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

2025-08-15

AI Summary

Learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems remains challenging, particularly when preserving physical consistency and achieving computational efficiency. Method: This paper proposes a nested Operator Inference framework that explicitly encodes modal hierarchy within the reduced space. It iteratively generates high-fidelity initial guesses with theoretical error bounds and prioritizes optimization of nonlinear interactions among dominant modes. The approach integrates data-driven modeling, hierarchical modal analysis, and parametric approximation, enabling dynamic basis updates and warm-start adaptive reconstruction. Contribution/Results: To our knowledge, this is the first method to explicitly prioritize optimization of dominant-mode interactions. Numerical experiments demonstrate a fourfold reduction in prediction error over standard approaches for a heat conduction problem. For a large-scale Greenland Ice Sheet model, it achieves an average prediction error of 3% and computational speedup exceeding 19,000×.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Develops adaptive data-driven reduced-order models from high-dimensional systems
• Improves accuracy via nested hierarchy and iterative initial guesses
• Enables dynamic updates for large-scale parameterized physics applications

Innovation

• Nested Operator Inference for adaptive ROM learning
• Warm-starting from previously learned models
• Hierarchical reduced space for error minimization