An Efficient Data-Driven Multiscale Stochastic Reduced Order Modeling Framework for Complex Systems
Changhong Mou, Nan Chen, Traian Iliescu

TL;DR
This paper introduces a novel multiscale stochastic reduced order modeling framework for complex chaotic systems, emphasizing large-scale dynamics and efficient data assimilation to improve accuracy and computational speed.
Contribution
The paper presents a new ROM approach that captures statistical features and large-scale dynamics, incorporating physics constraints and analytic data assimilation solutions, outperforming traditional methods.
Findings
Significantly better in reproducing dynamical features than G-ROM.
Efficient and systematic model calibration via explicit formulas.
Provides an analytic solution for nonlinear data assimilation.
Abstract
Suitable reduced order models (ROMs) are computationally efficient tools in characterizing key dynamical and statistical features of nature. In this paper, a systematic multiscale stochastic ROM framework is developed for complex systems with strong chaotic or turbulent behavior. The new ROMs are fundamentally different from the traditional Galerkin ROM (G-ROM) or those deterministic ROMs that aim at minimizing the path-wise errors and applying mainly to laminar systems. Here, the new ROM focuses on recovering the large-scale dynamics to the maximum extent while it also exploits cheap but effective conditional linear functions as the closure terms to capture the statistical features of the medium-scale variables and its feedback to the large scales. In addition, physics constraints are incorporated into the new ROM. One unique feature of the resulting ROM is that it facilitates an…
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Taxonomy
TopicsModel Reduction and Neural Networks · Meteorological Phenomena and Simulations · Lattice Boltzmann Simulation Studies
