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Chris has posted the relevant papers in a sibling comment, but let me try to give an intuitive explanation. Say you have some sort of electronic device like an
by KenoFischer 6y ago
Chris has posted the relevant papers in a sibling comment, but let me try to give an intuitive explanation. Say you have some sort of electronic device like an amplifier. It is made out of many individual transistors and parasitics, but its time evolution is overall guided mostly by the amplifier characteristics its supposed to implement plus boundary effects and corrections from the parasitics. So what you try to do is to learn a simpler system of equations that captures the time evolution plus a (highly-nonlinear, complicated) projection that recovers the signals of interest (if you don't care about reproducing interior signals, you can usually get away with a simpler model). Of course it's not obvious that this should actually work (though of course picking a model of the same size as the system plus an identity projection is always possible, so it'll always work for some size of the model being learned, just at that point you don't get a speedup), but our initial results show that it does seem to be very promising.
- amelius 6y agoSince this is based on ML, I would have trouble trusting the results. Can you verify the results with standard mathematical methods? E.g. solve a linear system using AI, then compute the residue and meaningfully interpret it? Would it be possible to apply ML techniques iteratively, and let the error approach zero?
- KenoFischer 6y agoSure, you can always just run the baseline simulation and compare error rates. You can also do fancier analyses to get some rough idea of robustness and maximum error rates (over your particular parameter domain).
- Sukera 6y agoWould this integrate with e.g. Measurements.jl?
- KenoFischer 6y agoFrom an implementation perspective of course, so you can get error propagation on the baseline simulator. For the actual ML part, you'd get Measurements complaining that it doesn't know how to propagate bounds through the surrogate. You can do some estimation of what that propagation would look like, but it's a research project.
- ChrisRackauckas 6y agoThe error propagation won't be through measurements, because that blows up linearly. There's other approaches which give much more promising results.
- gugagore 6y agoIt seems that there are two related but distinct ways to simplifying a model: 1. projections / disregarding some dimension, followed by some model in this latent space, followed by an injection back into the native space. The model is simpler by virtue of operating in a lower dimensional space. 2. using a "reduced-order model" or "surrogate model", but still operating in the same input/output space. The model is simpler by virtue of, e.g. using fewer derivatives or delays. And with 2, you can have have the simple model e.g. arise from first principles, and learn a _residual_ correction on top of it. And it sounds like the comment contains a bit of both. Am I getting that right?
- ChrisRackauckas 6y agoA bit of both.
- ptarmigan 6y agoDo you think such an approach could extend to the final verification stage of a large post-extraction chip? My impression is that speedups are most sorely needed in this final sign off phase where the number of nodes explodes with parasitic R's and C's, especially in modern technologies. Simulation times in weeks seem necessary now for sufficient verification accuracy of analog/mixed signal chips.
- KenoFischer 6y agoYes, we're looking at it. One of our benchmark cases for this work, will likely be a post-extraction structure from one of the Sky130 chips (not that it wouldn't work in a more moderns process, but the NDA issues become complicated while this is still a research project).