# ChatGPT for Programming Numerical Methods

arXiv: https://arxiv.org/abs/2303.12093 · HTML: https://mlsanity.com/paper/2303.12093/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 74 references that are in the map.
- First posted on arXiv 21 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [A Categorical Archive of ChatGPT Failures](https://mlsanity.com/paper/2302.03494/) (2023)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [An Analysis of the Automatic Bug Fixing Performance of ChatGPT](https://mlsanity.com/paper/2301.08653/) (2023)
- [ChatGPT Prompt Patterns for Improving Code Quality, Refactoring, Requirements Elicitation, and Software Design](https://mlsanity.com/paper/2303.07839/) (2023)
- [A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries](https://mlsanity.com/paper/2010.09469/) (2020)
- [Towards Human-Bot Collaborative Software Architecting with ChatGPT](https://mlsanity.com/paper/2302.14600/) (2023)
- [Let's have a chat! A Conversation with ChatGPT: Technology, Applications, and Limitations](https://mlsanity.com/paper/2302.13817/) (2023)
- [Point-Cloud Deep Learning of Porous Media for Permeability Prediction](https://mlsanity.com/paper/2107.14038/) (2021)

## Built on by (most cited first, 26 of 26)

- [A Systematic Study and Comprehensive Evaluation of ChatGPT on Benchmark Datasets](https://mlsanity.com/paper/2305.18486/) (2023)
- [A Survey on LLM-based Code Generation for Low-Resource and Domain-Specific Programming Languages](https://mlsanity.com/paper/2410.03981/) (2024)
- [MechAgents: Large language model multi-agent collaborations can solve mechanics problems, generate new data, and integrate knowledge](https://mlsanity.com/paper/2311.08166/) (2023)
- [Beyond Static Datasets: A Deep Interaction Approach to LLM Evaluation](https://mlsanity.com/paper/2309.04369/) (2023)
- [An Interdisciplinary Outlook on Large Language Models for Scientific Research](https://mlsanity.com/paper/2311.04929/) (2023)
- [Unlocking the Potential of ChatGPT: A Comprehensive Exploration of its Applications, Advantages, Limitations, and Future Directions in Natural Language Processing](https://mlsanity.com/paper/2304.02017/) (2023)
- [Physics-informed PointNet: On how many irregular geometries can it solve an inverse problem simultaneously? Application to linear elasticity](https://mlsanity.com/paper/2303.13634/) (2023)
- [Unreflected Acceptance -- Investigating the Negative Consequences of ChatGPT-Assisted Problem Solving in Physics Education](https://mlsanity.com/paper/2309.03087/) (2023)
- [Humans are Still Better than ChatGPT: Case of the IEEEXtreme Competition](https://mlsanity.com/paper/2305.06934/) (2023)
- [Can ChatGPT implement finite element models for geotechnical engineering applications?](https://mlsanity.com/paper/2501.02199/) (2025)
- [CFDLLMBench: A Benchmark Suite for Evaluating Large Language Models in Computational Fluid Dynamics](https://mlsanity.com/paper/2509.20374/) (2025)
- [The Unintended Consequences of Censoring Digital Technology -- Evidence from Italy's ChatGPT Ban](https://mlsanity.com/paper/2304.09339/) (2023)
- [A Misleading Gallery of Fluid Motion by Generative Artificial Intelligence](https://mlsanity.com/paper/2405.15406/) (2024)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [Unstructured and structured data: Can we have the best of both worlds with large language models?](https://mlsanity.com/paper/2304.13010/) (2023)
- [Evaluating GPT's Programming Capability through CodeWars' Katas](https://mlsanity.com/paper/2306.01784/) (2023)
- [Extracting Norms from Contracts Via ChatGPT: Opportunities and Challenges](https://mlsanity.com/paper/2404.02269/) (2024)
- [Flow Matching and Diffusion Models via PointNet for Generating Fluid Fields on Irregular Geometries](https://mlsanity.com/paper/2601.03030/) (2026)
- [When Giant Language Brains Just Aren't Enough! Domain Pizzazz with Knowledge Sparkle Dust](https://mlsanity.com/paper/2305.07230/) (2023)
- [Automated Repair of Declarative Software Specifications in the Era of Large Language Models](https://mlsanity.com/paper/2310.12425/) (2023)
- [Designing Silicon Brains using LLM: Leveraging ChatGPT for Automated Description of a Spiking Neuron Array](https://mlsanity.com/paper/2402.10920/) (2024)
- [On the robustness of ChatGPT in teaching Korean Mathematics](https://mlsanity.com/paper/2502.11915/) (2025)
- [Vision Mamba for Permeability Prediction of Porous Media](https://mlsanity.com/paper/2510.14516/) (2025)
- [NLP for Knowledge Discovery and Information Extraction from Energetics Corpora](https://mlsanity.com/paper/2402.06964/) (2024)
- [On Languaging a Simulation Engine](https://mlsanity.com/paper/2402.16482/) (2024)
- [Large language models for partial differential equation workflows](https://mlsanity.com/paper/2608.03600/) (2026)

## Abstract (arXiv)

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.