DeepSeek vs. ChatGPT vs. Claude: A comparative study for scientific computing and scientific machine learning tasks

• Recently developed LLMs (DeepSeek, ChatGPT, and Claude) and reasoning-optimized models are compared in solving scientific computing and machine learning problems. • Challenging problems in numerical methods, physics-informed machine learning, and operator learning are designed and tested. • Reasoning and hybrid-reasoning models perform better than non-reasoning models. • LLMs still face challenges in solving scientific problems correctly without human intervention. Large language models (LLMs) have emerged as powerful tools for addressing 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 nontrivial 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.