A Combined Data-driven and Physics-driven Method for Steady Heat Conduction Prediction using Deep Convolutional Neural Networks

• URL: http://arxiv.org/abs/2005.08119v1
• Date: Sat, 16 May 2020 22:29:37 GMT
• Title: A Combined Data-driven and Physics-driven Method for Steady Heat Conduction Prediction using Deep Convolutional Neural Networks
• Authors: Hao Ma and Xiangyu Hu and Yuxuan Zhang and Nils Thuerey and Oskar J. Haidn
• Abstract summary: We propose a combined-driven method for learning acceleration and more accurate solutions. For the data-driven based method, the introduction of physical equation not only is able to speed up the convergence, but also produces physically more consistent solutions. For the physics-driven based method, it is observed that the combined method is able to speed up the convergence up to 49.0% by using a not very restrictive coarse reference.
• Score: 39.46616349629182
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: With several advantages and as an alternative to predict physics field, machine learning methods can be classified into two distinct types: data-driven relying on training data and physics-driven using physics law. Choosing heat conduction problem as an example, we compared the data- and physics-driven learning process with deep Convolutional Neural Networks (CNN). It shows that the convergences of the error to ground truth solution and the residual of heat conduction equation exhibit remarkable differences. Based on this observation, we propose a combined-driven method for learning acceleration and more accurate solutions. With a weighted loss function, reference data and physical equation are able to simultaneously drive the learning. Several numerical experiments are conducted to investigate the effectiveness of the combined method. For the data-driven based method, the introduction of physical equation not only is able to speed up the convergence, but also produces physically more consistent solutions. For the physics-driven based method, it is observed that the combined method is able to speed up the convergence up to 49.0\% by using a not very restrictive coarse reference.

Related papers

• Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations [0.0]
  We present a method that employs physics-informed deep learning techniques for solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase contrast. We benchmark our methodology against the standard finite element method, demonstrating accurate yet faster predictions.
  arXiv  Detail & Related papers  (2024-01-04T17:01:54Z)
• Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks [68.8204255655161]
  We introduce a technique with which it is possible to learn approximate solutions to the steady-state Navier--Stokes equations in varying geometries without the need of parametrization. The results of our physics-aware CNN are compared to a state-of-the-art data-based approach.
  arXiv  Detail & Related papers  (2023-08-04T05:09:06Z)
• Neural Operator: Is data all you need to model the world? An insight into the impact of Physics Informed Machine Learning [13.050410285352605]
  We provide an insight into how data-driven approaches can complement conventional techniques to solve engineering and physics problems. We highlight a novel and fast machine learning-based approach to learning the solution operator of a PDE operator learning.
  arXiv  Detail & Related papers  (2023-01-30T23:29:33Z)
• Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations [62.81701992551728]
  We present a physics-informed framework for solving time-dependent partial differential equations. Our model utilizes discrete cosine transforms to encode spatial and recurrent neural networks. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations.
  arXiv  Detail & Related papers  (2022-02-24T20:46:52Z)
• Numerical Approximation in CFD Problems Using Physics Informed Machine Learning [0.0]
  The thesis focuses on various techniques to find an alternate approximation method that could be universally used for a wide range of CFD problems. The focus stays over physics informed machine learning techniques where solving differential equations is possible without any training with computed data. The extreme learning machine (ELM) is a very fast neural network algorithm at the cost of tunable parameters.
  arXiv  Detail & Related papers  (2021-11-01T22:54:51Z)
• Physical Gradients for Deep Learning [101.36788327318669]
  We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. We propose a novel hybrid training approach that combines higher-order optimization methods with machine learning techniques.
  arXiv  Detail & Related papers  (2021-09-30T12:14:31Z)
• DeepPhysics: a physics aware deep learning framework for real-time simulation [0.0]
  We propose a solution to simulate hyper-elastic materials using a data-driven approach. A neural network is trained to learn the non-linear relationship between boundary conditions and the resulting displacement field. The results show that our network architecture trained with a limited amount of data can predict the displacement field in less than a millisecond.
  arXiv  Detail & Related papers  (2021-09-17T12:15:47Z)
• Conditional physics informed neural networks [85.48030573849712]
  We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. We show that a single deep neural network can learn the solution of partial differential equations for an entire class of problems.
  arXiv  Detail & Related papers  (2021-04-06T18:29:14Z)
• Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations [79.71184760864507]
  This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA) In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. We show that the new method class has characteristics not found in previous alignment methods.
  arXiv  Detail & Related papers  (2020-09-28T15:05:39Z)
• Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem [0.0]
  We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The proposed methodology is a simple and elegant way to instill physical knowledge to machine-learning algorithms.
  arXiv  Detail & Related papers  (2020-01-15T08:20:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.