Before revision:  However, most of the existing deep learning-based methods either assume strong physics prior, or depend on specific initial and boundary conditions, or require data in dense regular grid making them inapt for modeling unknown PDEs from sparsely-observed data. This paper presents a deep learning-based collocation method for modeling dynamical systems driven by unknown PDEs when data sites are sparsely distributed .
After revision:  However, most of the existing deep learning-based methods either assume strong physics prior, or depend on specific initial and boundary conditions, or require data in a dense grid when the governing PDEs are unknown. In contrast, our method focuses on learning prediction models for unknown PDE-driven dynamics only from sparsely observed data .