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I'd like to use Monte Carlo (if it's useful to know, the Numpy Monte Carlo tools) to solve (arbitrary) nonlinear systems of equations where a solution might otherwise be given by optimization techniques such as least-squares minimization, etc.

I know it to be possible, however I've never used Monte Carlo in this way, nor have I used the Numpy Monte Carlo tools. How might Monte Carlo be applied to such a task and, more importantly, why does it work, intuitively?

Unfortunately, I cannot find much out there on this topic, and what I have found lacks detail and is somewhat 'hand-wavy'. I'd like to understand it on a deeper level than "it just works".

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