Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Kadeethum, Teeratorn; Ballarin, Francesco; Choi, Youngsoo; O’Malley, Daniel; Yoon, Hongkyu; Bouklas, Nikolaos

doi:10.1016/j.advwatres.2021.104098

Cited by 59 publications

(67 citation statements)

References 62 publications

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“…It is also shown that CAE-GPR has the ability to provide highly accurate estimates of the expansion coefficients, providing prediction errors that are very close to projection errors. Although previous works [19,20] have shown that the autoencoders do not offer a remarkable advantage in performance over POD for some problems, highly non-linear problems such as the lid-driven cavity problem presented benefit significantly from the use of deep learning for ROM construction. Future work will extend this ROM framework to larger problems where the spatial arrangement of full-order states is not uniform and investigate constructing nonlinear trial manifolds using variational autoencoders (VAEs), which have been shown to provide a more interpretable low-dimensional code.…”

Section: Discussionmentioning

confidence: 99%

“…When using autoencoders for ROMs, the entire network is trained in the offline stage, while only the decoder is used in the online stage for rapid evaluation of unseen solutions. To the best of our knowledge, there have been two attempts at using convolutional autoencoders for non-intrusive ROMs; one utilizing them for vehicle aerodynamic simulation [19] and another for natural convection in porous media [20]. The first found that using autoencoders only offers a very slight improvement over POD-based methods.…”

Section: Introductionmentioning

confidence: 99%

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Non-intrusive reduced-order modeling using convolutional autoencoders

Rakesh¹,

Fidkowski²,

Maki³

2022

Preprint

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The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB methods perform poorly, failing to provide an efficient subspace for the solution space. The use of nonlinear manifolds for ROMs has gained traction in recent years, showing increased performance for certain nonlinear problems over linear methods. Deep learning has been popular to this end through the use of autoencoders for providing a nonlinear trial manifold for the solution space. In this work, we present a non-intrusive ROM framework for steady-state parameterized partial differential equations (PDEs) that uses convolutional autoencoders (CAEs) to provide a nonlinear solution manifold and is augmented by Gaussian process regression (GPR) to approximate the expansion coefficients of the reduced model. When applied to a numerical example involving the steady incompressible Navier-Stokes equations solving a lid-driven cavity problem, it is shown that the proposed ROM offers greater performance in prediction of full-order states when compared to a popular method employing POD and GPR over a number of ROM dimensions.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-intrusive reduced-order modeling using convolutional autoencoders

Rakesh¹,

Fidkowski²,

Maki³

2022

Preprint

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“…Among various interpolation techniques, such as Gaussian processes [41,42], radial basis functions [43,44], Kriging [45,46], neural networks (NNs) have been most popular due to their strong flexibility and capability supported by the universal approximation theorem [47]. NN-based surrogates have been applied to various physical simulations, such as fluid dynamics [48], particle simulations [49], bioinformatics [50], deep Koopman dynamical models [51], porous media flow [52,53,54,55], etc. However, pure black-box NN-based surrogates lack interpretability and suffer from unstable and inaccurate generalization performance.…”

Section: Introductionmentioning

confidence: 99%

gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification

He¹,

Choi²,

William³

et al. 2022

Preprint

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A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust datadriven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. An interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residualbased error indicator and random-subset evaluation is introduced to search for the optimal training samples on-the-fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, an efficient k-nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 66 to 4,417× speed-up with 1 to 5% relative errors.

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“…whilst the first use of a convolutional autoencoder came 16 years later and was applied to Burgers Equation, advecting vortices and lid-driven cavity flow [31]. In the few years since 2018, many papers have appeared, in which convolutional autoencoders have been applied to sloshing waves, colliding bodies of fluid and smoke convection [32]; flow past a cylinder [33][34][35]; the Sod shock test and transient wake of a ship [36]; air pollution in an urban environment [37][38][39]; parametrised time-dependent problems [40]; natural convection problems in porous media [41]; the inviscid shallow water equations [42]; supercritical flow around an airfoil [43]; cardiac electrophysiology [44]; multiphase flow examples [45]; the Kuramoto-Sivashinsky equation [46]; the parametrised 2D heat equation [47]; and a collapsing water column [48]. Of these papers, those which compare autoencoder networks with POD generally conclude that autoencoders can outperform POD [31,33], especially when small numbers of reduced variables are used [41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

“…Once the low-dimensional space has been found, the snapshots are projected onto this space, and the resulting reduced variables (either POD coefficients or latent variables of an autoencoder) can be used to train a neural network, which attempts to learn the evolution of the reduced variables in time (and/or their dependence on a set of parameters). From the references in this paper alone, many examples exist of feed-forward and recurrent neural networks having been used for the purpose of learning the evolution of time series data, for example, by Multi-layer perceptrons [12,13,40,41,43,[54][55][56][57][58][59][60], Gaussian Process Regression [11,45,[61][62][63] and Long-Short Term Memory networks [31,32,34,35,38,51,64]. When using these types of neural network to predict in time, if the reduced variables stray outside of the range of values encountered during training, the neural network can produce unphysical, divergent results [39,51,52,64,65].…”

Section: Introductionmentioning

confidence: 99%

An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes

Heaney,

Wolffs,

Tómasson

et al. 2022

Preprint

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The modelling of multiphase flow in a pipe presents a significant challenge for high-resolution computational fluid dynamics (CFD) models due to the high aspect ratio (length over diameter) of the domain. In subsea applications, the pipe length can be several hundreds of kilometres versus a pipe diameter of just a few inches.Approximating CFD models in a low-dimensional space, reduced-order models have been shown to produce accurate results with a speed-up of orders of magnitude. In this paper, we present a new AI-based nonintrusive reduced-order model within a domain decomposition framework (AI-DDNIROM) which is capable of making predictions for domains significantly larger than the domain used in training. This is achieved by (i) using a domain decomposition approach; (ii) using dimensionality reduction to obtain a low-dimensional space in which to approximate the CFD model; (iii) training a neural network to make predictions for a single subdomain; and (iv) using an iteration-by-subdomain technique to converge the solution over the whole domain. To find the low-dimensional space, we explore several types of autoencoder networks, known for their ability to compress information accurately and compactly. The performance of the autoencoders is assessed on two advection-dominated problems: flow past a cylinder and slug flow in a pipe. To make predictions in time, we exploit an adversarial network which aims to learn the distribution of the training data, in addition to learning the mapping between particular inputs and outputs. This type of network has shown the potential to produce realistic outputs. The whole framework is applied to multiphase slug flow in a horizontal pipe for which an AI-DDNIROM is trained on high-fidelity CFD simulations of a pipe of length 10 m with an aspect ratio of 13:1, and tested by simulating the flow for a pipe of length 98 m with an aspect ratio of almost 130:1. Statistics of the flows obtained from the CFD simulations are compared to those of the AI-DDNIROM predictions to demonstrate the success of our approach.

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Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: Comparison with linear subspace techniques

Cited by 59 publications

References 62 publications

Non-intrusive reduced-order modeling using convolutional autoencoders

Non-intrusive reduced-order modeling using convolutional autoencoders

gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification

An AI-based Domain-Decomposition Non-Intrusive Reduced-Order Model for Extended Domains applied to Multiphase Flow in Pipes

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