Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories

This work introduces a non-intrusive model reduction approach for learning\nreduced models from partially observed state trajectories of high-dimensional\ndynamical systems. The proposed approach compensates for the loss of\ninformation due to the partially observed states by constructing non-Markovian\nreduced models that make future-state predictions based on a history of reduced\nstates, in contrast to traditional Markovian reduced models that rely on the\ncurrent reduced state alone to predict the next state. The core contributions\nof this work are a data sampling scheme to sample partially observed states\nfrom high-dimensional dynamical systems and a formulation of a regression\nproblem to fit the non-Markovian reduced terms to the sampled states. Under\ncertain conditions, the proposed approach recovers from data the very same\nnon-Markovian terms that one obtains with intrusive methods that require the\ngoverning equations and discrete operators of the high-dimensional dynamical\nsystem. Numerical results demonstrate that the proposed approach leads to\nnon-Markovian reduced models that are predictive far beyond the training\nregime. Additionally, in the numerical experiments, the proposed approach\nlearns non-Markovian reduced models from trajectories with only 20% observed\nstate components that are about as accurate as traditional Markovian reduced\nmodels fitted to trajectories with 99% observed components.\n