  Solving partial differential equations (PDEs) in Euclidean space with
closed-form symbolic solutions has long been a dream for mathematicians.
Inspired by deep learning, Physics-Informed Neural Networks (PINNs) have shown
great promise in numerically solving PDEs. However, since PINNs essentially
approximate solutions within the continuous function space, their numerical
solutions fall short in both precision and interpretability compared to
symbolic solutions. This paper proposes a novel framework: a closed-form
\textbf{Sym}bolic framework for \textbf{PDE}s (SymPDE), exploring the use of
deep reinforcement learning to directly obtain symbolic solutions for PDEs.
SymPDE alleviates the challenges PINNs face in fitting high-frequency and
steeply changing functions. To our knowledge, no prior work has implemented
this approach. Experiments on solving the Poisson's equation and heat equation
in time-independent and spatiotemporal dynamical systems respectively
demonstrate that SymPDE can provide accurate closed-form symbolic solutions for
various types of PDEs.
