Propagation models are essential for modeling and simulating dynamic processes such as epidemics and information diffusion. However, existing tools struggle to scale to large-scale graphs that emerge across social networks, epidemic networks and so on, due to limited algorithmic efficiency, weak scalability, and high communication overhead. We present FS_GPlib, a unified library that enables efficient, high-fidelity propagation modeling on Web-scale graphs. FS_GPlib introduces a dual-acceleration framework: it combines micro-level synchronous message-passing updates with macro-level batched Monte Carlo simulation, leveraging high-dimensional tensor operations for parallel execution. To further enhance scalability, it supports distributed simulation via a novel target-node-based graph partitioning strategy that minimizes communication overhead while maintaining load balance. Theoretically, we show that under ideal assumptions, the runtime of simulations converges approximately to a constant. Extensive experiments demonstrate up to 35,000× speedup over standard libraries such as NDlib and execution of a full Monte Carlo simulation on a Web-scale (billion-edge) graph in 11 seconds while maintaining high simulation fidelity. FS_GPlib supports 29 propagation models—including epidemic and opinion dynamics and dynamic network models—and offers a lightweight Python API compatible with mainstream data science ecosystems. By addressing the unique challenges of modeling diffusion and cascades on the Web, FS_GPlib provides a scalable, extensible, and theoretically grounded solution for large-scale propagation analysis in epidemiology, social media analysis, and online network dynamics. Code available at: https://github.com/Allen-Ciel/FS_GPlib.

Inferring latent interaction structures from observational time series is a fundamental yet challenging problem in dynamical systems. Existing deep learning methods employ unidirectional information aggregation via incoming edges, failing to identify the mutual dependencies prevalent in real dynamics as well as the feedback effects induced by sampling intervals, which leads to inferential bias. To address this, we propose the D ual- A ttention R elational I nference (DARI), a framework designed to learn latent interaction structures from dynamical observations. DARI employs a coupled bidirectional attention mechanism to model forward and feedback dynamics, effectively decoupling information flow from the underlying interaction structure. Extensive synthetic experiments demonstrate competitive structural recovery performance across diverse graph topologies, including undirected, directed, and weighted graphs. Experiments on COVID-19 data further show that the inferred transmission structures are consistent with real-world population mobility patterns. In addition, the elimination of costly edge-wise computations in DARI leads to substantial gains in both runtime and memory efficiency. Code is available at https://anonymous.4open.science/r/DARI-778C .