Physics Consistency and Latent Dynamics in Spatiotemporal Physics Field Generation

Data-driven models for spatiotemporal physical field generation, such as flow and acoustic fields, often deviate from governing equations and lack interpretability in latent temporal dynamics. To address these challenges, we propose HMT-PF, a hybrid Mamba-Transformer architecture for physical field generation. The framework incorporates a query-based gradient computation mechanism and a physics-informed fine-tuning strategy to enhance physical consistency. Analysis of the latent space reveals that the initial latent state vector evolves as an autonomous dynamical system under the Mamba backbone. Principal component analysis (PCA) indicates that a small number of dominant modes in initial latent state vector govern the key evolution patterns of the physical field, while a Jacobian-based temporal sensitivity analysis characterizes the intrinsic dynamical structure and stability of the latent evolution. Experiments across five benchmark datasets demonstrate strong performance, and physics-informed fine-tuning further reduces physical residuals, highlighting the effectiveness of the proposed latent-level fusion strategy. An empirical scaling law between prediction error and physical residual is identified, revealing a consistent exponential relationship in the low-error regime. Based on this observation, an dual-metric framework is proposed to jointly evaluate numerical accuracy and physical realism.