Smooth and Sparse Latent Dynamics in Operator Learning with Jerk Regularization
This work addresses the need for more efficient and accurate spatiotemporal modeling in scientific and engineering applications, though it is incremental as it builds on existing operator learning methods.
The paper tackled the problem of suboptimal compression and limited extrapolation in data-driven reduced-order models for spatiotemporal forecasting by introducing a continuous operator learning framework with jerk regularization, which improved accuracy and convergence speed in a 2D unsteady flow problem.
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 limited extrapolation ability over time. To address these issues, this paper introduces a continuous operator learning framework that incorporates jerk regularization into the learning of the compressed latent space. This jerk regularization promotes smoothness and sparsity of latent space dynamics, which not only yields enhanced accuracy and convergence speed but also helps identify intrinsic latent space coordinates. Consisting of an implicit neural representation (INR)-based autoencoder and a neural ODE latent dynamics model, the framework allows for inference at any desired spatial or temporal resolution. The effectiveness of this framework is demonstrated through a two-dimensional unsteady flow problem governed by the Navier-Stokes equations, highlighting its potential to expedite high-fidelity simulations in various scientific and engineering applications.