Reduced Models with Nonlinear Approximations of Latent Dynamics for Model Premixed Flame Problems

Wayne Isaac Tan Uy, Christopher R. Wentland, Cheng Huang, Benjamin Peherstorfer

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Efficiently reducing models of chemically reacting flows is often challenging because their characteristic features such as sharp gradients in the flow fields and couplings over various time and length scales lead to dynamics that evolve in high-dimensional spaces. In this work, we show that online adaptive reduced models that construct nonlinear approximations by adapting low-dimensional subspaces over time can predict well latent dynamics with properties similar to those found in chemically reacting flows. The adaptation of the subspaces is driven by the online adaptive empirical interpolation method that takes sparse residual evaluations of the full model to compute low-rank basis updates of the subspaces. Numerical experiments with a premixed flame model problem show that reduced models based on online adaptive empirical interpolation accurately predict flame dynamics far outside of the training regime and in regimes where traditional static reduced models, which keep reduced spaces fixed over time and so provide only linear approximations of latent dynamics, fail to make meaningful predictions.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computational Science and Engineering
PublisherSpringer Science and Business Media Deutschland GmbH
Pages241-259
Number of pages19
DOIs
StatePublished - 2024

Publication series

NameLecture Notes in Computational Science and Engineering
Volume151
ISSN (Print)1439-7358
ISSN (Electronic)2197-7100

Keywords

  • Chemically reacting flows
  • Empirical interpolation
  • Kolmogorov barrier
  • Model reduction
  • Transport-dominated problems

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Engineering
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

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