When to Aggregate: Delay-Aware Message Scheduling with Physics-Motivated Operator Decomposition for Dynamics Prediction

Graph neural networks have become a core paradigm for dynamics prediction by explicitly modeling spatial interactions among entities. Most existing approaches rely on synchronous message passing, in which all graph components are updated at every propagation layer. Although effective, this paradigm couples propagation depth with interaction-update frequency: increasing the processor depth not only expands the receptive field but also forces every local interaction to undergo additional transformations. This coupling can be undesirable for autoregressive dynamics, where different interactions may evolve at different rates. In this paper, we propose an asynchronous graph propagation scheme that regulates message aggregation by activating only a subset of edges at each layer. This edge-level mechanism enables information to propagate in a staggered manner, decoupling update frequency from propagation depth without modifying the underlying model architecture. It is model-agnostic and can be integrated into existing message-passing neural networks with minimal implementation effort. We further reinterpret graph propagation as the numerical integration of edge-local and node-local physics-motivated generators and decompose the latent dynamics into complementary operators. Extensive experiments across diverse benchmarks show that asynchronous propagation and operator decomposition consistently improve forecasting accuracy.