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.
翻译:我们提出一个端到端框架,学习部分差异方程式,将初始数据生成、边界条件选择以及物理学知情神经操作员的使用结合起来,解决物理学现象研究和建模中普遍存在的部分差异方程式。我们首先表明,我们的方法复制了文献中其他地方出版的其他神经操作员的准确性和性能,以学习1D波方程式和1D汉堡方程式。随后,我们运用物理学知情神经操作员学习新型方程式,包括2D布尔格方程式在标语、视线和矢量类型中的预测。最后,我们表明,我们的方法也适用于学习2D线性和非线性浅水方程式的物理,这涉及三个相伴的部分差异方程式。我们发布了我们的人工智能模拟和科学软件,以产生初步数据和边界条件,研究广泛的物理动机情景。我们提供了源代码、一个互动网站,以直观地显示我们的物理学知情神经操作员预测,以及用于科学数据和学习枢纽的辅导。