# What Is Reduced Order Modeling?

Reduced order modeling (ROM) and model order reduction (MOR) are techniques for reducing the computational complexity or storage requirement of a computer model, while preserving the expected fidelity within a controlled error. Working with surrogate models can simplify analysis and control design.

Scientists and engineers use ROM techniques to create system-level simulations, design control systems, optimize product designs, and build digital twin applications. MATLAB®, Simulink®, and add-on products let you build accurate ROMs using various reduced order modeling methods.

## Why Use Reduced Order Modeling?

Large-scale, high-fidelity nonlinear models can take hours or even days to simulate. System analysis and design can require thousands or hundreds of thousands of simulations, presenting a significant computational challenge. Also, linearizing complex models can result in high-fidelity models containing states that do not contribute to the dynamics of interest in your application.

In these cases, you can use reduced order modeling methods to significantly speed up simulations and analysis of higher-order large-scale systems. You can achieve this speed up by trading off the model accuracy for reduced computational complexity. The accuracy reduction is based on frequency ranges, accuracy tolerances, and other characteristics important for your application. Reduced order modeling is also useful for combining multiple complex component-level simulation models into system-level simulations used for control analysis and design.

You can also use reduced order modeling to create digital twins to represent the current state of the operational asset, or to run real-time simulations of complex physical models for testing on hardware.

## Reduced Order Modeling Methods

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

Model-based methods rely on mathematical or physical understanding of the underlying model. Some of these 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 a ROM that accurately represents the underlying system. Data-driven ROMs can be either static or dynamic models. Techniques such as curve fitting and lookup tables are useful for creating static ROMs. Dynamic ROMs can be developed using deep learning techniques such as LSTM, feedforward neural nets, and neural ODEs, which 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 function based on machine learning algorithm available in Statistics and Machine Learning Toolbox.

When creating model-based and data-driven reduced order models, engineers need to decide what trade-offs they are willing to make to speed up a model. 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 is when the reduced order model captures only steady-state system behavior. When creating data-driven ROMs, engineers sacrifice physical insights of the model. The most suitable type of ROM technique depends on the application.

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, AI with Model-Based Design, Reduced Order Modeling