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Solving inverse problems has been around forever, agreed. Not just in geosciences but also aerospace, biology, etc. But, some of the ways that people are beginn
by ChrisRackauckas 7y ago
Solving 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!)