4 ms·

I'm having a lot of trouble understanding how "just add AI" is going to make electronics simulation 1000x faster.

adgjlsfhk1 6y ago
the TLDR is that for a lot of high dimensional PDE models, you get a better trade off of speed vs accuracy by using a NN for part of the model that is inefficient to calculate the full physics for. This is already having a lot of success in climate modeling, where NN based solutions do a better job of dealing with some atmospheric effects than previous efforts.
- Sukera 6y ago
  Sounds similar to what stockfish (leading chess computer engine) does. In newer versions, position evaluation comes at least in part from a NN, which lead to an improvement in playing strength. edit: similar in approach, not as a 1:1 mapping. Replace a deterministic model with a faster, slightly fuzzy one.
  - dreamcompiler 6y ago
    Chess position evaluation is always going to be somewhat subjective and statistical. Electronics simulation is neither; it's physics.
  - gugagore 6y ago
    This can be a useful connection, but I believe it's worth fleshing out in case it is misleading What's the alternative to using a NN for position evaluation? I can think of two: 1. Do minimax search until you have a winner or a stalemate. Then you have the exact value of the position. Well, this is the problem we're actually trying to solve to begin with, and it's also impractical to do for chess and any interesting game. This is what necessitates an approximation to position evaluation. 2. A human expert writes a position evaluation function. It determines a huge handful of features, a simple example being how many pieces I have - how many pieces you have, and some way to combine those features into a score. In surrogate modeling, you can get ground-truth data to evaluate your approximation against. You're approximating another model that you can compute, it's just too slow for practical use. In chess, we don't know THE position evaluation function. We can certainly get data about it, but we don't know it in the same way we know PDE models. To be clear, I am not saying we _know_ the PDE models are accurate with respect to reality. That's the science part, to determine if the model arising from empirical evidence or first-principles that are themselves arising from empirical evidence, actually summarizes empirical evidence.
ChrisRackauckas 6y ago
There are ways to surrogatize portions of a simulation, replacing large portions with ML-trained surrogates. There are already demonstrations in different domains (on highly stiff differential-algebraic equations) showing that you can get these kinds of speedups at around 99% accuracy. https://arxiv.org/abs/2010.04004 https://arxiv.org/abs/2010.04004 https://arxiv.org/abs/2103.05244 https://arxiv.org/abs/2103.05244
- vlovich123 6y ago
  > can get these kinds of speedups at around 1% accuracy Shouldn't this be at around "at around 99% accuracy" or "within around 1% accuracy loss"?
  - ChrisRackauckas 6y ago
    Thanks, fixed.
deleted 6y ago
[deleted]
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 ago
  Since 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 ago
    Sure, 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 ago
      Would this integrate with e.g. Measurements.jl?
      - KenoFischer 6y ago
        From 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.

the TLDR is that for a lot of high dimensional PDE models, you get a better trade off of speed vs accuracy by using a NN for part of the model that is inefficient to calculate the full physics for. This is already having a lot of success in climate modeling, where NN based solutions do a better job of dealing with some atmospheric effects than previous efforts.

Sukera 6y ago
Sounds similar to what stockfish (leading chess computer engine) does. In newer versions, position evaluation comes at least in part from a NN, which lead to an improvement in playing strength. edit: similar in approach, not as a 1:1 mapping. Replace a deterministic model with a faster, slightly fuzzy one.
- dreamcompiler 6y ago
  Chess position evaluation is always going to be somewhat subjective and statistical. Electronics simulation is neither; it's physics.
- gugagore 6y ago
  This can be a useful connection, but I believe it's worth fleshing out in case it is misleading What's the alternative to using a NN for position evaluation? I can think of two: 1. Do minimax search until you have a winner or a stalemate. Then you have the exact value of the position. Well, this is the problem we're actually trying to solve to begin with, and it's also impractical to do for chess and any interesting game. This is what necessitates an approximation to position evaluation. 2. A human expert writes a position evaluation function. It determines a huge handful of features, a simple example being how many pieces I have - how many pieces you have, and some way to combine those features into a score. In surrogate modeling, you can get ground-truth data to evaluate your approximation against. You're approximating another model that you can compute, it's just too slow for practical use. In chess, we don't know THE position evaluation function. We can certainly get data about it, but we don't know it in the same way we know PDE models. To be clear, I am not saying we _know_ the PDE models are accurate with respect to reality. That's the science part, to determine if the model arising from empirical evidence or first-principles that are themselves arising from empirical evidence, actually summarizes empirical evidence.

ChrisRackauckas 6y ago

There are ways to surrogatize portions of a simulation, replacing large portions with ML-trained surrogates. There are already demonstrations in different domains (on highly stiff differential-algebraic equations) showing that you can get these kinds of speedups at around 99% accuracy. https://arxiv.org/abs/2010.04004 https://arxiv.org/abs/2010.04004 https://arxiv.org/abs/2103.05244 https://arxiv.org/abs/2103.05244

vlovich123 6y ago
> can get these kinds of speedups at around 1% accuracy Shouldn't this be at around "at around 99% accuracy" or "within around 1% accuracy loss"?
- ChrisRackauckas 6y ago
  Thanks, fixed.

deleted 6y ago

[deleted]

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 ago
Since 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 ago
  Sure, 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 ago
    Would this integrate with e.g. Measurements.jl?
    - KenoFischer 6y ago
      From 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.