# Reduced Order Modeling

## Reduce the computational complexity of your models for simplified yet accurate surrogates

Reduced order modeling (ROM), or model order reduction (MOR), is a technique that can reduce the computational complexity or storage requirement of a computer model, while preserving the expected fidelity with controlled error. Working with lower-order surrogate models can simplify analysis and control design. Simpler models are also easier to understand and manipulate than high-order models.

Scientists and engineers use ROM-related techniques to create system-level simulations, design control systems, optimize product designs, and build digital twin applications.

### Why Use Reduced Order Modeling?

High-fidelity models can involve large-scale, nonlinear dynamical system behavior whose simulations can take hours or even days. Some applications require the model to be simulated thousands of times. Running many high-fidelity simulations presents a significant computational challenge.

Also, high-fidelity models obtained by linearizing complex models, interconnecting model elements, or other sources can contain states that do not contribute much to the dynamics of particular interest to your application.

### Reduced Order Modeling Methods

MATLAB® and Simulink® support reduced order modeling techniques. Traditional reduced order modeling methods rely on 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 and others such as proper orthogonal decomposition (POD) are suitable for ODE/DAE-based models.

Many techniques such as singular value decomposition (SVD), eigenvalue decomposition (EVD), principal  component analysis (PCA)lookup tables, interpolation, and curve fitting are also useful as part of model order reduction.  In the domain of control design, techniques such as balanced truncation and pole-zero simplification are often used to simplify the system model.

In the field of artificial intelligence, properly designed and trained AI models often use reduced order models (ROM) for systems in the ODE/DAE modeling space.

See also: Simscape Multibody™, Control System Toolbox™, Simulink Control Design™, Partial Differential Equation Toolbox™, Deep Learning Toolbox™, Statistics and Machine Learning Toolbox™