Reduced Order Modeling

Reduced order modeling (ROM) and model order reduction (MOR) are techniques for reducing the computational complexity of a full-order, high-fidelity model while preserving the expected fidelity within a satisfactory error. Working with reduced order models (ROMs) can simplify analysis and control design.

Engineers use ROM-related techniques to perform system-level simulations, create virtual sensors, design control systems, optimize product designs, and build digital twin applications. MATLAB^®, Simulink^®, and add-on products let you build accurate ROMs using various computational methods.

Why Use Reduced Order Modeling?

High-fidelity third-party FEA/CAE/CFD models can take hours or even days to simulate. Performing hardware-in-the-loop testing, control design, and system-level analysis on such models can present significant computational challenges or sometimes be infeasible. Also, linearizing complex models can result in high-fidelity models containing states that do not contribute to the dynamics of interest in your application.

To address these challenges, you can replace high-fidelity component-level models with reduced order models that trade off accuracy for reduced computational complexity. The accuracy reduction is based on accuracy tolerances, frequency ranges, and other characteristics important for your application. Reduced order modeling is also useful for creating virtual sensors to estimate or predict signals of interest when measuring those signals using a physical sensor is impractical or infeasible.

You can also use reduced order modeling to create digital twins to make it more computationally efficient and suitable for periodic updates to represent the current state of the operational asset.

Reduced Order Modeling Methods

There are two main classes of techniques for building reduced order models: model based and data driven.

Model-based ROM methods rely on a mathematical or physical understanding of the underlying model. The appropriate ROM method depends on the model’s structure and scale. Some ROM techniques, such as the Craig-Bampton method in structural mechanics, are designed for specific PDE-based models. Other techniques, such as linearization, support both sparse and nonsparse models, making them versatile for different system sizes. On the other hand, balanced truncation and zero-pole truncation are better suited for nonsparse and sparse models, respectively. Learn more about available model-based ROM methods and selection.

Data-driven methods use input/output data from the original high-fidelity first-principles model to construct either a dynamic or static reduced order model that accurately represents the underlying system. To create dynamic ROM, you can use the Simulink Add-On for Reduced Order Modeling to set up design of experiments, generate input/output data, and train and evaluate suitable reduced order models using preconfigured templates that cover various ROM techniques. You can develop dynamic ROMs using an LSTM, feedforward neural nets, neural ODEs, and other deep learning techniques with Deep Learning Toolbox™. Other techniques for building dynamics ROMs include nonlinear ARX and Hammerstein-Wiener models using System Identification Toolbox™. Nonlinear ARX models can use regression functions based on machine learning algorithms available in Statistics and Machine Learning Toolbox™. To create a suitable static ROM, you can use classic machine learning models, curve fitting, lookup tables, and neural networks.

When creating model-based and data-driven reduced order models, you need to decide what sacrifices you are willing to make. For example, when creating a model-based ROM, you might need to eliminate system dynamics beyond a certain frequency in the reduced model. An extreme case of that is when the reduced order model captures only steady-state system behavior while ignoring transient dynamic effects. Creating data-driven ROMs involves sacrificing physical insights of the model; what type of ROM technique is used and what sacrifices are made depend on your particular application.