which surrender the one-shot efficiency and resolution invariance that define the operator paradigm.