A Novel CNN-Based Poisson Solver for Fluid Simulation

Xiao, Xiangyun; Zhou, Yanqing; Wang, Hui; Yang, Xubo

doi:10.1109/tvcg.2018.2873375

Cited by 42 publications

(36 citation statements)

References 39 publications

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“…The idea was first developed by Yang et al [26] using MLP. Xiao et al [27] used a CNN to solve the Poisson equation on large computational domains combining a physical and a supervised MSE loss function. Similarly, Özbay [28], resolve the Poisson equation with two coupled convolutional neural networks.…”

Section: Introductionmentioning

confidence: 99%

Towards an hybrid computational strategy based on Deep Learning for incompressible flows

Ajuria-Illaramendi

Alguacil

Bauerheim

et al. 2020

Aiaa Aviation 2020 Forum

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The Poisson equation is present in very different domains of physics and engineering. In most cases, this equation can not be solved directly and iterative solvers are used. For many solvers, this step is computationally intensive. In this study, an alternative resolution method based on neural networks is evaluated for incompressible flows. A fluid solver coupled with a Convolutional Neural Network is developed and trained on random cases with constant density to predict the pressure field. Its performance is tested in a plume configuration, with different buoyancy forces, parametrized by the Richardson number. The neural network is compared to a traditional Jacobi solver. The performance improvement is considerable, although the accuracy of the network is found to depend on the flow operating point: low errors are obtained at low Richardson numbers, whereas the fluid solver becomes unstable with large errors for large Richardson number. Finally, a hybrid strategy is proposed in order to benefit from the calculation acceleration while ensuring a user-defined accuracy level. In particular, this hybrid CFD-NN strategy, by maintaining the desired accuracy whatever the flow condition, makes the code stable and reliable even at large Richardson numbers for which the network was not trained for. This study demonstrates the capability of the hybrid approach to tackle new flow physics, unseen during the network training.

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Section: Introductionmentioning

confidence: 99%

Towards an hybrid computational strategy based on Deep Learning for incompressible flows

Ajuria-Illaramendi

Alguacil

Bauerheim

et al. 2020

Aiaa Aviation 2020 Forum

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“…In the fluid mechanics community, works of Tompson et al (2016) and Xiao et al (2018) pioneered the usage of CNNs to solve the Poisson equation. While both use their models within the framework of a complete CFD solver to simulate the motion of smoke plumes around objects, the architectures used and training methodologies are different.…”

Section: Cnns and The Poisson Equationmentioning

confidence: 99%

Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh

Özbay

Hamzehloo

Laizet

et al. 2021

DCE

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The Poisson equation is commonly encountered in engineering, for instance, in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the present work, we propose a novel fully convolutional neural network (CNN) architecture to infer the solution of the Poisson equation on a 2D Cartesian grid with different resolutions given the right-hand side term, arbitrary boundary conditions, and grid parameters. It provides unprecedented versatility for a CNN approach dealing with partial differential equations. The boundary conditions are handled using a novel approach by decomposing the original Poisson problem into a homogeneous Poisson problem plus four inhomogeneous Laplace subproblems. The model is trained using a novel loss function approximating the continuous $ {L}^p $ norm between the prediction and the target. Even when predicting on grids denser than previously encountered, our model demonstrates encouraging capacity to reproduce the correct solution profile. The proposed model, which outperforms well-known neural network models, can be included in a CFD solver to help with solving the Poisson equation. Analytical test cases indicate that our CNN architecture is capable of predicting the correct solution of a Poisson problem with mean percentage errors below 10%, an improvement by comparison to the first step of conventional iterative methods. Predictions from our model, used as the initial guess to iterative algorithms like Multigrid, can reduce the root mean square error after a single iteration by more than 90% compared to a zero initial guess.

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“…It means that at each combination of a, b, and H 0 = |H 0 |, the neural network is trained to solve the direct (forward) problem. In the neural network based model, the excitation field is assumed to be H 0 (see Equation (16)), while 0 is zero. 100 training points have distributed inside the domain (0; 0.05) m.…”

Section: Inverse B − H Curve Identification Of Carbon Steel Aisi 4140mentioning

confidence: 99%

“…The inductor's current was monitored with a Rogowski coil, while the surface temperature of the billet, in the central part of the inductor, has been measured by a thermocouple. From the current value and the inductor topology, an estimation of H 0 (excitation field), needed for Equation (16), is obtained. The used material properties are: electrical resistivity 35E−08 Ωm (at 200 • C), B-H curve with a = 270 and b = 0.577, thermal conductivity 41 W/m K (at 200 • C), specific heat 500 J/kg • C (at 200 • C), density 7800 kg/m 3 [43].…”

Section: An Electromagnetic-thermal Coupled Analysis For Induction Hementioning

confidence: 99%

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Solving 1D non‐linear magneto quasi‐static Maxwell's equations using neural networks

Baldan

Nacke

2021

IET Science Measure & Tech

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Electromagnetics (EM) can be described, together with the constitutive laws, by four PDEs, called Maxwell's equations. "Quasi-static" approximations emerge from neglecting particular couplings of electric and magnetic field related quantities. In case of slowly time varying fields, if inductive and resistive effects have to be considered, whereas capacitive effects can be neglected, the magneto quasi-static (MQS) approximation applies. The solution of the MQS Maxwell's equations, traditionally obtained with finite differences and elements methods, is crucial in modelling EM devices. In this paper, the applicability of an unsupervised deep learning model is studied in order to solve MQS Maxwell's equations, in both frequency and time domain. In this framework, a straightforward way to model hysteretic and anhysteretic non-linearity is shown. The introduced technique is used for the field analysis in the place of the classical finite elements in two applications: on the one hand, the B-H curve inverse determination of AISI 4140, on the other, the simulation of an induction heating process. Finally, since many of the commercial FEM packages do not allow modelling hysteresis, it is shown how the present approach could be further adopted for the inverse magnetic properties identification of new magnetic flux concentrators for induction applications. Recently, deep learning emerges as a powerful technique in many applications, including computer vision, speech recognition, natural language process, and bioinformatics. There is This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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A Novel CNN-Based Poisson Solver for Fluid Simulation

Cited by 42 publications

References 39 publications

Towards an hybrid computational strategy based on Deep Learning for incompressible flows

Towards an hybrid computational strategy based on Deep Learning for incompressible flows

Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh

Solving 1D non‐linear magneto quasi‐static Maxwell's equations using neural networks

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