Learning of physical systems: from inference to control

To characterize a physical system to behave as desired, either its underlying governing rulesmust be known a priori or the system itself be accurately measured. The complexity of fullmeasurements of the system scales with its size. When exposed to real-world conditions, suchas perturbations or time-varying settings, the system calibrated for a fixed working conditionmight require non-trivial re-calibration, a process that could be prohibitively expensive, inefficientand impractical for real-world use cases.In this thesis, a learning procedure for solving highly ill-posed problems of modeling a system'sforward and backward response functions is proposed. In particular, deep neural networksare used to infer the input of a system from partial measurements of its outputs or to obtain adesired target output from a physical system.I showcase the applicability of the proposed methods for inference and control in opticalmultimode fibers. Amplitude/phase-encoded input of a multimode fiber is reconstructedfrom intensity-only measurements of the outputs. Conversely, the required input of the fiberfor 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 probabilisticneural network. The model is used to optimize the input stimuli so as to find the simplestspatiotemporal patterns that elicit the same neuronal spike responses as those elicited byhigh-dimensional stimuli.As demonstrated in this thesis, application of data-driven methods for characterization ofcomplex 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.