Learning Macroscopic Dynamics without Reconstructing Microscopic States

Zhichao Han, Yue Zhao, Qianxiao Li

Modeling the temporal evolution of macroscopic properties of complex systems is an important scientific task. To predict this evolution without full microscopic simulation, a common approach encodes microstates into compact latent states, learns their evolution, and reads out macroscopic predictions from the latent trajectory. These latent states are often learned through microstate reconstruction. However, with limited latent capacity, reconstruction can favor high-variance microscopic details over information needed for macroscopic prediction. Yet jointly learning latent states and their transition without reconstruction often fails to obtain latent dynamics that support accurate macroscopic prediction. We show that this failure can arise from latent scale collapse: shrinking the latent state scale reduces training loss while macroscopic evolution error remains large. Here, we propose a reconstruction-free framework to learn latent states with their dynamics for prescribed macroscopic prediction. Training alternates between updating the latent representation with the transition and next-state latent targets fixed, and updating the transition with the latent representation…