ChatGPT is a large language model recently released by the OpenAI company. In this technical report, we explore for the first time the capability of ChatGPT for programming numerical algorithms. Specifically, we examine the capability of GhatGPT for generating codes for numerical algorithms in different programming languages, for debugging and improving written codes by users, for completing missed parts of numerical codes, rewriting available codes in other programming languages, and for parallelizing serial codes. Additionally, we assess if ChatGPT can recognize if given codes are written by humans or machines. To reach this goal, we consider a variety of mathematical problems such as the Poisson equation, the diffusion equation, the incompressible Navier-Stokes equations, compressible inviscid flow, eigenvalue problems, solving linear systems of equations, storing sparse matrices, etc. Furthermore, we exemplify scientific machine learning such as physics-informed neural networks and convolutional neural networks with applications to computational physics. Through these examples, we investigate the successes, failures, and challenges of ChatGPT. Examples of failures are producing singular matrices, operations on arrays with incompatible sizes, programming interruption for relatively long codes, etc. Our outcomes suggest that ChatGPT can successfully program numerical algorithms in different programming languages, but certain limitations and challenges exist that require further improvement of this machine learning model.

翻译：ChatGPT是OpenAI公司最近发布的一种大型语言模型。在本技术报告中，我们首次探索了ChatGPT在数值算法编程中的能力。具体而言，我们考察了ChatGPT在以下方面的表现：用不同编程语言生成数值算法代码、调试和改进用户编写的代码、补全数值代码的缺失部分、将现有代码重写为其他编程语言、以及串行代码的并行化。此外，我们还评估了ChatGPT是否能识别给定代码是由人类还是机器编写的。为实现这一目标，我们考虑了多种数学问题，例如泊松方程、扩散方程、不可压缩纳维-斯托克斯方程、可压缩无粘流、特征值问题、线性方程组求解、稀疏矩阵存储等。此外，我们还举例说明了科学机器学习方法，如物理信息神经网络和卷积神经网络在计算物理中的应用。通过这些例子，我们研究了ChatGPT的成功之处、失败案例及其面临的挑战。失败案例包括生成奇异矩阵、数组尺寸不兼容的操作、以及较长代码的编程中断等。我们的结果表明，ChatGPT能够成功用不同编程语言编写数值算法，但存在某些局限性和挑战，需要进一步改进这一机器学习模型。