Reduced Order Modeling Based on Neural Networks

In a modern hypercompetitive world, time is the most valuable asset, thus the ability to cut through complexity and find solutions quickly is the key to success. Reduced Order Modeling (ROM) can help engineers and scientists to reduce the computation required without compromising the accuracy of the original physical model. Moreover, they can also use ROM instead of an actual physical system for workflows that require heavy computations, for example, design exploration.

What is Reduced Order Modeling?

Reduced Order Modeling and Model Order Reduction (MOR) are advanced techniques that allow scientists and engineers to tackle the computational and storage challenges associated with complex computer models.  These techniques enable engineers and researchers to tackle large-scale models efficiently by constructing reduced-dimensional representations that capture the essential behavior of the original system. These reduced models require fewer computational resources and storage, making them more computationally tractable without compromising the accuracy of the original physical model. The surrogate models obtained through ROM provide an efficient way for investigating the system’s dynamics, running simulations, and designing control systems. Engineers and researchers can use these techniques to obtain valuable insights and make informed decisions without feeling overwhelmed by the complexity of a full-scale model.

 

Use ROM to:

• Facilitate faster system-level desktop simulations by replacing detailed models with reduced order models
• Build a virtual sensor for measuring internal signals of interest within a complex system
• Build digital twins.

 

MATLAB and Simulink for Reduced Order Modeling

MATLAB, Simulink, and other MathWorks® products enable scientists and engineers to use various reduced order modeling methods to build accurate reduced order models (ROMs).

Reduced Order Modeling Methods

Here are some commonly used techniques for creating ROMs, along with the relevant tools you can utilize to implement them:

Data-Driven Method

A data-driven method for ROMs relies on collected input-output data from a high-fidelity first-principles model. These types of ROMs can be either static or dynamic. 

Dynamic ROMs

To develop dynamic ROMs, engineers can use the Deep Learning Toolbox to take the aforementioned input-output data and train a model using deep learning techniques such as LSTM, neural ODEs, and feedforward neural nets. Engineers can also use the Statistics and Machine Learning Toolbox or System Identification Toolbox to develop dynamic ROMs using techniques such as a nonlinear ARX.

Static ROMs

To develop static ROMs, engineers can use techniques such as curve fitting and lookup tables.

Model-Based Method

A model-based method for ROMs leverages a mathematical or physical understanding of the system model to simplify and construct reduced-order representations. Engineers can build ROMs using these techniques and models: 

• Craig-Bampton Method
• Linearization
• Linear Parameter-Varying (LPV) Models
• Balanced Truncation techniques
• Pole-Zero Simplification techniques.

This video explains how to use machine learning for run-time optimization and build an LSTM-ROM model.

Featured products

All products mentioned in this webinar are developed by MathWorks.

• MATLAB
• Simulink
• Deep Learning Toolbox
• Statistics and Machine Learning Toolbox
• System Identification Toolbox

Learn more

If you would like to take your education to the next level, check out our Training Services. But if you don’t have time to learn all the ins and outs of MATLAB software, you should still be aware of world-changing trends. Reach out to our Consulting team and see how you can benefit from Reduced Order Modeling.