Rollout-LaSDI: Enhancing the long-term accuracy of Latent Space Dynamics
This addresses the issue of long-term predictive accuracy in ROMs for computational physics, though it appears incremental as it builds on existing ROM frameworks.
The paper tackles the problem of reduced-order models (ROMs) for solving parameterized PDEs, which suffer from degraded accuracy over long time horizons, by introducing a flexible finite-difference scheme and a Rollout loss to train ROMs for accurate long-term predictions, demonstrating results on the 2D Burgers equation.
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.