Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

Maulik, Romit; Lusch, Bethany; Balaprakash, Prasanna

doi:10.48550/arxiv.2002.00470

Cited by 15 publications

(16 citation statements)

References 45 publications

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“…Other methods compress PDE solutions on to lower-dimensional manifolds. This has shown to improve accuracy and generalization capability of neural networks (Wiewel et al, 2020;Maulik et al, 2020;Kim et al, 2019;Murata et al, 2020;.…”

Section: Meshmentioning

confidence: 99%

A composable autoencoder-based iterative algorithm for accelerating numerical simulations

Ranade,

Hill,

et al. 2021

Preprint

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Numerical simulations for engineering applications solve partial differential equations (PDE) to model various physical processes. Traditional PDE solvers are very accurate but computationally costly. On the other hand, Machine Learning (ML) methods offer a significant computational speedup but face challenges with accuracy and generalization to different PDE conditions, such as geometry, boundary conditions, initial conditions and PDE source terms. In this work, we propose a novel ML-based approach, CoAE-MLSim (Composable AutoEncoder Machine Learning Simulation), which is an unsupervised, lower-dimensional, local method, that is motivated from key ideas used in commercial PDE solvers. This allows our approach to learn better with relatively fewer samples of PDE solutions. The proposed ML-approach is compared against commercial solvers for better benchmarks as well as latest ML-approaches for solving PDEs. It is tested for a variety of complex engineering cases to demonstrate its computational speed, accuracy, scalability, and generalization across different PDE conditions. The results show that our approach captures physics accurately across all metrics of comparison (including measures such as results on section cuts and lines).

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Section: Meshmentioning

confidence: 99%

A composable autoencoder-based iterative algorithm for accelerating numerical simulations

Ranade,

Hill,

et al. 2021

Preprint

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“…The LSTM nudging framework is highly modular and it can be implemented with other types of neural network architectures also based on the size or type of problems. For example, convolutional autoencoders are gaining popularity to find the nonlinear basis functions of complex physical systems and they are complemented with the LSTM network for learning the latent-space dynamics [75][76][77][78][79][80][81]. The LSTM nudging framework can be easily applied to high dimensional systems, where convolutional autoencoders are employed for dimensionality reduction and the LSTM is trained to learn the nudging dynamics in latent-space instead of high-dimensional space.…”

Section: Algorithm 4 Lstm Nudging (Training Phase)mentioning

confidence: 99%

Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows

Pawar,

Ahmed,

San

et al. 2020

Preprint

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Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows, but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor-corrector type nudging approaches are still attractive due to their simplicity of implementation when more complex methods need to be avoided. However, optimal estimate of nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long short-term memory (LSTM) embedding architecture to estimate the nudging term, which plays a role not only to force the state trajectories to the observations but also acts as a stabilizer. Furthermore, our approach relies on the power of archival data and the trained model can be retrained effectively due to power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging AI-friendly and modular hardware technologies and heterogeneous computing platforms, we articulate that our simplistic nudging framework turns out to be computationally more efficient than either the EKF or EnKF approaches.

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“…If the network is able to output the same data as the input, it implies that the high-dimensional original input or output can successfully be compressed into the bottleneck space referred to as the latent space. This idea has widely been accepted in the fluid dynamics community [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]. Regarding the data estimation, the success of a global flow field estimation from local sensor measurements [25,26] or lowresolution data [27,28,29] indicates the possibility that we only need to keep these input data of their problem settings and ML models to represent the high-dimensional original data.…”

Section: Introductionmentioning

confidence: 99%

Supervised convolutional network for three-dimensional fluid data reconstruction from sectional flow fields with adaptive super-resolution assistance

Matsuo¹,

Nakamura²,

Morimoto³

et al. 2021

Preprint

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The recent development of high-performance computing enables us to generate spatiotemporal high-resolution data of nonlinear dynamical systems and to analyze them for deeper understanding of their complex nature. This trend can be found in a wide range of science and engineering communities, which suggests that detailed investigations on efficient data handling in physical science must be required in future. To this end, we introduce the use of convolutional neural networks (CNNs) to achieve an efficient data storage and estimation of scientific big data derived from nonlinear dynamical systems.The CNN is utilized to reconstruct three-dimensional data from a few numbers of two-dimensional sections in a computationally friendly manner. The present model is a combination of two-and three-dimensional CNNs, which allows users to save only some of the two-dimensional sections to reconstruct the volumetric data. As an example of threedimensional data, we consider a fluid flow around a square cylinder at the diameter-based Reynolds number Re D of 300, and show that volumetric fluid flow data can successfully be reconstructed with the present method from as few as five sections. Furthermore, we also propose a combination of the present CNN-based reconstruction with an adaptive sampling-based super-resolution analysis to augment the data compression capability of the present methods. Our report can be a significant bridge toward practical data handling for not only the fluid mechanics field but also a vast range of physical sciences.

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Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

Cited by 15 publications

References 45 publications

A composable autoencoder-based iterative algorithm for accelerating numerical simulations

A composable autoencoder-based iterative algorithm for accelerating numerical simulations

Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows

Supervised convolutional network for three-dimensional fluid data reconstruction from sectional flow fields with adaptive super-resolution assistance

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