AI/Machine learning in fluid mechanics, engineering, physics

AI/Machine learning in fluid mechanics, engineering, physics

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AI/Machine learning in fluid mechanics, engineering, physics
AI/Machine learning in fluid mechanics, engineering, physics
Code Example: Discovering Equations from Raw Data with ML

Code Example: Discovering Equations from Raw Data with ML

Re-discovering Bernoulli's equation - what next?

Justin Hodges, PhD's avatar
Justin Hodges, PhD
Jun 30, 2025
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AI/Machine learning in fluid mechanics, engineering, physics
AI/Machine learning in fluid mechanics, engineering, physics
Code Example: Discovering Equations from Raw Data with ML
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🚨Spoiler: I think the highlight of this post is the code example I provide which re-discovers Bernoulli’s equation. Enjoy the hands-on example!


Although this conversation took place 8 years ago, I still remember it in vivid detail. It was 2017 in the last week of my internship in Princeton for AI/CFD research and I was at the coffee machine with my mentor. Who, fortunately for me, is one of the smartest people i’ve ever met and was tremendously lucky to learn from him.

Essentially, he was sharing all his wild dreams for fun and interesting AI projects he would carry out if he had the bandwidth. We weren’t really focusing on turbulence modeling all that often, but since we both had some background with it, that’s where our conversations often gravitated in our free time. In this chat, he was talked about how perhaps there would be some other form which better describes the nature of turbulence than the ones we had. Further, what if we could (with enough data) learn the form and structure of new equations to describe turbulence in addition to what we currently have. It was purely a fun ‘what if’ conversation, but we did spend some time in there talking about ways AI could be used.

Well, on this rainy Sunday from Orlando, I am happy to share with you a blog focused on this field in machine learning dedicated to discovering equations from raw data. I wrote a step-by-step hands-on example whereby we ‘re-discover’ Bernoulli equation from raw data, which I think is just plain fun and the highlight of the blog. As always, I will share related publications (summarizing and sharing PDF files) and learning resources that are super focused and practical.

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