Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence

Mohan, Arvind; Daniel, Don; Chertkov, Michael; Livescu, Daniel

doi:10.48550/arxiv.1903.00033

Cited by 40 publications

(53 citation statements)

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“…However, these works have been limited to 2D turbulent flows which are far less complicated than 3D turbulence both in terms of physics and computational tractability. The only relevant works aligned with our objective are the recent studies of (Mohan et al 2019 that their findings, though encouraging but seem suspicious.…”

Section: Introductionmentioning

confidence: 69%

“…Since the size of the dataset is memory intensive, similar to the conceptual design of (Mohan et al 2019), we first generate a low-dimensional representation of the velocity data and then pass it to a sequence prediction network that learns the positional and temporal correlations of the underlying data. Therefore, our framework will be composed of two separate models where one serves as a compression engine and the other performs prediction.…”

Section: Methodsmentioning

confidence: 99%

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Emulating Spatio-Temporal Realizations of Three-Dimensional Isotropic Turbulence via Deep Sequence Learning Models

Momenifar¹,

Diao²,

Tarokh³

et al. 2021

Preprint

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We use a data-driven approach to model a three-dimensional turbulent flow using cutting-edge Deep Learning techniques. The deep learning framework incorporates physical constraints on the flow, such as preserving incompressibility and global statistical invariants of velocity gradient tensor. The accuracy of the model is assessed using statistical and physics-based metrics. The data set comes from Direct Numerical Simulation of an incompressible, statistically stationary, isotropic turbulent flow in a cubic box. Since the size of the dataset is memory intensive, we first generate a lowdimensional representation of the velocity data, and then pass it to a sequence prediction network that learns the spatial and temporal correlations of the underlying data. The dimensionality reduction is performed via extraction using Vector-Quantized Autoencoder (VQ-AE), which learns the discrete latent variables. For the sequence forecasting, the idea of Transformer architecture from natural language processing is used, and its performance compared against more standard Recurrent Networks (such as Convolutional LSTM). These architectures are designed and trained to perform a sequence to sequence multi-class classification task in which they take an input sequence with a fixed length (k) and predict a sequence with a fixed length (p), representing the future time instants of the flow. Our results for the short-term predictions show that the accuracy of results for both models deteriorates across predicted snapshots due to autoregressive nature of the predictions. Based on our diagnostics tests, the trained Conv-Transformer model outperforms the Conv-LSTM one and can accurately, both quantitatively and qualitatively, retain the large scales and capture well the inertial scales of flow but fails at recovering the small and intermittent fluid motions.

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Section: Introductionmentioning

confidence: 69%

Section: Methodsmentioning

confidence: 99%

Emulating Spatio-Temporal Realizations of Three-Dimensional Isotropic Turbulence via Deep Sequence Learning Models

Momenifar¹,

Diao²,

Tarokh³

et al. 2021

Preprint

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show abstract

“…Neural networks have also been used to replace traditional PDE-based solvers, and serve as a standalone prediction tool. Popular approaches include auto-regressive timeseries predictions [10,11,12,13,14], Physics-Informed Neural Networks (PINNs) [15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems

Xu¹,

Pradhan²,

Duraisamy³

2021

Preprint

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The numerical simulations of physical systems are heavily dependent on meshbased models. While neural networks have been extensively explored to assist such tasks, they often ignore the interactions or hierarchical relations between input features, and process them as concatenated mixtures. In this work, we generalize the idea of conditional parametrization -using trainable functions of input parameters to generate the weights of a neural network, and extend them in a flexible way to encode information critical to the numerical simulations. Inspired by discretized numerical methods, choices of the parameters include physical quantities and mesh topology features. The functional relation between the modeled features and the parameters are built into the network architecture. The method is implemented on different networks, which are applied to several frontier scientific machine learning tasks, including the discovery of unmodeled physics, superresolution of coarse fields, and the simulation of unsteady flows with chemical reactions. The results show that the conditionally parameterized networks provide superior performance compared to their traditional counterparts. A network architecture named CP-GNet is also proposed as the first deep learning model capable of standalone prediction of reacting flows on irregular meshes.Preprint. Under review.

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“…Other than developing closure models for RANS and LES, researchers have been experi-menting with novel ML approaches to learn turbulence dynamics. In this regards, and just to name a few, we mention Mohan et al [40], where a Convolutional Long Short Term Memory (ConvLSTM) Neural Network was developed to learn spatio-temporal turbulence dynamics; studies of super-resolution allowing to reconstruct turbulence fields using underresolved data Fukami et al [41]; and Neural Ordinary Differential Equation (Neural ODE) for turbulence forecasting Portwood et al [42].…”

Section: Introductionmentioning

confidence: 99%

Physics-Informed Machine Learning of the Lagrangian Dynamics of Velocity Gradient Tensor

Tian¹,

Livescu²,

Chertkov³

2021

Preprint

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Reduced models describing the Lagrangian dynamics of the Velocity Gradient Tensor (VGT) in Homogeneous Isotropic Turbulence (HIT) are developed under the Physics-Informed Machine Learning (PIML) framework. We consider VGT at both Kolmogorov scale and coarse-grained scale within the inertial range of HIT. Building reduced models requires resolving the pressure Hessian and sub-filter contributions, which is accomplished by constructing them using the integrity bases and invariants of VGT. The developed models can be expressed using the extended Tensor Basis Neural Network (TBNN) introduced in [1]. Physical constraints, such as Galilean invariance, rotational invariance, and incompressibility condition, are thus embedded in the models explicitly. Our PIML models are trained on the Lagrangian data from a high-Reynolds number Direct Numerical Simulation (DNS). To validate the results, we perform a comprehensive out-of-sample test. We observe that the PIML model provides an improved representation for the magnitude and orientation of the small-scale pressure Hessian contributions. Statistics of the flow, as indicated by the joint PDF of second and third invariants of the VGT, show good agreement with the "ground-truth" DNS data. A number of other important features describing the structure of HIT are reproduced by the model successfully. We have also identified challenges in modeling inertial range dynamics, which indicates that a richer modeling strategy is required. This helps us identify important directions for future research, in particular towards including inertial range geometry into TBNN.

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Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence

Cited by 40 publications

References 0 publications

Emulating Spatio-Temporal Realizations of Three-Dimensional Isotropic Turbulence via Deep Sequence Learning Models

Emulating Spatio-Temporal Realizations of Three-Dimensional Isotropic Turbulence via Deep Sequence Learning Models

Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems

Physics-Informed Machine Learning of the Lagrangian Dynamics of Velocity Gradient Tensor

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