Nested Operator Inference for Adaptive Data-Driven Learning of Reduced-order Models
This incremental improvement addresses the need for more accurate and efficient reduced-order models in computational physics, particularly for large-scale dynamical systems like ice sheet modeling.
The paper tackled the problem of learning physics-informed reduced-order models from snapshot data by introducing a nested Operator Inference approach that prioritizes dominant modes, achieving a four times smaller error than standard methods on a heat conduction problem and an average 3% error with over 19,000 times speed-up on a Greenland ice sheet model.
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.