Stochastic Latent Twins: Learning Stochastic Solution Operators
Abstract
Scientific prediction under uncertainty requires more than a single future state: it requires the distribution of possible outcomes. We show that this distribution-valued evolution can be learned directly as a stochastic solution operator between arbitrary source and target times. We introduce Stochastic Latent Twins, which represent the physical state through a deterministic encoder-decoder while placing stochasticity entirely in a probability-valued latent evolution map. This separation makes the stochastic transition law independent of the state representation and enables direct probabilistic prediction without recursive time stepping. We establish an end-to-end Wasserstein approximation theory that separates representation and latent-transition errors, derive stability guarantees, and develop a distributional theory of physics conformity with latent-to-physical transfer bounds and conformity by construction. The resulting framework can be learned directly from observed transitions and supports forward prediction, backward conditional evolution, one-shot generation, and physics-conforming stochastic dynamics within the same formulation. Numerical experiments ranging from linear and non-Gaussian SDEs to stochastic Lorenz dynamics, generative modeling, a stochastic Hamiltonian system, and a two-dimensional stochastic Burgers equation verify the theory, expose the distinct roles of state representation and transition-family expressivity, compare favorably with recent stochastic and one-step generative methods, and demonstrate exact physical conservation by construction. More broadly, Stochastic Latent Twins provide a step toward scientific surrogates that represent not only the evolution of a system, but also its uncertainty and physical structure, opening new opportunities across uncertainty quantification, data assimilation, inverse problems, control, and digital twins.
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BibTeX
@misc{chung2026stochastic,
title = {{Stochastic Latent Twins: Learning Stochastic Solution Operators}},
author = {Matthias Chung and Jack Michael Solomon and Deepanshu Verma},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21084},
eprint = {2610.21084},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21084},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Stochastic Latent Twins: Learning Stochastic Solution Operators
AU - Matthias Chung
AU - Jack Michael Solomon
AU - Deepanshu Verma
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21084
UR - https://arxiv.org/abs/2610.21084
AB - Scientific prediction under uncertainty requires more than a single future state: it requires the distribution of possible outcomes. We show that this distribution-valued evolution can be learned directly as a stochastic solution operator between arbitrary source and target times. We introduce Stochastic Latent Twins, which represent the physical state through a deterministic encoder-decoder while placing stochasticity entirely in a probability-valued latent evolution map. This separation makes the stochastic transition law independent of the state representation and enables direct probabilistic prediction without recursive time stepping. We establish an end-to-end Wasserstein approximation theory that separates representation and latent-transition errors, derive stability guarantees, and develop a distributional theory of physics conformity with latent-to-physical transfer bounds and conformity by construction. The resulting framework can be learned directly from observed transitions and supports forward prediction, backward conditional evolution, one-shot generation, and physics-conforming stochastic dynamics within the same formulation. Numerical experiments ranging from linear and non-Gaussian SDEs to stochastic Lorenz dynamics, generative modeling, a stochastic Hamiltonian system, and a two-dimensional stochastic Burgers equation verify the theory, expose the distinct roles of state representation and transition-family expressivity, compare favorably with recent stochastic and one-step generative methods, and demonstrate exact physical conservation by construction. More broadly, Stochastic Latent Twins provide a step toward scientific surrogates that represent not only the evolution of a system, but also its uncertainty and physical structure, opening new opportunities across uncertainty quantification, data assimilation, inverse problems, control, and digital twins.
ER -