I'm curious, has anyone tried to apply ML to solving large linear systems?
Machine Learning’s ‘Amazing’ Ability to Predict Chaos
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Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#62Doesn't that mean that the neural net learned itself a numerical method to compute the solution of the equation, and that it is close enough in terms of approximation up to 7 Lyapukov times, and after that time, the approximation becomes not good enough and the system can't predict?
It doesn't sound like too groundbreaking...
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#63Doesn't that mean that the neural net learned itself a numerical method to compute the solution of the equation, and that it is close enough in terms of approximation up to 7 Lyapukov times, and after that time, the approximation becomes not good enough and the system can't predict? It doesn't sound like too groundbreaking...
I think it's blurring the line between modelling and simulation. You can find an efficient route down a hillside by pouring water down it, or a line of least resistance through a system by passing a current through it. Is the system learning a numerical solution, or performing one? I think this is like building a model of a system that is much closer to the territory than the map compared to a normal model, but still easier to work with than the territory.
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#64Earlier quoted context omitted.
Being dependent on the whim of a wealthy individual is saddening.
Could one be, instead, appreciative of and grateful to the considered, generous decision of that individual? how do you think he would respond to someone expressing one kind of feeling or the other?
Why do you think that I'm not? Lol
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#65Very cool! This looks like a very promising way to improve weather forecasts, predict wildfire movements (maybe?), and can maybe be used in control for chaotic systems? (Among other uses of course). It feels like every day I'm seeing deep learning make more mathematical tools obsolete. It's amazing how useful this tool has been.
When we started saving layers and gained nonlinear functions, it gained the ability to approximate any function, given enough time and data. These are big caveats.
RL can function with a lot less data. SVMs can run with a lot less time and space. Partial function application and expert modelling reduce data needed - and some of the best results are from ensemble suites. It's not obsoleting, it's another tool in the box.
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#66Earlier quoted context omitted.
It's actually kind of unclear what it means to predict results from an algorithmic simulation. Surely that's just trying to use a different method to simulate the process? I also don't see them mentioning anything about noise, so what exactly are they trying to achieve? Surely perfect prediction should already be possible, otherwise what are they comparing the output to?
Yeah, they're predicting the outcome of a chaotic but deterministic process based on the output data given. Surely they're discovering hidden (or obvious) regularities based specifically on the process being deterministic. As a counter example, the Smale Horseshoe [1] is an example of a inherently unpredictable map - it's approximately equivalent to choosing a real number "at random" and attempting to "predict" each…
This interpretation sounds right to me. I found it cool that the article characterizes success in terms of prediction accuracy out to N "Lyapunov times", a concept that is supposed to incorporate the unpredictability of the system. So perhaps discovering these regularities proves that in this implementation, the true Lyapunov time is longer.
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#67If there's an algorithm to create this 'randomness' then how can it be all that random?
Isn't it just learning to make an approximation of that algorithm, rather than actually predicting chaos?
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#68I'm curious, has anyone tried to apply ML to solving large linear systems?
Yes. Vladmir Vaptnik (1995)'s work on SVMs is probably the most recent, but linear regression is an ML technique as well.
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#69If there's an algorithm to create this 'randomness' then how can it be all that random? Isn't it just learning to make an approximation of that algorithm, rather than actually predicting chaos?
It’s working with imperfect information about the current state, which makes the algorithm that generates it useless.
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#70Don't be too seduced by the enticing ideas at the end of the article. The disconnect here is that success in learning how to predict the results of an algorithmic simulation is not really indicative of how it would perform with the decidedly non-algorithmic natural behavior of weather or earthquakes, phenomena which don't operate in a closed system with predefined limits and parameters. It sounds like the next step,…
I wouldn't say that natural behavior is non-algorithmic. Its more large scale hidden information algorithmic.
I agree but the point was to derogitate the computer simulation, which is literally algorithmic.