As a promising candidate for future wireless systems, large intelligent surfaces (LISs) recently emerged to serve considerate improvements in both spectral and energy efficiencies. These surfaces consist of large numbers of passive elements capable of intelligently reflecting the incident signals. Since the LIS employs passive elements, critical challenges are inherent in the channel training/estimation process in order to properly design the LIS reflection matrices. One challenge particularly is how to acquire the channel knowledge with low training overhead and power consumption solutions. In this paper, we first propose an energy-efficient novel LIS architecture where all the LIS elements are passive except few non-uniformly distributed active elements (connected to the baseband). Then, we develop an efficient solution to design the LIS reflection matrices, with negligible training overhead, leveraging deep learning tools. Given what we call environment descriptors, the LIS has the ability to learn the optimal LIS reflection matrices. The simulation results show that the developed solution can approach the optimal upper bound, when only a small fraction of the LIS elements are active, yielding a promising solution for LIS systems from both energy efficiency and training overhead perspectives.