Block-structured Operator Inference for coupled multiphysics model reduction

2025-11-07

AI Summary

Addressing the challenge of simultaneously preserving physical structure, achieving dimensionality reduction, and enabling modular regularization in reduced-order modeling (ROM) of multiphysics coupled systems, this paper proposes a block-structured operator inference (BSOI) method. BSOI explicitly encodes the dynamical structure of individual physical components and their coupling terms, rigorously maintaining system stability and second-order differential form. It reduces learning complexity via a block-diagonal plus coupling-term decomposition and supports physics-informed, module-specific regularization. Built upon a non-intrusive framework, it integrates structured differential equation modeling, data-driven parameter estimation, and joint optimization. Evaluated on the AGARD 445.6 wing aeroelastic benchmark, the BSOI-ROM achieves accuracy comparable to the full-order model across subsonic and supersonic regimes, while delivering an average 20% speedup in online prediction time.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Structured Learning
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the structure of the coupling terms. Once the multiphysics structure is specified, the reduced-order model is learned from snapshot data following the nonintrusive Operator Inference methodology. In addition to preserving physical system structure, which in turn permits preservation of system properties such as stability and second-order structure, the block-structured approach has the advantages of reducing the overall dimensionality of the learning problem and admitting tailored regularization for each physics component. The numerical advantages of the block-structured formulation over a monolithic Operator Inference formulation are demonstrated for aeroelastic analysis, which couples aerodynamic and structural models. For the benchmark test case of the AGARD 445.6 wing, block-structured Operator Inference provides an average 20% online prediction speedup over monolithic Operator Inference across subsonic and supersonic flow conditions in both the stable and fluttering parameter regimes while preserving the accuracy achieved with monolithic Operator Inference.

Problem

• Learning structured reduced-order models for coupled multiphysics systems
• Preserving physical system structure and properties during model reduction
• Improving computational efficiency over monolithic approaches in aeroelastic analysis

Innovation

• Block-structured formulation for multiphysics model reduction
• Specifies governing equations and coupling terms structure
• Learns reduced-order models nonintrusively from snapshot data