Flexi-Propagator For Partial Differential Equations*

We introduce a novel data-driven architecture that leverages an enhanced Variational Autoencoder (VAE) framework to predict solutions to non-linear partial differential equations (PDEs). Our method integrates an end-to-end learnable model for capturing temporal dynamics within the VAE architecture, allowing for the direct representation and evolution of the system's state in the latent space over time. A key innovation of our approach is its ability to predict the solution field for multiple future time steps in a single forward pass. This capability eliminates the need for conventional recursive one-step predictions, enhancing computational efficiency and improving prediction accuracy. We demonstrate the effectiveness of our model by learning low-dimensional representations and providing one-shot predictions for the nonlinear Burgers' equation. The model exhibits strong generalization across a broad spectrum of Reynolds numbers and time steps not encountered during training, underscoring its potential for predictive modeling in complex nonlinear dynamical systems. Additionally, the framework is extended to a parametric reduced-order model, embedding parametric information into the latent space to identify trends in system evolution.