High-fidelity simulation of spatiotemporal dynamics is computationally prohibitive, necessitating efficient super-resolution techniques to reconstruct high-resolution data from coarse-grained inputs. Traditional data-driven methods often lack physical constraints, and simple physics-informed learning struggles with irregular spatial geometries and intricately evolving temporal dynamics. To tackle these challenges, we propose a Physics-augmented Koopman-enhanced Graph Convolutional Network (P-K-GCN) for spatiotemporal super-resolution on irregular geometries. Specifically, a continuous spline-based GCN is first designed to extract spatial dependencies directly from coarse graph, and Koopman operator theory is incorporated to project the nonlinear dynamics into a compact latent space where temporal progression is linearized. Second, we augment the optimization objective with a physics-based loss to force the data-driven reconstructions to adhere to physical laws for improving predictive fidelity and robustness. Finally, we provide a rigorous theoretical analysis, establishing that the physics augmentation and Koopman regularization mathematically guarantees a reduction in super-resolution error by diminishing Rademacher complexity and tightening generalization bounds. We evaluate our framework on reconstructing spatially high-resolution cardiac electrodynamics across a 3D heart geometry from sparse low-resolution measurements. Numerical experiments demonstrate that our method achieves superior accuracy compared to baseline models.
Automated medical report generation, MRG, holds substantial value for alleviating radiologist workload and enhancing diagnostic efficiency. However, mainstream approaches typically treat diverse chest abnormalities as isolated classification targets. This paradigm often overlooks inherent disease co-occurrences and struggles to translate medical topological structures into explicit data correlations, constraining the model's reasoning capacity on complex or subtle lesions. To address this, we propose a Graph-Augmented Dual-Stream Medical Report Generation with Topological Internalization, GDMRG. Our framework introduces a Topological Knowledge Internalization module, TKI, which leverages a Graph Convolutional Network, GCN, to generate an explicit parameterized weight matrix based on global disease co-occurrence priors. This facilitates efficient topological knowledge injection without relying on external retrieval mechanisms. Building upon this, we construct a dual-stream classification system: the main branch generates discrete diagnostic prompts under topological constraints, while the auxiliary branch employs an asymmetric optimization strategy to dynamically calibrate decision boundaries for highly imbalanced samples. Concurrently, to establish a logical closed loop between diagnosis and visual grounding, we design a diagnostic-driven Diagnosis-Guided Spatial Attention, DGSA, that utilizes high-dimensional clinical semantics to recalibrate the visual encoder, mitigating feature hallucinations. Comprehensive experiments on the MIMIC-CXR dataset demonstrate that GDMRG achieves competitive clinical efficacy, CE, while maintaining natural language fluency. Furthermore, our model exhibits robust zero-shot generalization on the IU X-Ray dataset. In summary, this work presents an integrated and interpretable paradigm for medical report generation.