  We propose a platform based on neural networks to solve the image-to-image
translation problem in the context of squeeze flow of micro-droplets. In the
first part of this paper, we present the governing partial differential
equations to lay out the underlying physics of the problem. We also discuss our
developed Python package, sqflow, which can potentially serve as free,
flexible, and scalable standardized benchmarks in the fields of machine
learning and computer vision. In the second part of this paper, we introduce a
residual convolutional neural network to solve the corresponding inverse
problem: to translate a high-resolution (HR) imprint image with a specific
liquid film thickness to a low-resolution (LR) droplet pattern image capable of
producing the given imprint image for an appropriate spread time of droplets.
We propose a neural network architecture that learns to systematically tune the
refinement level of its residual convolutional blocks by using the function
approximators that are trained to map a given input parameter (film thickness)
to an appropriate refinement level indicator. We use multiple stacks of
convolutional layers the output of which is translated according to the
refinement level indicators provided by the directly-connected function
approximators. Together with a non-linear activation function, such a
translation mechanism enables the HR imprint image to be refined sequentially
in multiple steps until the target LR droplet pattern image is revealed. The
proposed platform can be potentially applied to data compression and data
encryption. The developed package and datasets are publicly available on GitHub
at https://github.com/sqflow/sqflow.
