Multi-agent reinforcement learning (MARL) requires effective coordination among multiple decision-making agents to achieve joint goals. Approaches based on a global value function face the curse of dimensionality, while fully decomposed centralized training with decentralized execution (CTDE) methods often suffer from relative overgeneralization. Coordination graphs mitigate this issue but typically fail to capture dynamic collaboration patterns that evolve over time and across tasks. We propose Dynamic Deep Factor Graphs (DDFG), a value decomposition algorithm that represents the global value via factor graphs and learns graph structures on the fly through a graph-generation policy, adapting to evolving inter-agent relations. We provide a theoretical upper bound on the approximation error of high-order decompositions and reveal how the maximum order $D$D trades off accuracy against computation, offering guidance for balancing performance and cost. Using max-sum for inference, DDFG efficiently derives joint policies. Experiments on higher-order predator-prey and SMAC show consistent gains over strong value-decomposition baselines, demonstrating improved sample efficiency and robustness in complex settings.

In this paper, we introduce a novel cooperative target tracking algorithm, namely the quantum-inspired belief propagation, aimed at rectifying the limitations observed in existing localization algorithms employed in multi-target cooperative tracking scenarios. Leveraging the principles of quantum superposition, our algorithm seeks to alleviate the uncertainty inherent in message fusion within belief propagation frameworks, thereby enhancing the accuracy and stability of multi-target cooperative localization. The utilization of the quantum Monte Carlo method facilitates the simulation of the message distribution process, with quantum particles embodying the superposition of multiple states concurrently. This approach effectively addresses the intractable integrations encountered in message updating on factor graphs, rendering the algorithm agnostic to the number of particles involved. Moreover, quantum unitary transformations and quantum black-box operations are deployed to encode factor graph function nodes for the propagation of quantum messages. This innovation surmounts the challenge posed by traditional factor graph function nodes’ inability to process quantum messages. Experimental findings corroborated the superiority of the proposed algorithm in terms of accuracy and robustness.

Material data forms the foundation of the Industrial Internet of Things (IIoT). The rapid advancement of big data technology has opened up new opportunities for material research and development, ushering in the era of data-driven paradigms. As the cornerstone for material genetic engineering technology, the material big data platform is expanding its data scale and facing an increasing demand for sharing in light of the continuous progress and widespread application of big data technology. However, this development also poses security challenges, including the risks of data leakage and tampering. To address these challenges, this article focuses on the National Materials Genetic Engineering Discrete Data Exchange Platform (MGED). It leverages blockchain technology to design a secure material big-data storage and sharing architecture, S-MBDA, ensuring the security and reliability of the material’s big data platform. Additionally, a verifiable retrieval scheme based on a two-layer index structure of bitmap and MPT tree is proposed to enhance the efficiency of blockchain-based retrieval. This scheme aims to guarantee the integrity of retrieval data while achieving efficient and accurate searches across heterogeneous data sources. Through integrating blockchain technology and adopting a novel retrieval scheme, the article presents a comprehensive approach to secure material data storage, sharing, and retrieval. The proposed architecture and scheme address the critical security concerns associated with material big data platforms and contribute to the efficient and accurate retrieval of heterogeneous data.