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Libbum | 3 years ago | on: Outside the safe operating space of a new planetary boundary for PFAS

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.

Libbum | 5 years ago | on: Differentiable Control Problems

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) + ....`

Neural networks only grow polynomially with dimensional, so at around 8 dimensional objects it becomes more efficient. In fact, this is why we have https://diffeqflux.sciml.ai/dev/layers/BasisLayers/

Libbum | 5 years ago | on: Differentiable Control Problems

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.

Libbum | 5 years ago | on: Differentiable Control Problems

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.

Libbum | 5 years ago | on: Differentiable Control Problems

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.

[0] https://diffeqflux.sciml.ai/dev/FastChain/ [1] https://github.com/ChrisRackauckas/universal_differential_eq... [2] https://diffeqflux.sciml.ai/dev/examples/local_minima/

Libbum | 5 years ago | on: Differentiable Control Problems

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.

[0]: https://sciml.ai/ [1]: https://datadriven.sciml.ai/dev/sparse_identification/sindy/ [2]: https://arxiv.org/abs/2001.04385

Libbum | 5 years ago | on: Ask HN: How do you read long PDFs?

I mostly read scientific papers. Quite a good number of them are two column. Haven't come across k2pdfopt before - I'll check it out, thanks!

Libbum | 5 years ago | on: Ask HN: How do you read long PDFs?

Version 1. But as I say, the hardware is good. Version 2 will have even better hardware specs, but the operating system I suspect will be the same.

Libbum | 5 years ago | on: Ask HN: How do you read long PDFs?

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.

Very nice hardware, just awful software.

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