Enhancing the predictability and retrodictability of stochastic processes

Scientific inference involves obtaining the unknown properties or behavior of a system in the light of what is known, typically, without changing the system. Here we propose an alternative to this approach: a system can be modified in a targeted way, preferably by a small amount, so that its properties and behavior can be inferred more successfully. For the sake of concreteness we focus on inferring the future and past of Markov processes and illustrate our method on two classes of processes: diffusion on random spatial networks, and thermalizing quantum systems.