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是由OpenAI公司最近发布的一种大型语言模型。在本技术报告中,我们首次探讨了ChatGPT在编写数值算法方面的能力。具体而言,我们考虑了ChatGPT在不同编程语言中生成数值算法代码的能力,用户编写代码的调试和改进,完善缺失的数值代码部分,将现有代码改写为其他编程语言,以及串行代码并行化的能力。此外,我们评估了ChatGPT是否能识别给定代码是由人还是由机器编写的。为实现此目标,我们考虑了多种数学问题,例如Poisson方程、扩散方程、不可压Navier-Stokes方程、可压粘性流、特征值问题、线性方程组求解、稀疏矩阵存储等。此外,我们通过物理学为基础的神经网络和卷积神经网络等科学机器学习实例进行了论证,并应用于计算物理学。通过这些例子,我们探讨了ChatGPT的成功、失败和挑战。失败的例子包括产生奇异矩阵、指定不兼容大小的数组操作、对相对较长的代码进行编程中断等。我们的研究结果表明,ChatGPT能够成功地在不同编程语言中编程数值算法,但也存在特定的局限性和挑战,需要进一步改进这种机器学习模型。