Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Models

TL;DR

This paper introduces a nested Operator Inference method that enhances data-driven reduced-order modeling by exploiting hierarchical structures, resulting in more accurate and efficient models for complex dynamical systems.

Contribution

The paper proposes a novel nested OpInf algorithm that iteratively constructs better initial guesses, improving accuracy and enabling model updates in reduced-order modeling.

Findings

Nested OpInf achieves four times smaller error than standard OpInf.

The method learns a ROM with 3% average error for Greenland ice sheet model.

It provides a computational speed-up factor above 19,000.

Abstract

This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy within the reduced space to iteratively construct initial guesses for the OpInf learning problem that prioritize the interactions of the dominant modes. The initial guess computed for any target reduced dimension corresponds to a ROM with provably smaller or equal snapshot reconstruction error than with standard OpInf. Moreover, our nested OpInf algorithm can be warm-started from previously learned models, enabling versatile application scenarios involving dynamic basis and model form updates. We demonstrate the performance of our algorithm on a cubic heat conduction problem, with nested OpInf achieving a four times smaller error than standard OpInf at a comparable offline time. Further, we apply nested OpInf to a large-scale, parameterized model of the Greenland ice sheet where, despite model form approximation errors, it learns a ROM with, on average, 3% error and computational speed-up factor above 19,000.