Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularization

arXiv:2402.15636v1 Announce Type: new
Abstract: Spatiotemporal modeling is critical for understanding complex systems across various scientific and engineering disciplines, but governing equations are often not fully known or computationally intractable due to inherent system complexity. Data-driven reduced-order models (ROMs) offer a promising approach for fast and accurate spatiotemporal forecasting by computing solutions in a compressed latent space. However, these models often neglect temporal correlations between consecutive snapshots when constructing the latent space, leading to suboptimal compression, jagged latent trajectories, and …

abstract arxiv complexity complex systems cs.ce cs.lg cs.na data data-driven dynamics engineering forecasting math.mp math.na math-ph modeling regularization systems type understanding