Constrained Image Generation Using Binarized Neural Networks with Decision Procedures
This addresses the challenge of computationally expensive PDE solving in image generation for materials science applications, though it appears incremental as it applies existing methods to a new domain.
The paper tackled the problem of generating binary images with specific topological and process constraints for applications like porous media in lithium-ion batteries, by using a binarized neural network to approximate a PDE solver and encoding the problem as a logical formula, resulting in the ability to produce random constrained images that satisfy both sets of constraints.
We consider the problem of binary image generation with given properties. This problem arises in a number of practical applications, including generation of artificial porous medium for an electrode of lithium-ion batteries, for composed materials, etc. A generated image represents a porous medium and, as such, it is subject to two sets of constraints: topological constraints on the structure and process constraints on the physical process over this structure. To perform image generation we need to define a mapping from a porous medium to its physical process parameters. For a given geometry of a porous medium, this mapping can be done by solving a partial differential equation (PDE). However, embedding a PDE solver into the search procedure is computationally expensive. We use a binarized neural network to approximate a PDE solver. This allows us to encode the entire problem as a logical formula. Our main contribution is that, for the first time, we show that this problem can be tackled using decision procedures. Our experiments show that our model is able to produce random constrained images that satisfy both topological and process constraints.