PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers

Understand

With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs.

• Physics-informed neural networks (PINNs) have recently emerged and succeeded in various forward and inverse PDE problems thanks to their excellent properties, such as flexibility, mesh-free solutions, and unsupervised training.
• However, their slower convergence speed and relatively inaccurate solutions often limit their broader applicability in many science and engineering domains.
• This paper proposes a new kind of data-driven PDEs solver, physics-informed cell representations (PIXEL), elegantly combining classical numerical methods and learning-based approaches.