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The revolution in digital simulation: why model reduction is the key to the future?
With the continuous advancement of science and technology, digital simulation plays an increasingly important role in various fields. However, the excessive complexity and large size of many modern mathematical models make their application in numerical simulations a challenge. In this context, model reduction technology emerged as the times require, and is gradually regarded as a key in the digital simulation revolution.
Basic concepts of model reduction
Model reduction, or model simplification, aims to reduce the computational complexity of mathematical models, especially in the simulation of large-scale dynamic systems and control systems. The core of this technology is to derive an approximate model called a "reduced order model" by reducing the state space dimensions or degrees of freedom associated with the model. This is especially important for scenarios that require a large number of simulations.
In many practical applications, a complete full-scale model cannot be realized due to limitations in computing resources or simulation requirements, which makes reduced-order models crucial.
Requirements for model reduction
In practical applications, the reduced-order model needs to meet the following requirements: First, the reduced-order model needs to maintain a small approximation error based on the full model; second, it must retain the properties and characteristics of the full model, such as Stability and passivity; finally, the techniques for model order reduction must be computationally efficient and robust.
Current order reduction technology
Current model reduction methods can be roughly divided into five categories, including:
- Appropriate orthogonal decomposition method
- Base reduction method
- Balanced Method
- Simplified physics or operation-based order reduction methods
- Nonlinear manifold method
Among them, the simplified physical method is similar to the traditional mathematical modeling method, building a simpler description of the system based on assumptions and simplifications. The remaining methods belong to projection-based order reduction, which rely on the projection of model equations or solutions to reduce them to smaller dimensions.
Application fields
The application scope of model reduction is very wide, including electronics, fluid mechanics, structural mechanics and many other fields. Problems in fluid mechanics often involve large-scale dynamic systems. In these problems, computational fluid dynamics (CFD) models often need to solve the Navier-Stokes equations. The degrees of freedom of these models often reach hundreds of thousands or even millions. .
For example, when modeling the flow field of an F16 fighter jet, the degree of freedom of the model was reduced from 2.1 million to only 90 degrees of freedom during the calculation process. This order reduction undoubtedly greatly improved the efficiency of the simulation.
The technology of model reduction is also applied in hemodynamics to help study the dynamic behavior of blood flowing in the vascular system, thereby promoting progress in the biomedical field.
Implementation of order reduction technology
There are currently a variety of implementation tools and libraries for order reduction technology on the market, such as RBmatlab, pyMOR, and KerMor. These tools not only meet the traditional order reduction needs, but also can reduce the order of nonlinear dynamic systems to obtain rapid results in design development and system simulation.
The emergence of these tools demonstrates the potential for continuous development of model reduction technology and its future application prospects.
Future Outlook
The future prospects of model reduction technology are exciting. With the enhancement of computing power and the advancement of data science, more and more complex systems will benefit from this technology. We see not only innovation in engineering, but also the potential for interdisciplinary collaboration and research. In the future, how to give full play to the advantages of model reduction technology will be an important challenge that scientists and engineers need to face.
In the world of digital simulation, can model reduction become one of the key technologies for exploring the unknown, and push us to further decipher the complex laws of natural phenomena?
