Babak Rahmani, Damien Loterie, Eirini Kakkava et al.
The output of physical systems is often accessible by measurements such as the 3D position of a robotic arm actuated by many actuators or the speckle patterns formed by shining the spot of a laser pointer on a wall. The selection of the input of such a system (actuators and the shape of the laser spot respectively) to obtain a desired output is difficult because it is an ill-posed problem i.e. there are multiple inputs yielding the same output. In this paper, we propose an approach that provides a robust solution to this dilemma for any physical system. We show that it is possible to find the appropriate input of a system that results in a desired output, despite the input-output relation being nonlinear and\or with incomplete measurements of the systems variables. We showcase our approach using an extremely ill-posed problem in imaging. We demonstrate the projection of arbitrary shapes through a multimode fiber (MMF) when a sample of intensity-only measurements are taken at the output. We show image projection fidelity as high as ~90 %, which is on par with the gold standard methods which characterize the system fully by phase and amplitude measurements. The generality as well as simplicity of the proposed approach provides a new way of target-oriented control in real-world applications.