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Very interesting - does this mean that you could also rephrase arbitrary differential equations as neural networks, then apply parallel computing to solve them?
by leggomylibro 8y ago
Very interesting - does this mean that you could also rephrase arbitrary differential equations as neural networks, then apply parallel computing to solve them?
Sorry if that question doesn't make sense; I'm not really clear on how ordinary differential equations are usually solved these days.
- Skunkleton 8y ago> I'm not really clear on how ordinary differential equations are usually solved these days. Its been a while, but I remember that despair and sadness are involved in some way.
- sdenton4 8y agoOh, that's what the paper meant when they said the solver was a black box...
- mabbo 8y ago"Black box" is the name of their liquor cabinet
- gigatexal 8y agoOh good at least another person here that feels the same about ODEs as I do. Math in college was rough for me.
- tomc1985 8y agoThat and some crazy variable voodoo
- Gladdyu 8y agoYou could express an arbitrary (well-behaved) ODE as a neural network by discretizing it in timesteps, but you would not extract any additional parallelism. In normal ODEs you can already compute each X_{i}(t)/dt in parallel, but you will still have to evaluate layer/time t completely before evaluating layer/time t+Dt as it feeds forward in both the NN and ODE case.
- tanderson92 8y agoYes and no: there is parallel time integration for ODEs which parallelizes using multigrid techniques.
- ChrisRackauckas 8y agoYes, but tests tend to show you need like >64 cores for things like parareal methods to do better than standard serial methods. So they exist, but aren't quite practical yet. Maybe a GPU-based one in specific cases can be interesting, but no one has been able to demonstrate an efficient enough code yet. It's definitely an interesting topic.
- tanderson92 8y agoThanks for the perspective on the actual performance of these algorithms. So yeah, as an algorithmic fact it isn't necessary to proceed sequentially, though perhaps not performant to proceed in parallel either. Anyway, I heard AMD has 64 cores on a single chip so it may not be too long..
- TheGrassyKnoll 8y agoNeuromorphic Supercomputer With 1 Million Cores Mimics the Human Brain https://www.tomshardware.com/news/human-brain-neuromorphic-supercomputer-manchester,38027.html
- AlexCoventry 8y agoHow do they cope with the interactions at the boundaries of the grid?
- deleted 8y ago[deleted]
- wenc 8y agoMultiple-shooting methods [1] for ODEs are amenable to parallelism in time. [1] https://en.wikipedia.org/wiki/Direct_multiple_shooting_method https://en.wikipedia.org/wiki/Direct_multiple_shooting_metho...
- marcosdumay 8y agoAll A are B does not lead to all B are A. And arbitrary differential equations are a hell of a class.