  We introduce a novel grid-independent model for learning partial differential
equations (PDEs) from noisy and partial observations on irregular
spatiotemporal grids. We propose a space-time continuous latent neural PDE
model with an efficient probabilistic framework and a novel encoder design for
improved data efficiency and grid independence. The latent state dynamics are
governed by a PDE model that combines the collocation method and the method of
lines. We employ amortized variational inference for approximate posterior
estimation and utilize a multiple shooting technique for enhanced training
speed and stability. Our model demonstrates state-of-the-art performance on
complex synthetic and real-world datasets, overcoming limitations of previous
approaches and effectively handling partially-observed data. The proposed model
outperforms recent methods, showing its potential to advance data-driven PDE
modeling and enabling robust, grid-independent modeling of complex
partially-observed dynamic processes.
