A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Kim, Youngkyu; Choi, Youngsoo; Widemann, David P.; Zohdi, Tarek I.

doi:10.48550/arxiv.2009.11990

Cited by 18 publications

(72 citation statements)

References 72 publications

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“…In optically thick regimes or intermediate regimes, it is easy to find an accurate closure relation. However, in optically thin regimes (or even the free streaming limit), the kinetic model does not possess intrinsic low dimensional structure, which makes any attempt at model reduction difficult [33,34,24,49]. To address this problem, we start from investigating the RTE in the free streaming limit and derive the exact closure relations with isotropic initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure

Huang,

Cheng,

Christlieb

et al. 2021

Preprint

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In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for radiative transfer equation in slab geometry. Instead of learning the unclosed high order moment, we propose to directly learn the gradient of the high order moment using neural networks. This new approach is consistent with the exact closure we derive for the free streaming limit and also provides a natural output normalization. A variety of benchmark tests, including the variable scattering problem, the Gaussian source problem and the two material problem, show both good accuracy and generalizability of our machine learning closure model.

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Section: Introductionmentioning

confidence: 99%

Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure

Huang,

Cheng,

Christlieb

et al. 2021

Preprint

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“…The PINN with the adaptive activation function had a more desirable feature for speeding up the convergence rate and improving the solution accuracy. KIM et al [28] presented a fast and accurate PINN ROM with a nonlinear manifold solution representation. The structure of NNs included two part, namely encoder and decoder.…”

Section: Related Workmentioning

confidence: 99%

A novel meta-learning initialization method for physics-informed neural networks

Liu,

Zhang,

Peng

et al. 2021

Preprint

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Physics-informed neural networks (PINNs) have been widely used to solve various scientific computing problems. However, large training costs limit PINNs for some real-time applications. Although some works have been proposed to improve the training efficiency of PINNs, few consider the influence of initialization. To this end, we propose a New Reptile initialization based Physics-Informed Neural Network (NRPINN). The original Reptile algorithm is a meta-learning initialization method based on labeled data. PINNs can be trained with less labeled data or even without any labeled data by adding partial differential equations (PDEs) as a penalty term into the loss function. Inspired by this idea, we propose the new Reptile initialization to sample more tasks from the parameterized PDEs and adapt the penalty term of the loss. The new Reptile initialization can acquire initialization parameters from related tasks by supervised, unsupervised, and semi-supervised learning. Then, PINNs with initialization parameters can efficiently solve PDEs. Besides, the new Reptile initialization can also be used for the variants of PINNs. Finally, we demonstrate and verify the NRPINN considering both forward problems, including solving Poisson, Burgers, and Schrödinger equations, as well as inverse problems, where unknown parameters in the PDEs are estimated. Experimental results show that the NRPINN training is much faster and achieves higher accuracy than PINNs with other initialization methods.

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“…Autoencoders have recently become popular for the nonlinear dimensionality reduction of datasets extracted from several high dimensional systems. These have been motivated by the extraction of coherent structures that parameterize low-dimensional embeddings in manifolds [23,24,25], and the utilization of these embeddings for efficient surrogate models of nonlinear dynamical systems [26,27,28,29,30]. In this work, we utilize convolutional autoencoders to identify low-dimensional representations of experimentally collected data for building parameter-observation maps where the former are obtained through meteorological and wind turbine data and the latter are LiDAR measurements collected in the wake generated by wind turbines.…”

Section: Convolutional Autoencodermentioning

confidence: 99%

Data-Driven Wind Turbine Wake Modeling via Probabilistic Machine Learning

Renganathan¹,

Maulik²,

Letizia³

et al. 2021

Preprint

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Wind farm design primarily depends on the variability of the wind turbine wake flows to the atmospheric wind conditions, and the interaction between wakes. Physics-based models that capture the wake flow-field with high-fidelity are computationally very expensive to perform layout optimization of wind farms, and, thus, data-driven reduced order models can represent an efficient alternative for simulating wind farms. In this work, we use real-world light detection and ranging (LiDAR) measurements of wind-turbine wakes to construct predictive surrogate models using machine learning. Specifically, we first demonstrate the use of deep autoencoders to find a low-dimensional latent space that gives a computationally tractable approximation of the wake LiDAR measurements. Then, we learn the mapping between the parameter space and the (latent space) wake flow-fields using a deep neural network. Additionally, we also demonstrate the use of a probabilistic machine learning technique, namely, Gaussian process modeling, to learn the parameter-space-latent-space mapping in addition to the epistemic and aleatoric uncertainty in the data. Finally, to cope with training large datasets, we demonstrate the use of variational Gaussian process models that provide a tractable alternative to the conventional Gaussian process models for large datasets. Furthermore, we introduce the use of active learning to adaptively build and improve a conventional Gaussian process model predictive capability. Overall, we find that our approach provides accurate approximations of the wind-turbine wake flow field that can be queried at an orders-of-magnitude cheaper cost than those generated with high-fidelity physics-based simulations.Keywords Wind turbine • renewable energy • wake • deep learning • Gaussian processes • lidar

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A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder

Cited by 18 publications

References 72 publications

Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure

Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure

A novel meta-learning initialization method for physics-informed neural networks

Data-Driven Wind Turbine Wake Modeling via Probabilistic Machine Learning

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