A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems
This work addresses pattern synthesis in reaction-diffusion systems, which is important for applications in materials science and biology, but it appears incremental as it builds on existing formal methods and optimization techniques.
The authors tackled the problem of detecting and generating patterns in reaction-diffusion systems by developing a novel spatial superposition logic with efficient learning from examples and model checking. They demonstrated that their approach performs well on test data and integrated it with particle swarm optimization to synthesize parameters for desired patterns.
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned image. We show that formulas in this logic can be efficiently learned from positive and negative examples of several types of patterns. We also demonstrate that pattern detection, which is implemented as a model checking algorithm, performs very well for test data sets different from the learning sets. We define a quantitative semantics for the logic and integrate the model checking algorithm with particle swarm optimization in a computational framework for synthesis of parameters leading to desired patterns in reaction-diffusion systems.