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 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 | Data Driven | |
|---|---|---|
| Static ROM | Dynamic ROM | |
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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 Reduced Order Modeler for MATLAB 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 dynamic 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.
Examples and How To
Model-Based Reduced Order Modeling
Data-Driven Reduced Order Modeling
Software Reference
Model-Based Reduced Order Modeling
Data-Driven Reduced Order Modeling
Reduced Order Modeling FAQs
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.
ROM enables faster simulations for hardware-in-the-loop testing, control design, virtual-sensor modeling, design optimization, and system-level analysis by replacing high-fidelity models that can take hours or days to simulate with computationally efficient surrogates that maintain acceptable accuracy.
Creating ROMs involves trading off accuracy for reduced computational complexity based on accuracy tolerances, frequency ranges, and other application-specific characteristics, such as eliminating system dynamics beyond certain frequencies or sacrificing physical insights in data-driven approaches.
The two main classes are model-based methods (such as Craig-Bampton, linearization, balanced truncation, and zero-pole truncation) and data-driven methods (including neural networks, LSTM, curve fitting, lookup tables, nonlinear ARX, and Hammerstein-Wiener models).
Model-based ROM methods rely on a mathematical or physical understanding of the underlying model, with the appropriate technique depending on the model’s structure and scale, such as balanced truncation for nonsparse models or zero-pole truncation for sparse models.
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.
The Reduced Order Modeler for MATLAB add-on provides an app for creating AI-based reduced order models of subsystems modeled in Simulink, including full-order, high-fidelity third-party simulation models. The app allows you to set up the design of experiments, generate input-output data, train and compare AI-based ROMs using preconfigured templates, and export reduced order models to Simulink for system-level simulation, control design, and HIL testing.
Yes, you can use the Reduced Order Modeler app to create AI-based ROMs of full-order high-fidelity models developed in different software by importing those models as functional mock-up units (FMUs) or as S-functions into Simulink.
Yes, you can deploy ROMs to a variety of edge devices through automatic code generation with Embedded Coder.
Yes, you can export ROMs as FMUs (with Simulink Compiler) for use outside of MATLAB and Simulink.
See also: Simscape Multibody, Control System Toolbox, Simulink Control Design, Partial Differential Equation Toolbox, LSTM examples and applications, support vector machine (SVM), physics-informed neural network
Reduced Order Modeler for MATLAB
Interactively set up the design of experiments, generate input-output data, and train AI models using pre-configured templates with Reduced Order Modeler for MATLAB.
