DeepSeek vs. ChatGPT vs. Claude: A Comparative Study for Scientific Computing and Scientific Machine Learning Tasks

TL;DR

This study compares DeepSeek, ChatGPT, and Claude, including their reasoning-optimized versions, in solving scientific computing and PDE problems, highlighting the superior performance of reasoning models.

Contribution

It provides a comprehensive evaluation of advanced LLMs for scientific computing tasks, emphasizing the impact of reasoning capabilities on performance.

Findings

Reasoning models outperform non-reasoning models in complex tasks.

ChatGPT o3-mini-high offers the fastest reasoning speed.

Hybrid-reasoning models show consistent and significant advantages.

Abstract

Large Language Models (LLMs) have emerged as powerful tools for tackling a wide range of problems, including those in scientific computing, particularly in solving partial differential equations (PDEs). However, different models exhibit distinct strengths and preferences, resulting in varying levels of performance. In this paper, we compare the capabilities of the most advanced LLMs--DeepSeek, ChatGPT, and Claude--along with their reasoning-optimized versions in addressing computational challenges. Specifically, we evaluate their proficiency in solving traditional numerical problems in scientific computing as well as leveraging scientific machine learning techniques for PDE-based problems. We designed all our experiments so that a non-trivial decision is required, e.g. defining the proper space of input functions for neural operator learning. Our findings show that reasoning and hybrid-reasoning models consistently and significantly outperform non-reasoning ones in solving challenging problems, with ChatGPT o3-mini-high generally offering the fastest reasoning speed.