Traditional wireless network design relies on optimization algorithms derived from domain-specific mathematical models, which are often inefficient and unsuitable for dynamic, real-time applications due to high complexity. Deep learning has emerged as a promising alternative to overcome complexity and adaptability concerns, but it faces challenges such as accuracy issues, delays, and limited interpretability due to its inherent black-box nature. This paper introduces a novel approach that integrates optimization theory with deep learning methodologies to address these issues. The methodology starts by constructing the block diagram of the optimization theory-based solution, identifying key building blocks corresponding to optimality conditions and iterative solutions. Selected building blocks are then replaced with deep neural networks, enhancing the adaptability and interpretability of the system. Extensive simulations show that this hybrid approach not only reduces runtime compared to optimization theory based approaches but also significantly improves accuracy and convergence rates, outperforming pure deep learning models.

Radio Frequency Energy Harvesting (RF-EH) networks are key enablers of massive Internet-ofthings by providing controllable and long-distance energy transfer to energy-limited devices. Relays, helping either energy or information transfer, have been demonstrated to significantly improve the performance of these networks. We first obtain the optimal solution to the scheduling and power control problem for the given relay selection. Then, the relay selection problem is formulated as a classification problem, for which two convolutional neural network (CNN) based architectures are proposed. While the first architecture employs conventional 2D convolution blocks and benefits from skip connections between layers; the second architecture replaces them with inception blocks, to decrease trainable parameter size without sacrificing accuracy for memory-constraint applications. To decrease the runtime complexity further, teacher-student learning is employed such that the teacher network is larger, and the student is a smaller size CNN-based architecture distilling the teacher's knowledge. A novel dichotomous searchbased algorithm is employed to determine the best architecture for the student network. Our simulation results demonstrate that the proposed solutions provide lower complexity than the state-of-art iterative approaches without compromising optimality. A. G. Onalan and S. Coleri are with the Department of Electrical and Electronics Engineering, and B.Kopru is with Department of Computer Engineering, Koc University, 34450, Istanbul, Turkey e-mail: {aonalan17, bkopru17, scoleri}@ku.edu.tr. Sinem Coleri acknowledges the support of the Scientific and Technological Research Council of Turkey 2247-A National Leaders Research Grant #121C314. Energy Harvesting (EH) is a promising alternative to fixed power supplies (e.g., batteries) for energy-constrained Internet-of-Things (IoT) applications, such as smart cities and wearable devices [1], by enabling the net-zero energy objective of sixth generation (6G) mobile networks [2]. The use cases and feasibility of wireless-powered IoT have been investigated in many standardization bodies, including IEEE 802.11 [3] and 3GPP [4]. Radio Frequency (RF) signals are preferred over other energy sources such as vibration and sun due to their independence from climate conditions, accessibility, and more predictable nature [5]. RF-EH network design follows two main protocols: Simultaneous Information and Power Transfer (SWIPT), in which power and information are sent simultaneously, and Wireless Powered Communication Networks (WPCN), in which power and information are sent consecutively in downlink (DL) and uplink (UL) [6].