Good read! I am developing PINNs at work and this certainly helped me recall important concepts. This post used deepxde library [2] to compose the PINN. Can anyone comment on how NVIDIA's modulus [2] compares to this? Modulus appears to be much more verbose and poorly documented.
[1]: https://github.com/lululxvi/deepxde [2]: https://github.com/nvidia/modulus
From "Physics-Based Deep Learning Book" (2021) https://news.ycombinator.com/item?id=28510010 :
> Physics-informed neural networks: https://en.wikipedia.org/wiki/Physics-informed_neural_networ...
I've never clearly understood the relationship/difference between PINNs and SciML (Scientific Machine Learning). The "how do they work" section here sounds pretty similar to how I've heard SciML described in the past.
From some searcing around, it sounds like maybe SciML is a broader concept with PINNs being a particular implementation of it? Maybe SciML started with PINN related ideas, but has broadened beyond that over time? Would appreciate an explanation from someone who's actively in this field.
Around a month ago there was a PINN post[1] on here and there was a healthy amount of skepticism in the comments. Even in the toxic positivity of LinkedIn, commentors say they're overhyped when a ML "Influencer" posts that one GIF with a MLP and PINN fitting to an oscillator. I would be interested to see what they're actively being used for.
I can also recommend Steve Brunton's playlist [0] on the topic of physics informed machine learning, as well as the book 'Data-driven Science & Engineering' [1] by him and Nathan Kutz.
[0] https://www.youtube.com/playlist?list=PLMrJAkhIeNNQ0BaKuBKY4...
Neural ODEs are also interesting.
Very well explained to a lay person.
Are PINNs the current state of the art in ML methods for solving PDEs? What are their limitations?
It's from the future. Must be really good :)
Physics informed neural networks 16 Feb 2026
The key intuition is calculating the loss function without actually knowing the exact solution ("labels" in supervised learning parlance). Note that this is not unique to PINN: there are existing numerical methods that do exactly this.
I used to solve PDEs for a living; and my academic background is in numerical solutions to PDEs before going into ML. In my industry and academic experience, PINN is a novel curiosity with perhaps niche applications that I am not as familiar with. Yes, I am aware of works of Bruton, Duvenaud et al (and was even in the same lab group with some of them). I am happy to be corrected and learn if PINN has found a strong application.
A better introduction to this approach and its critique here: https://arxiv.org/pdf/2206.02016