Data-driven modeling of rotating detonation waves

Mendible, Ariana; Koch, James; Lange, Henning; Brunton, Steven L.; Kutz, J. Nathan

doi:10.1103/physrevfluids.6.050507

Cited by 15 publications

(3 citation statements)

References 62 publications

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“…In addition, many of these methods do not consider additional invariances, such as scaling and/or rotation. Recently, an unsupervised machine learning procedure has been proposed for transport-dominated systems characterized by traveling waves [23,24]. This datadriven method, termed the Unsupervised Traveling Wave Identification with Shifting and Truncation (UnTWIST), can be applied with or without knowledge of the governing equations, providing an interpretable mathematical framework for ROMs exhibiting traveling wave phenomenon.…”

Section: Wave Motion In Reduced-order Modelsmentioning

confidence: 99%

“…To learn models for these underlying invariances, the UnTWIST method will be generalized [23]. UnTWIST is a recently-developed method that shows promising improvements in dimensionality reduction for complex wave shapes in both computational and experimental data [24]. This method, similar to other shift-based methods, learns a moving coordinate frame, given by the speed of a traveling wave.…”

Section: Unsupervised Traveling Wave Identification With Shifting And...mentioning

confidence: 99%

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Data-driven Modeling of Two-Dimensional Detonation Wave Fronts

Mendible¹,

Lowrie²,

Brunton³

et al. 2021

Preprint

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Historical experimental testing of high-altitude nuclear explosions (HANEs) are known to cause severe and detrimental effects to radio frequency signals and communications infrastructure. In order to study and predict the impact of HANEs, tractable computational approaches are required to model the complex physical processes involved in the detonation wave physics. Modern reduced-order models (ROMs) can enable long-time and many-parameter simulations with minimal computational cost. However, translational and scale invariances inherent to this type of wave propagation problem are known to limit traditional ROM approaches. Specifically, dimensionality reduction methods are typically ineffective in producing low-rank models when invariances are present in the data. In this work, an unsupervised machine learning method is used to discover coordinate systems that make such invariances amenable to traditional dimensionality reduction methods. The method, which has previously been demonstrated on one-dimensional translations, is extended to higher dimensions and additional invariances. A surrogate HANE system, i.e. a HANE-ROM, with one detonation wave is captured well at extremely low-rank. Two detonation-waves are also considered with various amounts of interaction between the waves, with improvements to low-rank models for multiple wave quantities with limited interaction.

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Section: Wave Motion In Reduced-order Modelsmentioning

confidence: 99%

Section: Unsupervised Traveling Wave Identification With Shifting And...mentioning

confidence: 99%

Data-driven Modeling of Two-Dimensional Detonation Wave Fronts

Mendible¹,

Lowrie²,

Brunton³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, these studies use a shifting operator on the snapshots (requiring interpolation in unstructured grids and some knowledge of the transport speed) to allow POD or DMD to (more) efficiently approximate advective systems. In their recent works, Mendible et al 186 employed an unsupervised traveling wave identification with shifting and truncation (UnTWIST) algorithm 185 to discover moving coordinate frames into which the data are shifted, thus overcoming limitations imposed by the underlying translational invariance of a rotating detonation engine system and allowing for the application of traditional dimensionality reduction techniques.…”

Section: Reduced Order Representationmentioning

confidence: 99%

On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues

Ahmed,

Pawar,

San

et al. 2021

Preprint

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For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr-Sommerfeld stability equation (1907) and numerous vortex models, of which the von Kármán vortex street (1911) is one of the most prominent. Subsequent ROMs typically relied on first principles, like mathematical Galerkin models, weakly nonlinear stability theory, and two-and three-dimensional vortex models. Aubry et al. (1988) pioneered, with the proper orthogonal decomposition (POD) model of the turbulent boundary layer, a new data-driven paradigm, which has become the most popular avenue. In early POD modeling, available data was used to build an optimal basis, which was then utilized in a classical Galerkin procedure to construct the ROM. But data has made a profound impact on ROMs beyond the Galerkin expansion. In this paper, we take a modest step and illustrate the impact of data-driven modeling on one significant ROM area. Specifically, we focus on ROM closures, which are correction terms that are added to classical ROMs in order to model the effect of the discarded ROM modes in under-resolved simulations. Through simple examples, we illustrate the main modeling principles used to construct classical ROMs, motivate and introduce modern ROM closures, and show how data-driven modeling, artificial intelligence, and machine learning have changed the standard ROM methodology over the last two decades. Finally, we outline our vision on how state-of-the-art data-driven modeling can continue to reshape the field of reduced order modeling.

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Front Transport Reduction for Complex Moving Fronts

et al. 2023

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This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction–diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be captured by linear reduction methods. Moreover, topological changes, such as splitting or merging of fronts pose difficulties for many nonlinear reduction methods and the small non-vanishing support of the underlying partial differential equations dynamics makes most nonlinear hyper-reduction methods infeasible. We propose a new decomposition method together with a hyper-reduction scheme that addresses these shortcomings. The decomposition uses a level-set function to parameterize the transport and a nonlinear activation function that captures the structure of the front. This approach is similar to autoencoder artificial neural networks, but additionally provides insights into the system, which can be used for efficient reduced order models. In addition to the presented decomposition method, we outline a tailored hyper-reduction method that is based on the reduced integration domain method. The capability of the approach is illustrated by various numerical examples in one and two spatial dimensions, including an advection–reaction–diffusion system with a Kolmogorov–Petrovsky–Piskunov reaction term and real life application to a two-dimensional Bunsen flame.

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Data-driven modeling of rotating detonation waves

Cited by 15 publications

References 62 publications

Data-driven Modeling of Two-Dimensional Detonation Wave Fronts

Data-driven Modeling of Two-Dimensional Detonation Wave Fronts

On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues

Front Transport Reduction for Complex Moving Fronts

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