We present an end-to-end framework to learn partial differential equations
that brings together initial data production, selection of boundary conditions,
and the use of physics-informed neural operators to solve partial differential
equations that are ubiquitous in the study and modeling of physics phenomena.
We first demonstrate that our methods reproduce the accuracy and performance of
other neural operators published elsewhere in the literature to learn the 1D
wave equation and the 1D Burgers equation. Thereafter, we apply our
physics-informed neural operators to learn new types of equations, including
the 2D Burgers equation in the scalar, inviscid and vector types. Finally, we
show that our approach is also applicable to learn the physics of the 2D linear
and nonlinear shallow water equations, which involve three coupled partial
differential equations. We release our artificial intelligence surrogates and
scientific software to produce initial data and boundary conditions to study a
broad range of physically motivated scenarios. We provide the source code, an
interactive website to visualize the predictions of our physics informed neural
operators, and a tutorial for their use at the Data and Learning Hub for
Science.

本文提出了一种端到端的框架，用于学习偏微分方程，首先通过物理感知神经算子实现了 1D 波动方程和 1D Burgers 方程的准确性和性能，并将其用于更多新的方程类型，以及在学习 2D 线性和非线性浅水方程中的应用。