Manifold-informed state vector subset for reduced-order modeling

Zdybał, Kamila; Sutherland, James C.; Parente, Alessandro

doi:10.1016/j.proci.2022.06.019

Cited by 20 publications

(13 citation statements)

References 31 publications

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“…They can be further exploited in the future to provide localized closure models for high-fidelity combustion simulations, or to improve local kinetic schemes. Future research can also focus on quantifying the parameterization quality coming from local PCA, for example using recently proposed quantitative metrics [47,48]. We note that VQPCA can be an adequate clustering technique whenever linear subspaces are anticipated in the data, regardless of the origin of the data.…”

Section: Discussionmentioning

confidence: 99%

Local manifold learning and its link to domain-based physics knowledge

Zdybał¹,

D’Alessio²,

Attili³

et al. 2023

Applications in Energy and Combustion Science

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Section: Discussionmentioning

confidence: 99%

Local manifold learning and its link to domain-based physics knowledge

Zdybał¹,

D’Alessio²,

Attili³

et al. 2023

Applications in Energy and Combustion Science

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“…Other preprocessing approaches involve data sampling to mitigate imbalance in observation density, or feature selection. The effect of data preprocessing alone can have a large impact on the resulting low-dimensional manifold topology constructed from such data 53,65 . To demonstrate how significant those changes can be, Fig.…”

Section: Cost Function Response To Feature Size and Non-uniquenessmentioning

confidence: 99%

“…All PCA projections are colored by the temperature. For the purpose of this demonstration, we use a newly developed feature selection algorithm that uses the cost function to guide the optimal selection of the variables from the original training data 65 . By minimizing the cost of the resulting data projection, we optimize the feature selection process from the point of view of manifold topology.…”

Section: Cost Function Response To Feature Size and Non-uniquenessmentioning

confidence: 99%

“…L-informed feature selection. We developed a feature selection algorithm that iteratively eliminates state variables from the dataset based on minimizing the cost, L , of PCA projections 65 . There are three inputs to the algorithm: the original dataset, X ∈ R N×Q , the target dependent variables, φ φ φ ∈ R N×m , and the target manifold dimensionality, q.…”

Section: Effect Of Hyper-parameters R and B On The Cost Functionmentioning

confidence: 99%

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Cost function for low-dimensional manifold topology assessment

Zdybał

Armstrong

Sutherland

et al. 2022

Sci Rep

Self Cite

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In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.

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“…However, research on this approach has so far been limited to simple cases, necessitating further extensions and investigations. Moreover, several studies also combine machine learning methods and traditional approaches to tackle the complex fuel problems, including using a data-driven method to reduce the full chemistry to a subspace manifold by linear and non-linear models − and using neural networks to predict the flamelet-generated manifolds. − …”

Section: Introductionmentioning

confidence: 99%

Clustering-Enhanced Deep Learning Method for Computation of Full Detailed Thermochemical States via Solver-Based Adaptive Sampling

Chen,

Mehl,

Faney

et al. 2023

Energy Fuels

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Detailed chemistry computations are indispensable in numerous complex simulation tasks, which focus on accurately capturing the ignition process or predicting pollutant levels. The machine learning method is a modern data-driven approach for predicting a full detailed thermochemical state-to-state behavior in reacting flow simulations. By combining unsupervised clustering algorithms to subdivide the composition space, the complexity of adaptive regression models for temporal dynamics can be significantly reduced. In this article, a more compact dataset is generated, which is essential for the clustering algorithm, by leveraging the adaptive CVODE solver time steps for data augmentation for stiff reactive states. A learning workflow that utilizes a deep residual network model (ResNet) in conjunction with an adaptive clustering algorithm is proposed. This approach aims to replace the stiff ordinary differential equation direct integration solver traditionally used for computing thermochemical species’ state-to-state temporal evolution for detailed chemistry simulations. The learning models are adaptively trained using the K-means clustering algorithm in the non-linear transformation space for different subspaces of dynamic systems. Three test cases, H2 (9 species), C2H4 (32 species), and CH4 (53 species), are investigated, each exhibiting varying complexities. The study demonstrates that the iterative predictions of thermochemical states align well with the results obtained from direct numerical integration. Additionally, employing multiple adaptive regression models in subdomains yields superior performance compared to a single regression model prediction case.

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Manifold-informed state vector subset for reduced-order modeling

Cited by 20 publications

References 31 publications

Local manifold learning and its link to domain-based physics knowledge

Local manifold learning and its link to domain-based physics knowledge

Cost function for low-dimensional manifold topology assessment

Clustering-Enhanced Deep Learning Method for Computation of Full Detailed Thermochemical States via Solver-Based Adaptive Sampling

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