It is surprisingly good!
Not clear if you can go without a manual step where you need to change the likes of SPEAKER_00 to Bob and SPEAKER_01 to Sarah, but I've not had it mess up on me at all transcribing 2 hour long conversations between 6 people.
You may have been reading a different version of the documentation. Documenter.jl outputs are dependent on the code actually running (and it's the package DifferentialEquations.jl uses to build its docs).
An additional thing to understand here is that PFAS is not a new boundary at all in the context of the planetary boundaries framework - they fall under the already defined category of Novel Entities.
Since that's a catch all category for many things (nuclear waste, other synthetic chemicals, there's even debate with the original authors of the framework if Artificial Intelligence should be considered), the boundary value itself is not currently defined.
One school of thought is that the boundary value for this category should be zero - as any synthetic substance is more than nature generates.
Regardless, papers like this one are helpful to piece together all of the novel entities research amd get a better picture of how this boundary interacts with the rest of the Earth System.
Yeah, this is the crux. Here's a comment from one of the devs when I asked about the polynomial vs NN basis:
The answer is quite simple really. Classical basis functions suffer from the curse of dimensionality because if you tensor product polynomial basis functions or things like Fourier basis, with N basis functions in each direction, then you have N^d parameters that are required in order to handle every combination `sin(x) + sin(2x) + ... + sin(y) + sin(2y) + ... + sin(x)sin(y) + sin(2x)sin(y) + ....`
I certainly agree with the NNs are used as hammers point. Until coming across the UODE concept I was of the opinion they were more parlour trick than anything useful. Here though, I could see some validity.
These comments are appreciated - I think a discussion like this is lacking in the SciML docs (or at least not visible enough). Will have a chat with some of the devs and see if there's something we can add.
I'm not entirely confident in answering that directly, so perhaps you can check my reasoning here.
If F is completely unknown, perhaps you start training with a 10 dimensional polynomial basis. What is the (computational) cost of obtaining your solution? Once you have it, will this polynomial accurately represent your system in any real world manner? Perhaps higher order parameters are needed to approximate trigonometric functions - are you able to easily add such functions to your training basis? If not - then your basis could be too restrictive to provide you with a minimal implementation of your control variable.
It looks like you work with this stuff far more than I have, so perhaps that's not an adequate answer.
Another way to look at this though: If you only wanted to characterise your system with polynomials, UODEs + SINDy can do this for you - the NN is simply the optimisation method that's in place of any other optimisation algorithm.
Since the network only acts on a small portion of the entire system, we can constrain it in such a way that dramatically simple NNs work just fine.
`FastChain(FastDense(3,32,tanh), FastDense(32,32,tanh), FastDense(32,2))` (from [0]) would take three inputs from your basis, run it through one hidden layer and provide you with two trained parameters.
This [1] example uses two hidden layers, its one of the more complex solutions I've seen so far. To move to this complexity from a simpler chain, we first make sure our solution is not in a local minima [2], then proceed to increase the parameter count if the NN fails to converge.
To respond to both the parent question, and this comment: indeed, this is black-box optimal control in essence.
However, this method is just one small aspect of the SciML [0] ecosystem now. The article is a little outdated in that sense.
Once obtaining your NN control parameter, it's now possible to use Sparse Identification of Nonlinear Dynamics (SINDy) on that parameter to recover equations of motion governing it [1].
The real promise of these methods is to use the universal approximator power of NNs to get around the 'curse of dimensionality' & uncover presently unknown representations of motion within any system. Take a look at [2] for a more detailed description.
I wouldn't recommend this. PDF support is horrible, particularly if you have a two column layout file. You cannot correctly zoom in far enough in most cases - in the sense that zoom is possible, just absolutely impractical. Without that, you generally need a magnifying glass to read the text on the display.
There are efforts to do exactly that. The Cuneiform Digital Library Initiative [0] has some interesting projects you may wish to browse [1] as an example.
I would strongly suggest serving this landing page via http/2.0 - your 504 requests over http/1.1 are currently taking 3.5 minutes for me to load 2MB of data.
My biggest project, it's about 6k loc. So maybe that's not what you meant by 'big', but many of the others here have listed a lot of closed source apps.