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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 t

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?

joe_the_user 9y ago
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 digit as you find it. Sure, if some implementation has chosen a number with repeating digits, you can "predict" those digits but this would have nothing to do with being an oracle for algorithm itself. More broadly, I think it's pretty established that any realistic model of weather is kind of an extension of this concept - it depends unstably on it's initial conditions (small changes in initial conditions result in large changes in final result after some period). [1] https://en.wikipedia.org/wiki/Horseshoe_map https://en.wikipedia.org/wiki/Horseshoe_map
- evrydayhustling 9y ago
  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.
isthatart 9y ago
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.

joe_the_user 9y ago

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 digit as you find it. Sure, if some implementation has chosen a number with repeating digits, you can "predict" those digits but this would have nothing to do with being an oracle for algorithm itself. More broadly, I think it's pretty established that any realistic model of weather is kind of an extension of this concept - it depends unstably on it's initial conditions (small changes in initial conditions result in large changes in final result after some period). [1] https://en.wikipedia.org/wiki/Horseshoe_map https://en.wikipedia.org/wiki/Horseshoe_map

evrydayhustling 9y ago
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.

isthatart 9y ago

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.