To characterize a physical system to behave as desired, either its underlying governing rules must be known a priori or the system itself be accurately measured. The complexity of full measurements of the system scales with its size. When exposed to real-world conditions, such as perturbations or time-varying settings, the system calibrated for a fixed working condition might require non-trivial re-calibration, a process that could be prohibitively expensive, inefficient and impractical for real-world use cases. In this thesis, a learning procedure for solving highly ill-posed problems of modeling a system's forward and backward response functions is proposed. In particular, deep neural networks are used to infer the input of a system from partial measurements of its outputs or to obtain a desired target output from a physical system. I showcase the applicability of the proposed methods for inference and control in optical multimode fibers. Amplitude/phase-encoded input of a multimode fiber is reconstructed from intensity-only measurements of the outputs. Conversely, the required input of the fiber for projecting a desired output is obtained using intensity-only measurements of the output. Next, the stochastic neural network of the retina in Salamander is modeled by a probabilistic neural network. The model is used to optimize the input stimuli so as to find the simplest spatiotemporal patterns that elicit the same neuronal spike responses as those elicited by high-dimensional stimuli. As demonstrated in this thesis, application of data-driven methods for characterization of complex large-scale real-world systems has proved useful in simplifying the measurement apparatus, end-to-end optimization of the system and automatic compensation of perturbation.