Trick or treat? Evaluating stability strategies in graph network-based simulators

Particle-based simulators are ubiquitous in science and engineering, but some are expensive both in terms of time and compute. In simulations where local interactions play a major role, graph network-based simulators (GNS) show promise to address these issues due to their ability to model local interactions and relationships through the graph structure. However, their autoregressive nature makes them susceptible to distribution shifts. Numerous strategies, or tricks, have been proposed to address this issue. In this work, we evaluate three of them: adding a random walk to the input, taking the loss of a sequence, and the pushforward trick. We find that these tricks fail to address the underlying problem, even when the dynamics are relatively simple.