  We present AROMA (Attentive Reduced Order Model with Attention), a framework
designed to enhance the modeling of partial differential equations (PDEs) using
local neural fields. Our flexible encoder-decoder architecture can obtain
smooth latent representations of spatial physical fields from a variety of data
types, including irregular-grid inputs and point clouds. This versatility
eliminates the need for patching and allows efficient processing of diverse
geometries. The sequential nature of our latent representation can be
interpreted spatially and permits the use of a conditional transformer for
modeling the temporal dynamics of PDEs. By employing a diffusion-based
formulation, we achieve greater stability and enable longer rollouts compared
to conventional MSE training. AROMA's superior performance in simulating 1D and
2D equations underscores the efficacy of our approach in capturing complex
dynamical behaviors.
