Title: Latent Space Learning for PDE Systems with Complex Boundary Conditions
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Scientific Machine Learning, Reduced-Order Modeling, Partial Differential Equations, Boundary Conditions

Abstract: Latent space Reduced Order Models (ROMs) in Scientific Machine Learning (SciML) can enhance and accelerate Partial Differential Equation (PDE) simulations. However, they often struggle with complex boundary conditions (BCs) such as time-varying, nonlinear, or state-dependent ones. Current methods for handling BCs in latent space have limitations due to representation mismatch and projection difficulty, impacting predictive accuracy and physical consistency. To address this, we introduce BAROM (Boundary-Aware Attention ROM). BAROM integrates: (1) explicit, RBM-inspired boundary treatment using a modified ansatz and a learnable lifting network for complex BCs; and (2) a non-intrusive, attention-based mechanism, inspired by Galerkin Neural Operators, to learn internal field dynamics within a POD-initialized latent space. Evaluations show BAROM achieves superior accuracy and robustness on benchmark PDEs with diverse complex BCs compared to established SciML approaches.

TL;DR: A framework that accurately and efficiently simulates complex physical systems (PDEs) by uniquely combining explicit, RBM-inspired boundary condition handling with an attention-based mechanism for learning internal field dynamics in a latent space.