Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy

Donello, Michael; Carpenter, Mark H.; Babaee, Hessam

doi:10.1137/20m1388565

Cited by 16 publications

(9 citation statements)

References 36 publications

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“…The velocity field is obtained by solving the incompressible Navier-Stokes equations and is independent of the species transport equation. The conditions are identical to those used in previous studies [6,7]. In particular, we solved the velocity field in the entire domain using the spectral/hp element method on an unstructured mesh with 4008 quadrilateral elements and polynomial order 5.…”

Section: (C) Stochastic Advection-diffusion-reaction Equationmentioning

confidence: 99%

“…Therefore, the solution to these massive MDEs is cost prohibitive due to the floating point operations (flops), memory and storage requirements. The discretization of many other PDEs can also be cast as MDEs, for example, kinetics equations [3][4][5], linear sensitivity analyses [6] and species transport equations in turbulent combustion [7].…”

Section: Introductionmentioning

confidence: 99%

“…they produce identical low-rank matrices [11,12], and their differences lie only in their numerical performance. TDB ROMs have also been used in other fields and applications including dynamical systems [13,14], combustion [7,15], linear sensitivity analysis [6], dynamical instabilities [16–18], deep learning [19] and singular vale decomposition (SVD) estimation for matrices that vary smoothly with a parameter [20].…”

Section: Introductionmentioning

confidence: 99%

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Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases

Donello,

Palkar,

Naderi

et al. 2023

Proc. R. Soc. A.

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Time-dependent basis reduced-order models (TDB ROMs) have successfully been used for approximating the solution to nonlinear stochastic partial differential equations (PDEs). For many practical problems of interest, discretizing these PDEs results in massive matrix differential equations (MDEs) that are too expensive to solve using conventional methods. While TDB ROMs have the potential to significantly reduce this computational burden, they still suffer from the following challenges: (i) inefficient for general nonlinearities, (ii) intrusive implementation, (iii) ill-conditioned in the presence of small singular values and (iv) error accumulation due to fixed rank. To this end, we present a scalable method for solving TDB ROMs that is computationally efficient, minimally intrusive, robust in the presence of small singular values, rank-adaptive and highly parallelizable. These favourable properties are achieved via oblique projections that require evaluating the MDE at a small number of rows and columns. The columns and rows are selected using the discrete empirical interpolation method (DEIM), which yields near-optimal matrix low-rank approximations. We show that the proposed algorithm is equivalent to a CUR matrix decomposition. Numerical results demonstrate the accuracy, efficiency and robustness of the new method for a diverse set of problems.

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Section: (C) Stochastic Advection-diffusion-reaction Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases

Donello,

Palkar,

Naderi

et al. 2023

Proc. R. Soc. A.

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“…As demonstrated in Ref. [27], the f-OTD can be very effectively employed in multi-dimensional combustion systems in a cost-effective manner by exploiting the correlations between the spatio-temporal sensitivities of species with respect to different parameters. Therefore, its implementation is recommended for large scale simulations of practical combustion systems [57,58] and reacting compressible flows [59].…”

Section: Pressure Effect On the Importance Of Reactionsmentioning

confidence: 99%

“…The f-OTD method is an on-the-fly reduced order modeling technique for computing sensitivities in evolutionary dynamical systems and it was recently introduced in Ref. [27]. An algorithm based on f-OTD was also recently developed for the skeletal model reduction [7].…”

Section: Introductionmentioning

confidence: 99%

Skeletal Reaction Model Generation for Atmospheric and High Pressure Combustion of Methane

Liu¹,

Babaee²,

Givi³

et al. 2022

Preprint

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Skeletal reaction models for atmospheric and high pressure combustion of methane are generated from detailed kinetics models through the forced-optimally time dependent (f-OTD) methodology. In the f-OTD method, local sensitivities are decomposed to the multiplication of two low-rank time-dependent matrices.The evolution equation of these matrices are derived from the governing equations of the system. Modeled sensitivities are then analyzed temporally to rank the species based on their importance and produce different skeletal models with different number of species. Skeletal reduction with the f-OTD method is conducted of two detailed kinetics models for methane combustion: the GRI-Mech 3.0 for atmospheric pressure and the FFCM-1 for high pressures. A series of skeletal models with different levels of accuracy are derived in each case. The performances of the generated models are compared against two detailed models (GRI-Mech 3.0 and FFCM-1) based on their ability in predicting ignition delays, laminar flame speeds, and flame extinctions. The effect of pressure on the significance of specific reactions are also analyzed for high pressure combustion.

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A DEIM Tucker tensor cross algorithm and its application to dynamical low-rank approximation

Ghahremani,

Babaee

2024

Computer Methods in Applied Mechanics and Engineering

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Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy

Cited by 16 publications

References 36 publications

Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases

Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases

Skeletal Reaction Model Generation for Atmospheric and High Pressure Combustion of Methane

A DEIM Tucker tensor cross algorithm and its application to dynamical low-rank approximation

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