  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. We adopt a grid structure from
the numerical methods to improve accuracy and convergence speed and overcome
the spectral bias presented in PINNs. Moreover, the proposed method enjoys the
same benefits in PINNs, e.g., using the same optimization frameworks to solve
both forward and inverse PDE problems and readily enforcing PDE constraints
with modern automatic differentiation techniques. We provide experimental
results on various challenging PDEs that the original PINNs have struggled with
and show that PIXEL achieves fast convergence speed and high accuracy. Project
page: https://namgyukang.github.io/PIXEL/
