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Given (small amounts of) time-series' data from a high-dimensional,fine-grained, multiscale dynamical system, we propose a generative frameworkfor learning an effective, lower-dimensional, coarse-grained dynamical modelthat is predictive of the fine-grained system's long-term evolution but also ofits behavior under different initial conditions. We target fine-grained modelsas they arise in physical applications (e.g. molecular dynamics, agent-basedmodels), the dynamics of which are strongly non-stationary but their transitionto equilibrium is governed by unknown slow processes which are largelyinaccessible by brute-force simulations. Approaches based on domain knowledgeheavily rely on physical insight in identifying temporally slow features andfail to enforce the long-term stability of the learned dynamics. On the otherhand, purely statistical frameworks lack interpretability and rely on largeamounts of expensive simulation data (long and multiple trajectories) as theycannot infuse domain knowledge. The generative framework proposed achieves theaforementioned desiderata by employing a flexible prior on the complex planefor the latent, slow processes, and an intermediate layer of physics-motivatedlatent variables that reduces reliance on data and imbues inductive bias. Incontrast to existing schemes, it does not require the a priori definition ofprojection operators from the fine-grained description and addressessimultaneously the tasks of dimensionality reduction and model estimation. Wedemonstrate its efficacy and accuracy in multiscale physical systems ofparticle dynamics where probabilistic, long-term predictions of phenomena notcontained in the training data are produced.

Physics-aware, probabilistic model order reduction with guaranteed stability