# Rollout-LaSDI: Enhancing the long-term accuracy of Latent Space Dynamics

arXiv: https://arxiv.org/abs/2509.08191 · HTML: https://mlsanity.com/paper/2509.08191/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Blessing of dimensionality: mathematical foundations of the statistical physics of data](https://mlsanity.com/paper/1801.03421/) (2018)
- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder](https://mlsanity.com/paper/2308.05882/) (2023)
- [tLaSDI: Thermodynamics-informed latent space dynamics identification](https://mlsanity.com/paper/2403.05848/) (2024)
- [A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling](https://mlsanity.com/paper/2403.10748/) (2024)
- [Weak-Form Latent Space Dynamics Identification](https://mlsanity.com/paper/2311.12880/) (2023)
- [Physics-informed active learning with simultaneous weak-form latent space dynamics identification](https://mlsanity.com/paper/2407.00337/) (2024)
- [Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulations](https://mlsanity.com/paper/2312.01021/) (2023)
- [mLaSDI: Multi-stage latent space dynamics identification](https://mlsanity.com/paper/2506.09207/) (2025)

## Built on by (most cited first, 2 of 2)

- [Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives](https://mlsanity.com/paper/2512.15997/) (2025)
- [Rollout-Decoded Reconstruction for Long-Horizon Prediction in Latent World Models](https://mlsanity.com/paper/2608.25017/) (2026)

## Abstract (arXiv)

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast approximations. While modern ROMs can solve parameterized families of PDEs, their predictive power degrades over long time horizons. We address this by (1) introducing a flexible, high-order, yet inexpensive finite-difference scheme and (2) proposing a Rollout loss that trains ROMs to make accurate predictions over arbitrary time horizons. We demonstrate our approach on the 2D Burgers equation.