# What Is 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 (HIL) 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. Some ROM techniques such as the Craig-Bampton method in structural mechanics are designed for specific PDE-based models. In linear system analysis, linearization, linear parameter-varying models, and techniques such as balanced truncation and pole-zero simplification are often used to simplify the system model.

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, Simulink Add-On for Reduced Order Modeling can help set up design of experiments (DOE), generate input/output data, and train and evaluate suitable reduced order models using preconfigured templates that cover various ROM techniques. Dynamic ROMs can be developed using deep learning techniques such as an LSTM, feedforward neural nets, and neural ODEs that are available 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 static ROM, curve fitting, Lookup Tables, and neural networks can be used to create a suitable model.

When creating model-based and data-driven reduced order models, engineers need to decide what sacrifices they are willing to make. For example, when creating a model-based ROM an engineer 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. Engineers sacrifice physical insights of the model when creating data-driven ROMs. What type of ROM technique is used and what sacrifices are made depends on a particular application.

## Software Reference

#### Data-Driven Reduced Order Modeling

See also: Simscape Multibody, Control System Toolbox, Simulink Control Design, Partial Differential Equation Toolbox, Deep Learning Toolbox, Statistics and Machine Learning Toolbox, System Identification Toolbox, long short-term memory (LSTM) examples and applications, support vector machine (SVM)