A Gaussian moment method and its augmentation via LSTM recurrent neural networks for the statistics of cavitating bubble populations

Bryngelson, Spencer H.; Charalampopoulos, Alexis; Sapsis, Themistoklis P.; Colonius, Tim

doi:10.1016/j.ijmultiphaseflow.2020.103262

Cited by 18 publications

(17 citation statements)

References 54 publications

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“…It was also accurate for highly damped dynamics, characteristic of low Reynolds numbers, as non-Gaussian statistics cannot present themselves. This result contrasts against a previous approach that assumed Gaussian statistics, which had demonstrably worse performance and higher computational costs [41]. The method would require more quadrature points for cases with more complicated dynamics, such as larger forcing.…”

Section: Discussionmentioning

confidence: 74%

“…We see that ε is smaller for CHyQMOM and CQMOM than Gaussian closure, though the difference is modest and more strongly associated with C p . The larger errors for smaller C p are associated with stronger bubble dynamics and the formation of non-Gaussian statistics, like skewness and kurtosis, that these closures do not represent [41]. One can represent higher-order statistics by carrying higher-order moments and thus inverting for a higher-order quadrature rule.…”

Section: Model Performancementioning

confidence: 99%

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Conditional moment methods for polydisperse cavitating flows

Bryngelson¹,

Fox²,

Colonius³

2021

Preprint

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The dynamics of cavitation bubbles are important in many flows, but their small sizes and high number densities often preclude direct numerical simulation. We present a computational model that averages their effect on the flow over larger spatiotemporal scales. The model is based on solving a generalized population balance equation (PBE) for nonlinear bubble dynamics and explicitly represents the evolving probability density of bubble radii and radial velocities. Conditional quadrature-based moment methods (QBMMs) are adapted to solve this PBE. A one-way-coupled bubble dynamics problem demonstrates the efficacy of different QBMMs for the evolving bubble statistics. Results show that enforcing hyperbolicity during moment inversion (CHyQMOM) provides comparable model-form accuracy to the traditional conditional method of moments and decreases computational costs by about ten times for a broad range of test cases. The CHyQMOM-based computational model is implemented in MFC, an open-source multi-phase and high-order-accurate flow solver. We assess the effect of the model and its parameters on a two-way coupled bubble screen flow problem.

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Section: Discussionmentioning

confidence: 74%

Section: Model Performancementioning

confidence: 99%

Conditional moment methods for polydisperse cavitating flows

Bryngelson¹,

Fox²,

Colonius³

2021

Preprint

Self Cite

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“…To overcome this problem, long short-term memory was developed. Despite that, LSTM has many drawbacks, for instance, the overfitting problem (Baek & Kim, 2018), computationally expensive (Bryngelson et al, 2020), and inconsistent performance when using various initial weight values (Massaoudi et al, 2021).…”

Section: Literature Reviewmentioning

confidence: 99%

Modeling the fluctuations of groundwater level by employing ensemble deep learning techniques

Afan

Osman

Essam

et al. 2021

Engineering Applications of Computational Fluid Mechanics

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This study proposes two techniques: Deep Learning (DL) and Ensemble Deep Learning (EDL) to predict groundwater level (GWL) for five wells in Malaysia. Two scenarios were proposed, scenario-1 (S1): GWL from 4 wells was used as inputs to predict the GWL in the fifth well and scenario-2 (S2): time series with lag time up to 20 days for all five wells. The results from S1 prove that the ensemble EDL generally performs superior to the DL in the estimation of GWL of each station using data of remaining four wells except the Paya Indah Wetland in which the DL method provide better estimates compared to EDL. Regarding S2, the EDL also exhibits superior performance in predicting daily GWL in all five stations compared to the DL model. Implementing EDL decreased the RMSE, NAE and RRMSE by 11.6%, 27.3% and 22.3% and increased the R, Spearman rho and Kendall tau by 0.4%, 1.1% and 3.5%, respectively. Moreover, EDL for S2 shows a high level of precision within less time lag, ranging between 2 and 4 compared to DL. Therefore, the EDL model has the potential in managing the sustainability of groundwater in Malaysia.

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“…42 Works have been specifically devoted to the application of neural networks to study and to model the dynamics of particles in flows and their size distributions. In this context, the improvement of physical models driving the PBE through ANN have been discussed, 43 control particle size strategies using ANN have been implemented, 44 particle size distributions have been approximated with ANN, 45 measurements of particle size distributions have been coupled with ANN, 46 memory effects were introduced in networks with feedback connections to progress in Gaussian moment methods 47 and dynamic modeling of component formation was coupled with a special class of ANN (regularisation networks), in order to predict the solid-liquid equilibrium in complex multi-phase flows. 48 Here, a combination of artificial neural networks (ANN) and convolutional neural networks (CNN) [49][50][51] is discussed.…”

Section: Please Cite This Article As Doi:101063/50031144mentioning

confidence: 99%

Solving the population balance equation for non-inertial particles dynamics using probability density function and neural networks: Application to a sooting flame

Seltz

Domingo

2021

Physics of Fluids

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Numerical modeling of non-inertial particles dynamics is usually addressed by solving a population balance equation (PBE). In addition to space and time, a discretisation is required also in the particle-size space, covering a large range of variation controlled by strongly nonlinear phenomena. A novel approach is presented in which a hybrid stochastic/fixed-sectional method solving the PBE is used to train a combination of an artificial neural network (ANN) with a convolutional neural network (CNN) and recurrent long short-term memory artificial neural layers (LSTM). The hybrid stochastic/fixed-sectional method decomposes the problem into the total number density and the probability density function (PDF) of sizes, allowing for an accurate treatment of surface growth/loss. After solving for the transport of species and temperature, the input of the ANN is composed of the thermochemical parameters controling the particle physics and of the increment in time. The input of the CNN is the shape of the particle size distribution (PSD) discretised in sections of size. From these inputs, in a flow simulation the ANN-CNN returns the PSD shape for the subsequent time step or a source term for the Eulerian transport of the particle size density. The method is evaluated in a canonical laminar premixed sooting flame of the literature and for a given level of accuracy (i.e., a given discretisation of the size space), a significant computing cost reduction is achieved (6 times faster compared to a sectional method with 10 sections and 30 times faster for 100 sections).

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A Gaussian moment method and its augmentation via LSTM recurrent neural networks for the statistics of cavitating bubble populations

Cited by 18 publications

References 54 publications

Conditional moment methods for polydisperse cavitating flows

Conditional moment methods for polydisperse cavitating flows

Modeling the fluctuations of groundwater level by employing ensemble deep learning techniques

Solving the population balance equation for non-inertial particles dynamics using probability density function and neural networks: Application to a sooting flame

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