# Learning Macroscopic Dynamics without Reconstructing Microscopic States

arXiv: https://arxiv.org/abs/2609.37392 · HTML: https://mlsanity.com/paper/2609.37392/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 40 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [VICReg: Variance-Invariance-Covariance Regularization for Self-Supervised Learning](https://mlsanity.com/paper/2105.04906/) (2021)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Data-Efficient Reinforcement Learning with Self-Predictive Representations](https://mlsanity.com/paper/2007.05929/) (2020)
- [LeWorldModel: Stable End-to-End Joint-Embedding Predictive Architecture from Pixels](https://mlsanity.com/paper/2603.19312/) (2026)
- [LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristics](https://mlsanity.com/paper/2511.08544/) (2025)
- [DeepMDP: Learning Continuous Latent Space Models for Representation Learning](https://mlsanity.com/paper/1906.02736/) (2019)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Temporal Predictive Coding For Model-Based Planning In Latent Space](https://mlsanity.com/paper/2106.07156/) (2021)
- [Bridging State and History Representations: Understanding Self-Predictive RL](https://mlsanity.com/paper/2401.08898/) (2024)
- [Goal-Aware Prediction: Learning to Model What Matters](https://mlsanity.com/paper/2007.07170/) (2020)
- [Understanding Self-Predictive Learning for Reinforcement Learning](https://mlsanity.com/paper/2212.03319/) (2022)
- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [tLaSDI: Thermodynamics-informed latent space dynamics identification](https://mlsanity.com/paper/2403.05848/) (2024)
- [Generalization capabilities of translationally equivariant neural networks](https://mlsanity.com/paper/2103.14686/) (2021)
- [Predictive Coding for Locally-Linear Control](https://mlsanity.com/paper/2003.01086/) (2020)
- [Constructing Custom Thermodynamics Using Deep Learning](https://mlsanity.com/paper/2308.04119/) (2023)
- [Continuity-Preserving Convolutional Autoencoders for Learning Continuous Latent Dynamical Models from Images](https://mlsanity.com/paper/2502.00754/) (2025)
- [Learning Macroscopic Dynamics from Partial Microscopic Observations](https://mlsanity.com/paper/2410.23938/) (2024)
- [Maximum Likelihood Learning of Latent Dynamics Without Reconstruction](https://mlsanity.com/paper/2505.23569/) (2025)
- [Learning Permutation-invariant Macroscopic Dynamics](https://mlsanity.com/paper/2605.30812/) (2026)

## Abstract (arXiv)

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.