Towards an hybrid computational strategy based on Deep Learning for incompressible flows (original) (raw)
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2017
We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent method. Of particular interest is to predict the unsteady fluid forces for different bluff body shapes at low Reynolds number. The discrete convolution process with a nonlinear rectification is employed to approximate the mapping between the bluff-body shape and the fluid forces. The deep neural network is fed by the Euclidean distance function as the input and the target data generated by the full-order Navier-Stokes computations for primitive bluff body shapes. The convolutional networks are iteratively trained using the stochastic gradient descent method with the momentum term to predict the fluid force coefficients of different geometries and the results are compared with the full-order computations. We attempt to provide a physical analogy of the stochastic gradient method with the momentum term with the simplified form of the incompress-ible Navier-Stokes momentum equation. We also construct a direct relationship between the CNN-based deep learning and the Mori-Zwanzig formalism for the model reduction of a fluid dynamical system. A systematic convergence and sensitivity study is performed to identify the effective dimensions of the deep-learned CNN process such as the convolution kernel size, the number of kernels * Corresponding author arXiv:1710.09099v3 [physics.flu-dyn] 15 Aug 2018 and the convolution layers. Within the error threshold, the prediction based on our deep convolutional network has a speed-up nearly four orders of magnitude compared to the full-order results and consumes an insignificant fraction of computational resources. The proposed CNN-based approximation procedure has a profound impact on the parametric design of bluff bodies and the feedback control of separated flows.
Physics of Fluids
The Riemann problem is fundamental to most computational fluid dynamics (CFD) codes for simulating compressible flows. The time to obtain the exact solution to this problem for real fluids is high because of the complexity of the fluid model, which includes the equation of state; as a result, approximate Riemann solvers are used in lieu of the exact ones, even for ideal gases. We used fully connected feedforward neural networks to find the solution to the Riemann problem for calorically imperfect gases, supercritical fluids, and high explosives and then embedded these network into a one-dimensional finite volume CFD code. We showed that for real fluids, the neural networks can be more than five orders of magnitude faster than the exact solver, with prediction errors below 0.8%. The same neural networks embedded in a CFD code yields very good agreement with the overall exact solution, with a speed-up of three orders of magnitude with respect to the same CFD code that use the exact Ri...
2021
Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the physicsdriven learning of complex flow fields with high resolutions. We propose the use of Convolutional neural networks (CNN) based U-net architectures to efficiently represent and reconstruct the input and output fields, respectively. By introducing Navier-Stokes equations and boundary conditions into loss functions, the physics-driven CNN is designed to predict corresponding steady flow fields directly. In particular, this prevents many of the difficulties associated with approaches employing fully connected neural networks. Several numerical experiments are conducted to investigate the behavior of the CNN approach, and the results indicate that a first-order accuracy has been achieved. Specifically for the case of a flow around a cylinder, different flow ...
Deep learning model for two-fluid flows
Physics of Fluids
Various industries rely on numerical tools to simulate multiphase flows due to the wide occurrence of this phenomenon in nature, manufacturing processes, or the human body. However, the significant computation burden required for such simulations directs the research interest toward incorporating data-based approaches in the solution loop. Although these approaches returned significant results in various domains, incorporating them in the computational fluid dynamics (CFD) field is wrangled by their casting aside of the already known governing constitutional laws along with the natural incompatibility of various models with unstructured irregular discretization spaces. This work suggests a coupling framework, between a traditional finite element CFD solver and a deep learning model, for tackling multiphase fluid flows without migrating the benefits of physics-enriched traditional solvers. The tailored model architecture, along with the coupling framework, allows tackling the require...
International Journal of Heat and Fluid Flow, 2022
High-fidelity models of multiphysics fluid flow processes are often computationally expensive. On the other hand, less accurate low-fidelity models could be efficiently executed to provide an approximation to the solution. Multi-fidelity approaches combine high-fidelity and low-fidelity data and/or models to obtain a desirable balance between computational efficiency and accuracy. In this manuscript, we propose a multi-fidelity approach where we combine data generated by a low-fidelity computational fluid dynamics (CFD) solution strategy (solver settings and resolution) and data-free physics-informed neural networks (PINN) to obtain improved accuracy. Specifically, transfer learning based on low-fidelity CFD data is used to initialize PINN. Subsequently, PINN with this physics-guided initialization is used to obtain the final results without any high-fidelity training data. The accuracy of the final results relies on the governing equations encoded in PINN together with the low-fidelity CFD data initialization. To investigate the accuracy of this approach, several partial differential equations were solved to predict velocity and temperature in different fluid flow, heat transfer, and porous media transport problems. Comparison with reference high-fidelity CFD data revealed that the proposed approach not only significantly improves the accuracy of low-fidelity CFD data but also improves the convergence speed and accuracy of PINN.
Physics-guided deep learning for generating turbulent inflow conditions
In this paper, we propose an efficient method for generating turbulent inflow conditions based on deep neural networks. We utilise the combination of a multiscale convolutional auto-encoder with a subpixel convolution layer (MSC SP-AE) and a long short-term memory (LSTM) model. Physical constraints represented by the flow gradient, Reynolds stress tensor and spectral content of the flow are embedded in the loss function of the MSC SP-AE to enable the model to generate realistic turbulent inflow conditions with accurate statistics and spectra, as compared with the ground truth data. Direct numerical simulation (DNS) data of turbulent channel flow at two friction Reynolds numbers Re τ = 180 and 550 are used to assess the performance of the model obtained from the combination of the MSC SP-AE and the LSTM model. The model exhibits a commendable ability to predict instantaneous flow fields with detailed fluctuations and produces turbulence statistics and spectral content similar to those obtained from the DNS. The effects of changing various salient components in the model are thoroughly investigated. Furthermore, the impact of performing transfer learning (TL) using different amounts of training data on the training process and the model performance is examined by using the weights of the model trained on data of the flow at Re τ = 180 to initialise the weights for training the model with data of the flow at Re τ = 550. The results show that by using only 25 % of the full training data, the time that is required for successful training can be reduced by a factor of approximately 80 % without affecting the performance of the model for the spanwise velocity, wall-normal velocity and pressure, and with an improvement of the model performance for the streamwise velocity. The results also indicate that using physics-guided deep-learning-based models can be efficient in terms of predicting the dynamics of turbulent flows with relatively low computational cost.
Accelerating Convergence of Fluid Dynamics Simulations with Convolutional Neural Networks
Periodica Polytechnica Mechanical Engineering, 2019
A novel technique to accelerate optimization-driven aerodynamic shape design is presented in the paper. The methodology of optimization-driven design is based on the automated evaluation of many similar shapes which are generated according to the output of an optimization algorithm. The vast amount of numerical simulations makes this process slow but the resource-intensive simulation part can be changed to so-called surrogate models or metamodels. However, there isn’t any guarantee of this solution’s accuracy.The motivation of this work was to develop an acceleration method to speedup optimization sessions without losing accuracy. Accordingly, the numerical simulation is kept in the pipeline but it is initialized with a velocity field that is close to the expected solution. This velocity field is generated by a predictive initializer that is based on a convolutional deep neural network. The network has to be trained before using it for initializing numerical simulations; the data ge...
Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations
2020
In this paper the physics- (or PDE-) integrated machine learning (ML) framework is investigated. The Navier-Stokes (NS) equations are solved using Tensorflow library for Python via Chorin-s projection method. The methodology for the solution is provided, which is compared with a classical solution implemented in Fortran. This solution is integrated with a neural network (NN). Such integration allows one to train a NN embedded in the NS equations without having the target (labeled training) data for the direct outputs from the NN; instead, the NN is trained on the field data (quantities of interest), which are the solutions for the NS equations. To demonstrate the performance of the framework, a case study is formulated: the 2D lid-driven cavity with non-constant velocity-dependent dynamic viscosity is considered. A NN is trained to predict the dynamic viscosity from the velocity fields. The performance of the physics-integrated ML is compared with classical ML framework, when a NN i...
Integration of neural networks with numerical solution of PDEs for closure models development
Physics Letters A, 2021
In this paper a physics-integrated (or PDE-integrated (partial differential equation)) machine learning (ML) framework is investigated. The Navier-Stokes equations are solved using the Tensorflow ML library for Python programming language via the Chorin's projection method. The methodology for the solution is provided, which is compared with a "classical" solution implemented in Fortran programming language. The Tensorflow solution is integrated with a deep feedforward neural network (DFNN). Such integration allows one to train a DFNN embedded in the Navier-Stokes equations without having the target (labeled training) data for the direct outputs from the DFNN; instead, the DFNN is trained on the field variables (quantities of interest), which are solutions for the Navier-Stokes equations (velocity and pressure fields). To demonstrate performance of the framework, a case study is formulated: 2D lid-driven cavity with non-constant velocity-dependent dynamic viscosity is considered. A DFNN is trained to predict dynamic viscosity fields from velocity fields. The performance of the physics-integrated ML is compared with "classical" ML framework, when a DFNN is directly trained on the available data (fields of dynamic viscosity). Both frameworks showed similar accuracy; however, despite its complexity and computational cost, the physics-integrated ML offers principal advantages, namely: (i) the target outputs (labeled training data) for a DFNN might be unknown and can be recovered using the knowledge base (PDEs); (ii) it is not necessary to extract and preprocess information (training targets) from big data, instead it can be extracted by PDEs; (iii) there is no need to employ a physics-or scale-separation assumptions to build a closure model for PDEs. The advantage (i) is demonstrated in this paper, while the advantages (ii) and (iii) are the subjects for future work. Such integration of PDEs with ML opens a door for a tighter data-knowledge connection, which may potentially influence the further development of the physics-based modelling with ML for data-driven thermal fluid models.
Day 3 Wed, February 23, 2022, 2022
Utilization of neural networks to solve physical problems has been receiving wide attention recently. These neural networks are commonly named physics-informed neural network (PINN), in which the physics are employed through the governing partial differential equations (PDEs). Traditional PINNs suffer from unstable performance when dealing with flow problems in highly heterogeneous domains. This work presents the applicability of the extended PINN (XPINN) method in solving heterogeneous problems. XPINN can create a full solution model to the solution of the governing PDEs by training the neural network on the PDEs and its constraints such as boundary and initial conditions, and known solution points. The heterogeneous problem is solved by performing domain decomposition, which divides the original heterogeneous domain into various homogeneous sub-domains. Each sub-domain incorporates its own PINN structure. The different PINNs are connected through interface conditions, allowing for...