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Stable by Construction: Variational Latent Markov Operators for Long-Horizon PDE Prediction

arXiv · AI, language, vision and robotics · article · Sep 15, 2026 · UTC

Neural PDE solvers provide efficient surrogates for time-dependent physical systems, but autoregressive prediction over long horizons remains challenging because local errors can induce distribution shift and accumulate under recursive deployment. We develop a variational approach to this problem by introducing latent Markov dynamics in which physical states are represented by latent distributions and evolved through probabilistic transitions. The framework is formulated directly on function spaces and specialized to functional Gaussian models, where structured latent perturbations induce a sp

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