TY - CHAP
T1 - Reduced Models with Nonlinear Approximations of Latent Dynamics for Model Premixed Flame Problems
AU - Uy, Wayne Isaac Tan
AU - Wentland, Christopher R.
AU - Huang, Cheng
AU - Peherstorfer, Benjamin
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - Chemically reacting flows
KW - Empirical interpolation
KW - Kolmogorov barrier
KW - Model reduction
KW - Transport-dominated problems
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U2 - 10.1007/978-3-031-55060-7_10
DO - 10.1007/978-3-031-55060-7_10
M3 - Chapter
AN - SCOPUS:85193608779
T3 - Lecture Notes in Computational Science and Engineering
SP - 241
EP - 259
BT - Lecture Notes in Computational Science and Engineering
PB - Springer Science and Business Media Deutschland GmbH
ER -