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{{Short description|Probabilistic problem-solving algorithm}}
{{distinguish|Monte Carlo algorithm}}
'''Monte Carlo methods''', or '''Monte Carlo experiments''', are a broad class of [[computation]]al [[algorithm]]s that rely on [[Resampling (statistics)|repeated]] [[random sampling]] to obtain numerical results. The underlying concept is to use [[randomness]] to solve problems that might be [[deterministic system|deterministic]] in principle. They are often used in [[physics|physical]] and [[mathematics|mathematical]] problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes:<ref>{{cite journal|author-last1=Kroese |author-first1=D. P. |author-last2=Brereton |author-first2=T. |author-last3=Taimre |author-first3=T. |author-last4=Botev |author-first4=Z. I. |year=2014 |title=Why the Monte Carlo method is so important today |journal = WIREs Comput Stat |volume=6 |issue=6 |pages=386–392 |doi=10.1002/wics.1314 |s2cid=18521840 |url=https://semanticscholar.org/paper/7a56b632de84d0b81f283750b11609a042890639}}</ref> [[optimization]], [[numerical integration]], and generating draws from a [[probability distribution]].
In physics-related problems, Monte Carlo methods are useful for simulating systems with many [[coupling (physics)|coupled]] [[degrees of freedom]], such as fluids, disordered materials, strongly coupled solids, and cellular structures (see [[cellular Potts model]], [[interacting particle systems]], [[McKean–Vlasov process]]es, [[kinetic theory of gases|kinetic models of gases]]).
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