The last time this came up, I spent some time investigating the use of analog computers for Monte Carlo simulations and it is absolutely fascinating how differential equations or stochastic differential equations are being implemented with analog components. There are already some chips available that integrate these components similar to FPGAs and some toy examples show promising results, but it looks like we are not completely there yet.
Nevertheless, if these chips get further developed, they could have a huge impact on neural networks (at least in terms of power consumption) and maybe Monte Carlo.
That would be really interesting - how do you generate the randomness?
Every so often when Matlab or Simulink won't integrate something simple, probably because of something I did, I wish I had an analog computer to compare to.
Randomness is impossible to eradicate from the analogue world, so you just take an existing noise source like a semiconductor junction and connect it to an amplifier.
Some care is needed to get something that works across a wide temperature range, and avoids being easy to overwhelm with outside noise sources, but it's a problem with lots of existing solutions.
I mean in a practical way for a monte carlo simulation - usually in analog setup you set parameters with discretes, so you are going to need to do things like feeding a transconductance amplifier with your noise source. You're also going to worry about shaping and otherwise parameterizing your distribution - do you need uniformly distributed noise? gaussian noise? what are your limits?
I can imagine a lot of practical pitfalls and awkward half-solutions to trying to do an analog monte carlo; I was wondering how the OP went about it.
There is actually a fascinating thesis by Yipeng Huang ("Hybrid Analog-Digital Co-Processing for Scientific Computation") that discusses toy models (i.e. Black-Scholes and variants).
As usual, you have a Wiener process and thus need Gaussian noise. Yipeng Huang found that some noise stemming from a resistor ladder of the chip provided Gaussian white noise and he could control the mean by feeding it with a DAC and he also had some way to control the variance by changing some multipliers (but I can't tell you exactly how that worked). Nevertheless, this was the analog part and he faced issues with DC drift.
Alternatively, he looked into generating the noise digitally with a microcontroller.
