Surrogate and Compact Modeling: Theory for the User

Welcome to the PhD course Surrogate and compact modeling: theory for the user (code: 01TCORV). The last edition of the course took place during March 2019: the course will be inactive during academic year 2019/20.

Course description

Surrogate or black-box models are compact mathematical representations that attempt to mimic the behavior of a system without insights on its internal structure or physical governing equations. Surrogates find application in several engineering domains due to their ability to approximate the system behavior with good accuracy, often starting from limited input-output information. Therefore, they offer an effective solution for carrying out fast numerical simulation in analysis and design flows (e.g., for exploring the design space, what-if, optimization and sensitivity analyses).

Surrogate modeling bridges various approaches from the disciplines of system identification, approximation theory, model order reduction and machine learning. Identification approaches (addressed in Part I of the course) are adequate for systems known from input-output measurements, whereas approximation or reduction approaches (addressed in Part II) are most useful when “internal” and/or possibly large-scale system descriptions are available, such as semi-discretized Partial Differential Equations.

This course focuses on the presentation of the essential mathematical background and on the application of prominent methods for the generation of surrogate models of linear and nonlinear systems. An engineering approach is adopted, with emphasis on the practical user aspects. The students are guided to build surrogate models via the application of ready-to-use Matlab templates and routines. The example problems selected in the practice sessions are simple enough to lower the technical barrier and to highlight the key modeling aspects, thus showing what the users can expect from the identification framework to solve their modeling problems.

Final evaluation is carried through the assessment of individual homework projects, which will be selected based on students’ interest in their respective reference application fields.

Course topics

PART I Surrogate modeling via identification

  1. Introduction
    1. classification and characteristics of a (dynamical) system
    2. overview of the modeling resources presented in the course
    3. surrogate modeling resources (books, toolboxes, …)
  2. Identification basics
    1. overview of linear vector spaces
    2. some important aspects of system identification: parameter estimation, model complexity, …
  3. Identification of dynamical systems from t-domain responses
    1. linear systems
    2. nonlinear systems

PART II: Surrogate modeling via order reduction

  1. Background: Linear Time Invariant (LTI) Systems – definitions and properties
  2. Reducing LTI Systems: early approaches
    1. Modal analysis
    2. Rational interpolation
    3. Padé approximation and Asymptotic Waveform Evaluation
  3. Reducing LTI Systems
    1. The Projection Framework
    2. Krylov subspaces
    3. Moment matching (Arnoldi, Lanczos, PRIMA algorithms)
    4. Single and multi-point moment matching
    5. Truncated Balanced Realizations (TBR)
  4. Data-driven Model Order Reduction (frequency-domain)
    1. The Vector Fitting algorithms
    2. The Loewner Framework
  5. Preserving or enforcing stability and passivity
  6. Advanced topics: parameterized and nonlinear systems

For additional information, please contact the course instructors

Prof. Igor Stievano (igor.stievano@polito.it)
Prof. Stefano Grivet-Talocia (stefano.grivet@polito.it)