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

2025/09/09 by Robert Stephany, Youngsoo Choi, Stephany, Robert +1 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Model Reduction and Neural Networks #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2509.08191

openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Latent Space Dynamics Identification for Interface Tracking with Application to Shock-Induced Pore Collapse
• mLaSDI: Multi-stage latent space dynamics identification
• Physics-informed active learning with simultaneous weak-form latent space dynamics identification
• A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
• tLaSDI: Thermodynamics-informed latent space dynamics identification
• Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulations
• Weak-Form Latent Space Dynamics Identification
• GPLaSDI: Gaussian Process-based interpretable Latent Space Dynamics Identification through deep autoencoder
• Language Models are Few-Shot Learners
• Universal Differential Equations for Scientific Machine Learning
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Attention Is All You Need
• Data-driven discovery of partial differential equations
• Deep Residual Learning for Image Recognition
• ImageNet classification with deep convolutional neural networks
• The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows

Cited by

• Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives

Related

• Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives
• A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
• Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers
• mLaSDI: Multi-stage latent space dynamics identification
• Sequential decoder training for improved latent space dynamics identification