Stochastic latent twins learn distributions of future states in scientific systems
Stochastic Latent Twins: Learning Stochastic Solution Operators
Computational Engineering, Finance, and Science
Summary
When predicting how things change in the future, it's important to understand the range of possible outcomes, not just one answer. The authors present a new approach called Stochastic Latent Twins that separates the way a system is represented from how its uncertainties evolve over time. This method allows predictions about future states and their uncertainties directly without stepping through each moment in time. It also ensures the predictions respect physical laws by design and works well on various complex scientific problems.
What this means in practice
- •For data assimilation teams: Use the model to improve predictions of physical systems by directly capturing uncertainty in observed state transitions without recursive simulation.
- •For industrial control engineers: Incorporate stochastic latent twins for forward and backward prediction of system dynamics with guaranteed physical conservation in automated control settings.
Authors
Matthias Chung, Jack Michael Solomon, Deepanshu Verma
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.