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This is an aside to the main point of the article, but I have to take issue with a couple of quotes: > For a long time scientific computing has kept machine le
by jofer 7y ago
This is an aside to the main point of the article, but I have to take issue with a couple of quotes:
> For a long time scientific computing has kept machine learning at an arm's length because its lack of interpretability and structure mean that, despite it’s tremendous predicitve success, it is almost useless for answering these kinds of central scientific questions.
> However, the recent trend has been to merge the two disciplines, allowing explainable models that are data-driven, require less data than traditional machine learning, and utilize the knowledge encapsulated in centuries of scientific literature.
Recent trend?? This is the norm in every scientific field I've even slightly worked in... This quote just described what we call "inverse theory" in the geosciences. It's the root of pretty much everything we do and has been for many decades. Those of in the scientific computing world have hardly been keeping machine learning at arm's length... A lot of machine learning methods come from scientific fields (e.g. gaussian processes).
There's more to machine learning than CNNs, and many fields have been using machine learning much longer terms like "data science" and "AI" have been around. We just trend towards parametric approaches or approaches that can be reasoned about more clearly. (E.g. lots of convex optimization problems and interpolation/"super-resolution" problems.) Those are machine learning methods as well.
All that said, most of what they're talking about in this article is about approximating solutions to differential equations with purely non-parametric approaches. That is somewhat new and is a much narrower topic, which this article does a nice job of describing. (I don't really take objection to the article as a whole, but a few sentences in it strike me as presumptuous.)
- ChrisRackauckas 7y agoSolving inverse problems has been around forever, agreed. Not just in geosciences but also aerospace, biology, etc. But, some of the ways that people are beginning to use universal function approximators inside of scientific simulators is new. The techniques are very similar to traditional inverse problems though: use adjoint equations for gradients and update parameters with some optimizer. It's just now they models include more non-mechanistic terms to fit. There were hints of it before with latent force models, but I am not sure of anyone using this idea to successfully solve 100 dimensional PDEs until 2 years ago. >There's more to machine learning than CNNs. Most definitely agreed. I think there's a lot to do with utilizing all of the methods of machine learning neural networks and beyond, automatically within scientific simulation codes.
- jofer 7y agoYeah, using non-parametric methods to approximate PDEs is really what this article is about, and it is a recent and very fruitful trend. I got a bit unnecessarily up-in-arms about phrasing. (edit: And I just realized you're the author -- excellent work by the way!)