An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion

Phillips, Toby; Heaney, Claire E.; Smith, Paul N.; Pain, Christopher C.

doi:10.48550/arxiv.2008.10532

Cited by 5 publications

(6 citation statements)

References 52 publications

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“…we seek a reduced order approximation in an optimal linear subspace [50,90,63,68,91,92]. If the problem does not allow such representation, nonlinear variants (e.g., autoencoders) could be considered as data compression tools [98,99,100,101]. Here, we prefer to employ POD because it is generally faster than the nonlinear variants.…”

Section: Proper Orthogonal Decomposition (Pod)mentioning

confidence: 99%

Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation

2021

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A simulation tool capable of speeding up the calculation for linear poroelasticity problems in heterogeneous porous media is of large practical interest for engineers, in particular, to effectively perform sensitivity analyses, uncertainty quantification, optimization, or control operations on the fluid pressure and bulk deformation fields. Towards this goal, we present here a non-intrusive model reduction framework using proper orthogonal decomposition (POD) and neural networks, based on the usual offline-online paradigm. As the conductivity of porous media can be highly heterogeneous and span several orders of magnitude, we utilize the interior penalty discontinuous Galerkin (DG) method as a full order solver to handle discontinuity and ensure local mass conservation during the offline stage. We then use POD as a data compression tool and compare the nested POD technique, in which time and uncertain parameter domains are compressed consecutively, to the classical POD method in which all domains are compressed simultaneously. The neural networks are finally trained to map the set of uncertain parameters, which could correspond to material properties, boundary conditions, or geometric characteristics, to the collection of coefficients calculated from an L 2 projection over the reduced basis. We then perform a non-intrusive evaluation of the neural networks to obtain coefficients corresponding to new values of the uncertain parameters during the online stage. We show that our framework provides reasonable approximations of the DG solution, but it is significantly faster. Moreover, the reduced order framework can capture sharp discontinuities of both displacement and pressure fields resulting from the heterogeneity in the media conductivity, which is generally challenging for intrusive reduced order methods. The sources of error are presented, showing that the nested POD technique is computationally advantageous and still provides comparable accuracy to the classical POD method. We also explore the effect of different choices of the hyperparameters of the neural network on the framework performance.Keywords poroelasticity • reduced order modeling • neural networks • discontinuous Galerkin • heterogeneity • finite element

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Section: Proper Orthogonal Decomposition (Pod)mentioning

confidence: 99%

Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation

2021

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“…Data-driven modelling of nonlinear fluid flows incorporating adversarial networks have been successfully being studied previously (Cheng et al, 2020;Xie et al, 2018). This extended abstract applies PC-based adversarial autoencoder (Makhzani et al, 2015) and adversarial training to a LSTM network, based on a ROM Phillips et al, 2020) of an urban air pollution simulation in an unstructured mesh. The motivation of using adversarial autoencoders relies in the ability of the adversarial training to match the aggregated posterior of the encoder with an arbitrary prior distribution.…”

Section: Introductionmentioning

confidence: 99%

Adversarial autoencoders and adversarial LSTM for improved forecasts of urban air pollution simulations

Quilodrán-Casas,

Arcucci,

Mottet

et al. 2021

Preprint

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This paper presents an approach to improve the forecast of computational fluid dynamics (CFD) simulations of urban air pollution using deep learning, and most specifically adversarial training. This adversarial approach aims to reduce the divergence of the forecasts from the underlying physical model. Our twostep method integrates a Principal Components Analysis (PCA) based adversarial autoencoder (PC-AAE) with adversarial Long short-term memory (LSTM) networks. Once the reduced-order model (ROM) of the CFD solution is obtained via PCA, an adversarial autoencoder is used on the principal components time series. Subsequentially, a Long Short-Term Memory network (LSTM) is adversarially trained on the latent space produced by the PC-AAE to make forecasts. Once trained, the adversarially trained LSTM outperforms a LSTM trained in a classical way. The study area is in South London, including three-dimensional velocity vectors in a busy traffic junction.

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“…The main works can be divided into two parts based on the steady-state and time-dependent PPDEs. Firstly, the works on steady-state PPDEs can be divided into supervised learning [13,14] and unsupervised learning [15,16]. Secondly, since time-dependent PPDEs also involve time variables, the requirements for its generalization ability are also stronger.…”

Section: Introductionmentioning

confidence: 99%

Solving time-dependent parametric PDEs by multiclass classification-based reduced order model

Chen¹,

Jiang²,

Shu³

2021

Preprint

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In this paper, we propose a network model, the multiclass classification-based ROM (MC-ROM), for solving time-dependent parametric partial differential equations (PPDEs). This work is inspired by the observation of applying the deep learning-based reduced order model (DL-ROM) [1] to solve diffusion-dominant PPDEs. We find that the DL-ROM has a good approximation for some special model parameters, but it cannot approximate the drastic changes of the solution as time evolves. Based on this fact, we classify the dataset according to the magnitude of the solutions, and construct corresponding subnets dependent on different types of data. Then we train a classifier to integrate different subnets together to obtain the MC-ROM. When subsets have the same architecture, we can use transfer learning technology to accelerate the offline training. Numerical experiments show that the MC-ROM improves the generalization ability of the DL-ROM both for diffusion-and convection-dominant problems, and maintains the DL-ROM's advantage of good approximation ability. We also compare the approximation accuracy and computational efficiency of the proper orthogonal decomposition (POD) which is not suitable for convection-dominant problems. For diffusion-dominant problems, the MC-ROM can save about 100 times online computational cost than the POD with a slightly better approximation in the reduced space of the same dimension.

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An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion

Cited by 5 publications

References 52 publications

Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation

Data-driven reduced order modeling of poroelasticity of heterogeneous media based on a discontinuous Galerkin approximation

Adversarial autoencoders and adversarial LSTM for improved forecasts of urban air pollution simulations

Solving time-dependent parametric PDEs by multiclass classification-based reduced order model

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