Dynamic Mode Decomposition Analysis of High-Fidelity CFD Simulations of the Sinus Ventilation

Calmet, Hadrien; Pastrana, Daniel; Lehmkuhl, O.; Yamamoto, Takahisa; Kobayashi, Yoshiki; Tomoda, Koichi; Houzeaux, Guillaume; Vázquez, Mariano

doi:10.1007/s10494-020-00156-8

Cited by 11 publications

(4 citation statements)

References 26 publications

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“…The main idea of the method is to efficiently compute the regression of linear/nonlinear terms to a least-square linear dynamics approximation from experimental or numerical observable data. Despite its first appearance in the fluid dynamics context [ 55 , 56 ], DMD has been used in many other applications such as epidemiology [ 51 ], biomechanics [ 16 ], urban mobility [ 3 ], climate [ 44 ] and aeroelasticity [ 28 ], especially in structure extraction from data and control-oriented methods.…”

Section: Numerical Methods and Dynamic Mode Decompositionmentioning

confidence: 99%

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Barros

Grave

Viguerie

et al. 2021

Engineering with Computers

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Dynamic mode decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The classical procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion–reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD’s ability to extrapolate in time (short-time future estimates).

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Section: Numerical Methods and Dynamic Mode Decompositionmentioning

confidence: 99%

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Barros

Grave

Viguerie

et al. 2021

Engineering with Computers

View full text Add to dashboard Cite

show abstract

“…The method is completely equation-free and data-driven, meaning that little to no assumptions on data must be considered for its applications. DMD was first applied in fluid dynamics applications [47,49], being expanded to many other applications such as epidemiology [44,4], urban mobility [2], biomechanics [15], climate [37] and aeroelasticity [20], especially in structure extraction from data and control-oriented methods. The method consists of creating a linear map of the dynamics of a given spatio-temporal dataset, even if the dynamics is nonlinear, by projecting the finite-dimensional nonlinear data using an infinite dimension operator able to linearly represent the flow map present on (6) for all time steps.…”

Section: Partial Differential Equations and Dynamic Mode Decompositionmentioning

confidence: 99%

Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems

Viguerie,

Barros,

Grave

et al. 2021

Preprint

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Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in data, and effectiveness in providing reasonably accurate predictions for certain problems, particularly over short-to-medium time frames. Despite these successes, the application of DMD to certain problems featuring highly nonlinear transient dynamics remains challenging. In such cases, DMD may not only fail to provide acceptable predictions but may indeed fail to recreate the data in which it was trained, restricting its application to diagnostic purposes (i.e., feature identification and extraction). For many such problems in the biological and physical sciences, the structure of the system obeys a compartmental framework, in which the transfer of mass within the system moves within states. In these cases, the behavior of the system may not be accurately recreated by applying DMD to a single quantity within the system, as proper knowledge of the system dynamics, even for a single compartment, requires that the behavior of other compartments is taken into account in the DMD process. In the present work, we demonstrate, theoretically and numerically, that, when performing DMD on a fully coupled PDE system with compartmental structure, one may recover useful predictive behavior, even when DMD performs poorly when acting compartment-wise. We also establish that important physical quantities, such as mass conservation, are maintained in the coupled-DMD extrapolation. The mathematical and numerical analysis suggests that DMD, properly applied, may be a powerful tool when applied to this common class of problems. In particular, we show interesting numerical applications to a continuous delayed-SIRD model for Covid-19, and to a problem from additive manufacturing considering a

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“…Cannon et al 2013;Radulesco et al 2019;Cherobin et al 2020) or a certain flow rate through the passageways (see e.g. Lindemann et al 2013;Calmet et al 2020;Brüning et al 2020)). The first choice does not appear to possess a clear physiological rationale, whereas the second implies a comparison under the constraint of the same oxygen consumption rate.…”

Section: Introductionmentioning

confidence: 99%

On the comparison between pre- and post-surgery nasal anatomies via computational fluid dynamics

Segalerba,

Dini Ciacci,

Quadrio

et al. 2023

Biomech Model Mechanobiol

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Nasal breathing difficulties (NBD) are widespread and difficult to diagnose; the failure rate of their surgical corrections is high. Computational fluid dynamics (CFD) enables diagnosis of NBD and surgery planning, by comparing a pre-operative (pre-op) situation with the outcome of virtual surgery (post-op). An equivalent comparison is involved when considering distinct anatomies in the search for the functionally normal nose. Currently, this comparison is carried out in more than one way, under the implicit assumption that results are unchanged, which reflects our limited understanding of the driver of the respiratory function. The study describes how to set up a meaningful comparison. A pre-op anatomy, derived via segmentation from a CT scan, is compared with a post-op anatomy obtained via virtual surgery. State-of-the-art numerical simulations for a steady inspiration carry out the comparison under three types of global constraints, derived from the field of turbulent flow control: a constant pressure drop (CPG) between external ambient and throat, a constant flow rate (CFR) through the airways and a constant power input (CPI) from the lungs can be enforced. A significant difference in the quantities of interest is observed depending on the type of comparison. Global quantities (flow rate, pressure drop and nasal resistance) as well as local ones are affected. The type of flow forcing affects the outcome of the comparison between pre-op and post-op anatomies. Among the three available options, we argue that CPG is the least adequate. Arguments favouring either CFR or CPI are presented.

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Dynamic Mode Decomposition Analysis of High-Fidelity CFD Simulations of the Sinus Ventilation

Cited by 11 publications

References 26 publications

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems

On the comparison between pre- and post-surgery nasal anatomies via computational fluid dynamics

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