Self-assembly formation is a key research topic for realizing practical applications in swarm robotics. Due to its inherent complexity, designing high-performance self-assembly formation strategies and proposing corresponding macroscopic models remain formidable challenges and present an open research frontier. Taking inspiration from crystallization, this paper introduces a distributed self-assembly formation strategy by defining free, moving, growing, and solid states for robots. Robots in these states can spontaneously organize into user-specified two-dimensional shape formations with lattice structures through local interactions and communications. To address the challenges posed by complex spatial structures in modeling a macroscopic model, this work introduces the structural features estimation method. Subsequently, a corresponding non-spatial macroscopic model is developed to predict and analyze the self-assembly behavior, employing the proposed estimation method and a stock and flow diagram. Real-robot experiments and simulations validate the flexibility, scalability, and high efficiency of the proposed self-assembly formation strategy. Moreover, extensive experimental and simulation results demonstrate the model’s accuracy in predicting the self-assembly process under different conditions. Model-based analysis indicates that the proposed self-assembly formation strategy can fully utilize the performance of individual robots and exhibits strong self-stability.

In the digital twin modeling of aero-engine turbine blades, traditional CFD requires extensive computational time. Existing data-driven models also struggle to achieve multi-physics decoupling and high-accuracy predictions with extremely small sample constraints. To overcome these challenges, a multitask generative adversarial network (M-GAN) is proposed for multi-physics digital twin modeling. By incorporating a multi-branch attention mechanism into the U-Net generator, this method achieves the decoupling and prediction of multi-physics fields. Additionally, a multi-objective adaptive loss optimization strategy based on uncertainty weighting is proposed to mitigate gradient interference and mode collapse during the joint training of multiple coupled physical fields. Based on the proposed M-GAN, a high-performance digital twin model for turbine blades is developed using only 10 training samples, achieving accurate predictions of pressure, temperature, and airflow angle fields. The test results demonstrate that, on a test set comprising 90 different operating conditions, the average prediction error across all physical fields is only 1.85%, indicating strong cross-physics prediction capability, generalization, and robustness. This approach provides a solid algorithmic foundation for real-time, high-precision mapping in turbine blade digital twin systems.