Using deep learning to learn physics of conduction heat transfer

Edalatifar, Mohammad; Tavakoli, Mohammad Bagher; Ghalambaz, Mohammad; Setoudeh, Farbod

doi:10.1007/s10973-020-09875-6

Cited by 58 publications

(14 citation statements)

References 30 publications

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“…[15] Used the Finite volume method to discretize the Laplace equation and generated 100000 different cases of 19 elements of geometry and temperature values, then fed the data to a 21-neuron network to solve the temperature distribution problem. [4] Introduced Mean of the maximum of square error MMaSE as loss function for the steady-state heat transfer problem, then used data sets of different geometries to train the convolutional autoencoder network to infer the Laplace equation's solution without an iterative computational step.…”

Section: Related Workmentioning

confidence: 99%

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DiffusionNet: Accelerating the solution of Time-Dependent partial differential equations using deep learning

Asem

2020

Preprint

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We present our deep learning framework to solve and accelerate the Time-Dependent partial differential equation's solution of one and two spatial dimensions. We demonstrate DiffusionNet solver by solving the 2D transient heat conduction problem with Dirichlet boundary conditions. The model is trained on solution data calculated using the Alternating direction implicit method. We show the model's ability to predict the solution from any combination of seven variables: the starting time step of the solution, initial condition, four boundary conditions, and a combined variable of the time step size, diffusivity constant, and grid step size. To improve speed, we exploit our model capability to predict the solution of the Time-dependent PDE after multiple time steps at once to improve the speed of solution by dividing the solution into parallelizable chunks. We try to build a flexible architecture capable of solving a wide range of partial differential equations with minimal changes. We demonstrate our model flexibility by applying our model with the same network architecture used to solve the transient heat conduction to solve the Inviscid Burgers equation and Steady-state heat conduction, then compare our model performance against related studies. We show that our model reduces the error of the solution for the investigated problems.

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Section: Related Workmentioning

confidence: 99%

“…We use data provided by [4] , which is composed of different geometries solutions of the Laplace equation. The data is composed of 64 × 64 images, the input image has two channels, and the output has one channel.…”

Section: Steady State Heat Conductionmentioning

confidence: 99%

DiffusionNet: Accelerating the solution of Time-Dependent partial differential equations using deep learning

Asem

2020

Preprint

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“…Similarly, deep neural networks (DNNs) have been introduced to serve as regression models by enforcing temperature prediction into an image-to-image regression problem. For instance, the fully connected neural network(FCNN) models Zakeri et al (2019), the fully convolutional neural networks Edalatifar et al (2021), the conditional generative adversarial networks Farimani et al (2017) and others Chen et al (2021). Especially, Chen et al Chen et al (2020) proposed a new deep learning surrogate-assisted heat source layout optimization method, using the feature pyramid network Lin et al (2017) as the surrogate model to evaluate thermal performance accurately under different input layouts.…”

Section: Introductionmentioning

confidence: 99%

A physics and data co-driven surrogate modeling approach for temperature field prediction on irregular geometric domain

Bao¹,

Wen²,

Zhang³

et al. 2022

Preprint

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In the whole aircraft structural optimization loop, thermal analysis plays a very important role. But it faces a severe computational burden when directly applying traditional numerical analysis tools, especially when each optimization involves repetitive parameter modification and thermal analysis followed. Recently, with the fast development of deep learning, several Convolutional Neural Network (CNN) surrogate models have been introduced to overcome this obstacle. However, for temperature field prediction on irregular geometric domains (TFP-IGD), CNN can hardly be competent since most of them stem from processing for regular images. To alleviate this difficulty, we propose a novel physics and data co-driven surrogate modeling method. First, after adapting the Bezier curve in geometric parameterization, a body-fitted coordinate mapping is introduced to generate coordinate transforms between the irregular physical plane and regular computational plane. Second, a physics-driven CNN surrogate with partial differential equation (PDE) residuals as a loss function is utilized for fast meshing (meshing surrogate); then, we present a data-driven surrogate model based on the multi-level reduced-order method, aiming to learn solutions of temperature field in the above regular computational plane (thermal surrogate). Finally, combining the grid position information provided by the meshing surrogate with the scalar temperature field information provided by the thermal surrogate (combined model), we reach an end-to-end surrogate model from geometric parameters to temperature field prediction on an irregular geometric domain. Numerical results demonstrate that our method can significantly improve accuracy prediction on a smaller dataset while reducing the training time when compared with other CNN methods.

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“…The ML techniques shows promising results, specifically in genomics [4,5], public health [6,11,12,13,14], and medicine [7,8,9,10], both are becoming more significant in our aging societies. Deep neural networks (DNNs), as one of the most prominent tools of ML, have been adopted to tackle various physics problems including turbulence [15], flow control [16], heat transfer [17], and combustion [18]. These deep learning applications have grown drastically in recent years, mainly on learning physical equations and inferring dynamics.…”

Section: Introductionmentioning

confidence: 99%

BubbleNet: Inferring micro-bubble dynamics with semi-physics-informed deep learning

Zhai,

Zhou,

2021

Preprint

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Micro-bubbles and bubbly flows are widely observed and applied to medicine, involves deformation, rupture, and collision of bubbles, phase mixture, etc. We study bubble dynamics by setting up two numerical simulation cases: bubbly flow with a single bubble and multiple bubbles, both confined in the microtube, with parameters corresponding to their medical backgrounds. Both the cases have their medical background applications. Multiphase flow simulation requires high computation accuracy due to possible component losses that may be caused by sparse meshing during the computation. Hence, data-driven methods can be adopted as a useful tool. Based on physics-informed neural networks (PINNs), we propose a novel deep learning framework BubbleNet, which entails three main parts: deep neural networks (DNN) with sub nets for predicting different physics fields; the physics-informed part, with the fluid continuum condition encoded within; the time discretized normalizer (TDN), an algorithm to normalize field data per time step before training. We apply the traditional DNN and our BubbleNet to train the simulation data and predict the physics fields of both the two bubbly flow cases. Results indicate our framework can predict the physics fields more accurately, estimating the prediction absolute errors. The proposed network can potentially be applied to many other engineering fields.

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Using deep learning to learn physics of conduction heat transfer

Cited by 58 publications

References 30 publications

DiffusionNet: Accelerating the solution of Time-Dependent partial differential equations using deep learning

DiffusionNet: Accelerating the solution of Time-Dependent partial differential equations using deep learning

A physics and data co-driven surrogate modeling approach for temperature field prediction on irregular geometric domain

BubbleNet: Inferring micro-bubble dynamics with semi-physics-informed deep learning

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