Why wouldn't it? A lot of misunderstanding out there in both machine learning and nonlinear dynamics.
Machine Learning’s ‘Amazing’ Ability to Predict Chaos
71–77 of 77 posts
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#72Don'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,…
It sounds like the next step, but even if weather were reducible to machine-discoverable patterns, you first must face the need to collect an immense amount of high-resolution condition data from around the globe on an ongoing basis. There has been some success using Ensemble Kalman Filters (EnKF) to predict hurricanes [1]. I think that these filters sit somewhere between machine learning and deterministic models. Th…
> machine learning and deterministic models
This is a confusing distinction. Aren't lots of machine learning algorithms deterministic? Sure, some include stochastic elements or components, but even those can be deterministic, e.g. by reusing the same seed for the random number generators.
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#73Don'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,…
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?
I believe (but I might be wrong) that are compared the results of two different methods: (a) "algorithmic" where solution(t+1) = algo(solution(t)) and errors accumulate with time steps, vs. (b) based on sufficiently many available pairs (initial_1, solution_1), ...,(initial_N,solution_N), each solution_i a function of time t \in [0,T], a NN (or another gadget) builds a function ALGO(initial)=solution so that the errors in time of solution(t) wrt real_solution(t) are uniform, where real_solution is the real solution for the initial condition initial.
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#74Doesn'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…
> Is the system learning a numerical solution, or performing one?
Is there a real difference? Any learning must be, fundamentally, an algorithm, so learning is performing.
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#75Can we have more publishing like Quanta magazine? It's just perfect in terms of reporting from the frontier, being easy to unsetstand, and not talking down to you.
It's funded by Jim Simons, of the hedge fund Renaissance Technologies. A mathematician with money, trying to promote mathematics. Quanta magazine is a fantastic service. But the other Renaissance magnate, Bob Mercer, as his own media hobby funded Breitbart News.
I always wondered how Quanta put such high quality material out in a traditionally low-profit industry. Now I know!
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#76Earlier quoted context omitted.
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…
> Is the system learning a numerical solution, or performing one? Is there a real difference? Any learning must be, fundamentally, an algorithm, so learning is performing.
This is a deep topic but one good treatment of is in the works of David Deutsch: https://www.cs.indiana.edu/~dgerman/hector/deutsch.pdf
Re: Machine Learning’s ‘Amazing’ Ability to Predict Chaos
#77Earlier quoted context omitted.
Nope, given our current theories time travel is practically impossible. On the other hand we know that chaotic systems are functions and that matrices can approximate any function.
If you’re going to be that pedantic, I’ll see your pedantry and raise you. Time travel is not only possible, but routine, just in the forward direction only. It’s only travel into the past which is probably impossible, and to be even more pedantic and abstract, impossible only in our observable spacetime geometry.
So is with the chaotic systems: we know for sure that approximating them is just a matter of boundary conditions: that is - the more you know about the starting points, the better you approximate the real world.
I mean, there might be a case where we will finally get to the point where we are just "good enough" at measuring the boundary conditions to predict weather for the next year, but it has got nothing to do with obtaining the knowledge about chaotic systems themselves.