Abstract Reliable non-destructive hardness measurement, such as using magnetic properties, is a critical requirement in industrial quality assurance and structural health monitoring, where destructive testing is impractical or economically infeasible. Despite its importance, extracting physically meaningful and predictive features from frequency-domain magnetic signals remains challenging, particularly in scenarios where annotated measurement data are scarce and expensive to obtain. In this study, the challenge of extracting physically meaningful features from limited data is addressed by proposing a complex-valued autoencoder. This architecture is designed to jointly encode magnitude and frequency information into a compact latent representation, thereby preserving phase-sensitive structural dependencies that are typically lost in standard approaches. The method was evaluated on a real-world dataset of high-strength alloys with sparse annotations. It is demonstrated that the proposed complex-valued representations yield significantly improved regression performance, characterized by lower prediction error and reduced variance compared to a classical real-valued baseline. These results indicate that leveraging the algebraic structure of complex-valued networks offers a superior approach for non-destructive testing in low-data regimes, enabling more stable and accurate industrial inspection systems.

In real decision-making scenarios involving multi-agent games, such as intelligent unmanned systems, military confrontations, and autonomous navigation, the coupling of participant strategies and the incompleteness of perceived information make the accurate inference of dynamic game trajectories a critical and challenging task. To address this problem, this paper proposes a game trajectory modeling method that integrates a cross-attention mechanism with a moving diffusion process, termed CARM-Diff (Cross-Attention Autoregressive Moving Diffusion Model). The model combines autoregressive structures with cross-attention to capture the temporal evolution of sequences while explicitly modeling strategic interactions between agents. We design a lightweight feature extraction module and, leveraging the Markov property of diffusion models, introduce a deterministic evolution process of historical states to simulate noise, thereby enhancing the model’s capability to learn local temporal patterns. Meanwhile, a cross-attention mechanism is introduced in the reverse diffusion stage to guide the model in focusing on the opponent’s historical sequential behavior, enabling more precise capture of inter-agent influences. Furthermore, we design a residual gated trajectory modeling structure that fuses the agent’s own behavioral evolution with interaction effects induced by opponents. Gating factors are dynamically generated through multilayer perceptrons to achieve adaptive information fusion. We construct a dynamic trajectory dataset based on an underwater pursuit-evasion game to validate our approach, and the proposed CARM Diff framework is generalizable to a wide range of multi-agent interactive systems. Experimental results show that CARM-Diff outperforms mainstream baseline methods in both prediction accuracy and dynamic interaction modeling, demonstrating the effectiveness and practical potential of the proposed model.