In cyber-physical systems governed by nonlinear partial differential equations (PDEs), real-time control is often limited by sparse sensor data and high-dimensional system dynamics. Deep reinforcement learning (DRL) has shown promise for controlling such systems, but training DRL agents directly on full-order simulations is computationally intensive. This paper presents a sensor-driven, non-intrusive reduced-order modeling (NIROM) framework called FAE-CAE-LSTM, which combines convolutional and fully connected autoencoders with a long short-term memory (LSTM) network. The model compresses high-dimensional states into a latent space and captures their temporal evolution. A DRL agent is trained entirely in this reduced space, interacting with the surrogate built from sensor-like spatiotemporal measurements, such as pressure and velocity fields. A CNN-MLP reward estimator provides data-driven feedback without requiring access to governing equations. The method is tested on benchmark systems including Burgers’ equation, the Kuramoto–Sivashinsky equation, and flow past a circular cylinder; accuracy is further validated on flow past a square cylinder. Experimental results show that the proposed approach achieves accurate reconstruction, robust control, and significant computational speedup over traditional simulation-based training. These findings confirm the effectiveness of the FAE-CAE-LSTM surrogate in enabling real-time, sensor-informed, scalable DRL-based control of nonlinear dynamical systems.

Purpose: Wireless sensor networks (WSNs) consist of multiple sensor nodes that are often randomly distributed in the environment and operate independently without human intervention. However, the limited power supply of these nodes presents a significant challenge for WSNs, making the development of energy-saving algorithms critical to increase network lifespan. Node clustering is a commonly used solution to reduce data transfer nodes and achieve data aggregation. Furthermore, the mobility of nodes in the network is often overlooked but can impact energy consumption. Design/methodology/approach: This study proposes a Dynamic Dual Head Clustering algorithm for WSNs (DDHCWSN) to reduce energy consumption. Instead of re-clustering in each round, the DDHCWSN updates existing clusters based on energy and position, allowing normal nodes to send data to the closest cluster head (CH) node. The algorithm considers two CHs, one for data aggregation and the other for sending data to the base station (BS), which can have a better effect on network power consumption. Findings: To evaluate the proposed method and compare it with state-of-the-art methods in the field of WSN clustering, three different criteria (scalability, network energy consumption and network lifetime) in six different scenarios are considered. According to the obtained results, it can be said that the proposed algorithm shows acceptable behavior in networks with low density, unlike other algorithms. In large networks, DDHCWSN has a longer lifetime than others. Although in small networks, CRDP and DMH-Leach algorithm performed better, but DDHCWSN also performed well. Originality/value: The main topics of the proposed algorithm are: (1) Dividing the network into different areas and then generating clusters based on them. (2) Using two separate CHs, one to communicate with members of cluster (data aggregation) and the other to communicate with other CHs and BSs. (3) Updating clusters instead of re-clustering nodes. (4) Select single or multi-hop mode.