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2 results

  • 13 - Data-Driven Methods and Reduced-Order Modeling

  • from Part III - Least Squares and Optimization
  • Kevin W. Cassel, Illinois Institute of Technology
  • Book:
    Matrix, Numerical, and Optimization Methods in Science and Engineering
    Published online:
    18 February 2021
    Print publication:
    04 March 2021, pp 642-698

  • Summary

    Reduced-order modeling is an active area of research by which simplified models of experimental or numerical data can be generated that are faithful to the behavior of the unerlying system.These methods are based on Galerkin projection, which is motivated by variational methods, or some other method of weighted residuals and allow for the projection of any governing differential equation onto an appropriate set of basis vectors or functions.These basis vectors or functions can be obtained using proper-orthogonal decomposition (POD) or one of its extensions or alternatives.Galerkin projection and POD are applied to continuous and discrete data sets.

Matrix, Numerical, and Optimization Methods in Science and Engineering
  • Kevin W. Cassel
  • Published online:
    18 February 2021
    Print publication:
    04 March 2021
  • Address vector and matrix methods necessary in numerical methods and optimization of linear systems in engineering with this unified text. Treats the mathematical models that describe and predict the evolution of our processes and systems, and the numerical methods required to obtain approximate solutions. Explores the dynamical systems theory used to describe and characterize system behaviour, alongside the techniques used to optimize their performance. Integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. Consolidating, generalizing, and unifying these topics into a single coherent subject, this practical resource is suitable for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.