Projection-based model reduction of dynamical systems using space–time subspace and machine learning

Chi Hoang, Kenny Chowdhary, Kookjin Lee, Jaideep Ray

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and displacement fields. The proposed methodology develops a low-dimensional parametrization of these quantities of interest using space–time bases combined with machine learning methods. In particular, the space–time solutions are sought in a low-dimensional space–time linear trial subspace that can be obtained by computing tensor decompositions of usual state-snapshots data. The mapping between the input parameters and the basis expansion coefficients (or generalized coordinates) is approximated using four different machine learning techniques: multivariate polynomial regression, k-nearest-neighbors, random forests and neural networks. The relative costs and effectiveness of the four machine learning techniques are explored through three engineering problems: steady heat conduction, unsteady heat conduction and unsteady advective–diffusive–reactive system. Numerical results demonstrate that the proposed method performs well in terms of both accuracy and computational cost, and highlights the important point that the amount of model training data available in an engineering setting is often much less than it is in other machine learning applications, making it essential to incorporate knowledge from physical models.

Original languageEnglish (US)
Article number114341
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Feb 1 2022


  • Data-driven reduced models
  • Model reduction
  • Non-intrusive reduced models
  • Physics-based machine learning
  • Space–time bases
  • Surrogate models

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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