Learning Macroscopic Dynamics without Reconstructing Microscopic States

2026-09-29

AI Summary

This study addresses the challenge that, under limited latent variable capacity, microstate reconstruction induces information loss for macroscopic prediction, while joint training is prone to scale collapse. To overcome these issues, this work proposes a reconstruction-free framework that learns system dynamics by alternately updating latent representations and transition models, enabling direct recursive prediction of macroscopic evolution from initial microstates. Theoretically, it elucidates the mechanism of reconstruction misalignment, proves the occurrence of scale collapse, and establishes sufficient conditions for local convergence. Empirically, the proposed approach achieves significantly superior macroscopic prediction accuracy over baseline methods across diverse complex systems, including epidemic spreading, particle mixing, and polymer stretching.

Abstract

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 fixed. At inference, the trained model predicts macroscopic states recursively from an initial microstate. Our theoretical analysis characterizes reconstruction misalignment and scale collapse under joint training, and gives a sufficient condition for local convergence to correct latent dynamics for our method. Experiments on epidemic spreading on a lattice, mixing of two particle species, and polymer stretching demonstrate that the proposed method achieves substantially better macroscopic prediction over baselines.

Problem

• macroscopic dynamics
• latent representation
• scale collapse
• complex systems
• reconstruction-free

Innovation

• Macroscopic Dynamics
• Latent Scale Collapse
• Reconstruction-free Learning
• Alternating Training
• Latent Representation