  Reaction-diffusion systems are ubiquitous in nature and in engineering
applications, and are often modeled using a non-linear system of governing
equations. While robust numerical methods exist to solve them, deep
learning-based reduced ordermodels (ROMs) are gaining traction as they use
linearized dynamical models to advance the solution in time. One such family of
algorithms is based on Koopman theory, and this paper applies this numerical
simulation strategy to reaction-diffusion systems. Adversarial and gradient
losses are introduced, and are found to robustify the predictions. The proposed
model is extended to handle missing training data as well as recasting the
problem from a control perspective. The efficacy of these developments are
demonstrated for two different reaction-diffusion problems: (1) the
Kuramoto-Sivashinsky equation of chaos and (2) the Turing instability using the
Gray-Scott model.
