The prevalence of partial differential equations (PDEs) in modeling physics and the low speeds of numerical solvers demands more efficient solving methods. For this purpose, machine learning based methods have been proposed, but these are typically discrete, difficult to interpret and require large amounts of ground truth data to train. To address these issues, we propose a novel machine learning based solver that builds upon advancements in Gaussian based reconstruction. Our method represents the solution to a time-dependent target PDE purely in terms of Gaussians, making it completely continuous and meshless. These Gaussians are evolved by means of an autoregressive neural network that is applied to each Gaussian, integrating information from a local neighborhood of Gaussians. This enables the change of position, scale, rotation and value of the Gaussians to model the solution in a particle-like manner. Extensive experiments show the potential for Gaussians to model arbitrary physical phenomena. We also compare our approach to ground truth data and various state of the art methods, which demonstrates that the method performs well on short-term prediction, but does not match the state of the art for long-term prediction.