The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture is used to learn the underlying physical behaviour of fluid flows. The network is used to infer the solution of flow simulations, which will be shown for a wide range of generic channel flow simulations. Physical meaningful quantities can be computed on the obtained solution, e.g. the total pressure difference or the forces on the objects. A Spatial Transformer Network with thin-plate-splines is used for the interaction between the physical constraints and the geometric representation of the objects. Thus, a transformation from an initial to a target geometry is performed such that the object is fulfilling the given constraints. This method is fully differentiable i.e., gradient informations can be used for the transformation. This can be seen as an inverse design process. The advantage of this method over many other proposed methods is, that the physical constraints are based on the inferred flow field solution. Thus, we have a transferable model which can be applied to varying problem setups and is not limited to a given set of geometry parameters or physical quantities.
翻译：神经网络与物理方程式的相互作用具有广泛的应用范围。 我们提供了一种方法, 使神经网络能够转换受物理限制的物体。 因此, U- Net 结构被用来学习流体流的基本物理行为。 网络用来推断流体模拟的解决方案, 它将为广泛的通用通道流模拟而显示。 物理上有意义的数量可以在获得的解决方案上计算, 例如, 总压力差异或物体的强度。 一个带有薄模版线的空间变形器网络, 用于物体物理限制和几何表示的相互作用。 因此, 从初始向目标的几何测量进行转换, 使对象能够满足给定的制约。 这个方法完全不同, 即, 梯度信息可以用来进行变换。 这可以被看作是一个反向的设计过程。 这个方法的优势在于, 物理上的制约基于推断流场解决方案。 因此, 我们有一个可应用的可转移模型, 用于不同的问题设置, 并且不局限于一定的物理参数 。
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