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

TL;DR

This paper presents a non-intrusive method for learning non-Markovian reduced models from partially observed high-dimensional dynamical systems, improving prediction accuracy and efficiency with limited observed data.

Contribution

It introduces a data sampling scheme and a regression formulation to identify non-Markovian terms, enabling accurate reduced models from sparse observations.

Findings

Non-Markovian models outperform Markovian models in predictive accuracy.

The approach recovers non-Markovian terms comparable to intrusive methods.

Effective with only 20% observed components, matching traditional models with 99%.

Abstract

This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to the partially observed states by constructing non-Markovian reduced models that make future-state predictions based on a history of reduced states, in contrast to traditional Markovian reduced models that rely on the current reduced state alone to predict the next state. The core contributions of this work are a data sampling scheme to sample partially observed states from high-dimensional dynamical systems and a formulation of a regression problem to fit the non-Markovian reduced terms to the sampled states. Under certain conditions, the proposed approach recovers from data the very same non-Markovian terms that one obtains with intrusive methods that require the governing equations and discrete operators of the high-dimensional dynamical system. Numerical results demonstrate that the proposed approach leads to non-Markovian reduced models that are predictive far beyond the training regime. Additionally, in the numerical experiments, the proposed approach learns non-Markovian reduced models from trajectories with only 20% observed state components that are about as accurate as traditional Markovian reduced models fitted to trajectories with 99% observed components.