  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.
