论文标题
使用深卷积神经网络的稳定热传导预测的数据驱动和物理驱动的方法
A Combined Data-driven and Physics-driven Method for Steady Heat Conduction Prediction using Deep Convolutional Neural Networks
论文作者
论文摘要
有了几种优势，作为预测物理领域的替代方法，可以将机器学习方法归类为两种不同的类型：数据驱动的依赖于训练数据和使用物理法进行的物理驱动。选择热传导问题为例，我们将数据和物理驱动的学习过程与深卷积神经网络（CNN）进行了比较。它表明，误差与地面真相解决方案的融合和热传导方程的残留表现出显着的差异。基于此观察结果，我们提出了一种组合驱动的方法，用于学习加速和更准确的解决方案。通过加权损失功能，参考数据和物理方程能够同时推动学习。进行了几个数值实验以研究合并方法的有效性。对于基于数据驱动的方法，物理方程的引入不仅能够加快收敛速度，而且还会产生物理上更一致的解决方案。对于基于物理驱动的方法，观察到合并的方法能够使用不太限制的粗略参考来加快收敛速度高达49.0 \％。
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.
