  Physics-informed neural networks allow models to be trained by physical laws
described by general nonlinear partial differential equations. However,
traditional architectures struggle to solve more challenging time-dependent
problems due to their architectural nature. In this work, we present a novel
physics-informed framework for solving time-dependent partial differential
equations. Using only the governing differential equations and problem initial
and boundary conditions, we generate a latent representation of the problem's
spatio-temporal dynamics. Our model utilizes discrete cosine transforms to
encode spatial frequencies and recurrent neural networks to process the time
evolution. This efficiently and flexibly produces a compressed representation
which is used for additional conditioning of physics-informed models. We show
experimental results on the Taylor-Green vortex solution to the Navier-Stokes
equations. Our proposed model achieves state-of-the-art performance on the
Taylor-Green vortex relative to other physics-informed baseline models.

Computational Physics;Artificial Intelligence