Learning and controlling phase separation in complex geometries with differentiable physics

Phase separation is ubiquitous in nature and has recently become a major research interest due to its role in many essential processes in biological cells. While many models have been developed to describe this phenomena, systematic methods to incorporate data into the models and control phase separation are lacking. Here, starting with general theories from nonequilibrium thermodynamics, we write a differentiable physics simulator using adjoint methods for phase separation that can be used in learning, optimization, and control applications. In addition to differentiability with respect to bulk model parameters, the simulation can also be differentiated with respect to boundary condition parameters, time-dependent control parameters, and shape parameters. We utilize this framework to demonstrate how models of phase separation can be learned from noisy data. We also demonstrate optimizing the length of phase boundaries by changing the shape of the simulation domain. Finally, we show how to learn control procedures for boundary conditions in order to manipulate the motion of the separated phases. While we focus on these three specific examples, our approach is general to learning models for phase separation and controlling the dynamics of phase separation for engineering application.