DeepSeek vs. ChatGPT: Who’s Winning the AI Race in Scientific Computing?

Introduction: The AI Showdown in Science

AI-powered chatbots like ChatGPT and DeepSeek have taken the world by storm, making everyday tasks like writing, coding, and problem-solving easier. But when it comes to solving high-level scientific and mathematical problems, how well do these large language models (LLMs) actually perform?

That’s exactly what a new research study set out to answer. The authors compared ChatGPT o3-mini-high and DeepSeek R1, two of the most advanced AI models designed for reasoning, in tough mathematical and scientific machine learning tasks. The results? ChatGPT o3-mini-high consistently delivered faster, more accurate solutions.

This blog post dives into how these AI models stack up in different scientific computing challenges and what their strengths and weaknesses mean for researchers and engineers.

Why This Matters: AI in Scientific Computing

LLMs are more than just chatbots—they’re being integrated into scientific workflows, from solving complex equations to training deep-learning models. The ability of AI to handle these tasks efficiently could revolutionize fields like physics, engineering, and biomedical research.

But there’s a catch: scientific problems require extreme accuracy, logical consistency, and deep reasoning. A single mistake in an AI-generated solution could lead to completely wrong results. That’s why evaluating these models on real-world scientific tasks is so important.

The AI Contenders: ChatGPT vs. DeepSeek

The study analyzed four different AI models from OpenAI and DeepSeek:

1. ChatGPT 4o – A general-purpose AI model with strong reasoning and coding skills.
2. ChatGPT o3-mini-high – A more compact but efficient model optimized for scientific and mathematical reasoning.
3. DeepSeek V3 – A broad-based AI model trained across multiple domains, including math and coding.
4. DeepSeek R1 – A specialized AI model fine-tuned for logical reasoning and structured problem-solving.

The key question: Can these models tackle high-level scientific computing challenges, and if so, which one does it best?

Experiment 1: Solving Stiff Equations in Chemistry

The first challenge focused on solving the Robertson chemical reaction problem, a notoriously stiff system of ordinary differential equations (ODEs). These equations are tricky because they require implicit numerical methods to solve accurately.

How did the AI models perform?
- ChatGPT o3-mini-high and DeepSeek R1 recognized the challenge and correctly implemented implicit methods.
- The other two models, ChatGPT 4o and DeepSeek V3, failed, using explicit methods that led to unstable solutions.

🔹 Winner: ChatGPT o3-mini-high, which not only solved the problem correctly but also implemented an adaptive time-stepping method for efficiency.

Experiment 2: Cracking Partial Differential Equations

Next, the researchers threw a 2D Poisson equation at the AI models. This type of mathematical problem appears frequently in engineering and physics simulations.

• DeepSeek models tended to rely on more iterative methods, while ChatGPT models used traditional finite difference techniques.
• DeepSeek R1 made crucial mistakes in the signs and scales of its calculations, leading to worse performance.
• ChatGPT o3-mini-high again showed superior speed and accuracy.

🔹 Winner: ChatGPT o3-mini-high, delivering the best combination of speed and precision.

Experiment 3: The Finite Element Method Struggle

One of the biggest challenges in numerical computing is applying the finite element method (FEM) to structural mechanics problems like beam equations.

Unfortunately:
- None of the models fully succeeded.
- Reasoning-optimized models (DeepSeek R1 and ChatGPT o3-mini-high) performed better, suggesting AI is on the right path but still not ready to replace human engineers in this area.

🔹 No clear winner here, but ChatGPT o3-mini-high again had fewer mistakes than the rest.

Experiment 4: AI Tackles Machine Learning Tasks

Aside from traditional numerical methods, the researchers also tested AI models in scientific machine learning, including:
- Training neural networks for image recognition (using the MNIST dataset).
- Physics-informed neural networks (PINNs) for solving equations directly with machine learning.
- Deep Operator Networks (DeepONet) for learning function-space mappings.

What happened?
- All models performed well in image recognition.
- Only ChatGPT o3-mini-high successfully implemented PINNs for solving physics problems 💡.
- DeepSeek R1 excelled in training DeepONets, but ChatGPT o3-mini-high still had the best balance of accuracy and efficiency.

🔹 Winner: ChatGPT o3-mini-high for its stronger problem-solving flexibility in scientific machine learning tasks.

Experiment 5: Cracking Complex Integrals

An integral equation with a singularity (a tricky computational problem) was another major test. The models needed to apply a mathematical transformation before using numerical quadrature.

• DeepSeek V3 failed outright by using an inappropriate built-in function.
• Other models transformed the integral correctly and used Gaussian quadrature methods.
• ChatGPT o3-mini-high achieved the most accurate results.

🔹 Winner: You guessed it—ChatGPT o3-mini-high.

Overall Results: The Verdict

Looking at all experiments, it's clear that ChatGPT o3-mini-high came out on top.

✅ More consistently correct solutions
✅ Faster response times
✅ Better at adapting solutions to each specific problem

DeepSeek R1 had some success, especially in neural operator learning, but its overall performance was weaker, and it made crucial mathematical mistakes in several cases. Non-reasoning models (DeepSeek V3 and ChatGPT 4o) struggled the most, making basic errors and failing to recognize problem complexity.

Key Takeaways

1. AI models are getting better at advanced scientific tasks, but reasoning-optimized models like ChatGPT o3-mini-high and DeepSeek R1 outperform general-purpose ones.

2. ChatGPT o3-mini-high is the most reliable AI model for scientific computing, consistently delivering faster and more accurate results.

3. While AI can assist in complex physics and engineering problems, it still makes mistakes—especially in applying advanced mathematical methods.

4. Scientific researchers using AI need to verify results carefully, as LLMs still struggle with mathematical reasoning in high-stakes applications.

Final Thoughts

So, should scientists and engineers start relying on AI models for complex scientific computing tasks? Not yet, but we’re getting closer.

Clearly, OpenAI and DeepSeek are locked in an intense battle to dominate the AI reasoning space, especially in scientific and mathematical applications. If AI continues improving at this pace, human researchers could soon have incredibly powerful assistants to tackle the toughest mathematical and computational challenges. 🚀

That’s the future we’re heading toward—but for now, always double-check AI solutions, especially in science!

What do you think? Have you used AI assistants for technical problem-solving? Share your experience in the comments below! ⬇️