Learning to predict large-scale system changes without detailed simulations
Learning Macroscopic Dynamics without Reconstructing Microscopic States
Machine Learning
Summary
Predicting how big systems change over time usually needs simulating every tiny part, which is very slow. The authors found that trying to guess big-picture changes by first recreating every small part can miss what really matters. They propose a new way that skips the tiny details and directly learns how big-picture features change. This method avoids common training problems and predicts large-scale behavior better in examples like disease spread and particle mixing.
What this means in practice
- •For epidemic modelers: Predict how disease spreads across populations faster without simulating every individual.
- •For chemical process engineers: Model the mixing of particle species in reactors by focusing on large-scale characteristics instead of particle-level details.
Authors
Zhichao Han, Yue Zhao, Qianxiao Li
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.