3 ms·

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 inefficie

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.

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.