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* In [[microelectronics|microelectronics engineering]], Monte Carlo methods are applied to analyze correlated and uncorrelated variations in [[Analog signal|analog]] and [[Digital data|digital]] [[integrated circuits]].

* In [[microelectronics|microelectronics engineering]], Monte Carlo methods are applied to analyze correlated and uncorrelated variations in [[Analog signal|analog]] and [[Digital data|digital]] [[integrated circuits]].

* 在微电子工程中，蒙特卡罗方法被用于分析模拟和数字集成电路中相关和不相关的变化。

* 在'''微电子工程 Microelectronics Engineering'''中，蒙特卡罗方法被用于分析模拟和数字集成电路中相关和不相关的变化。

* In [[geostatistics]] and [[geometallurgy]], Monte Carlo methods underpin the design of [[mineral processing]] [[process flow diagram|flowsheets]] and contribute to [[quantitative risk analysis]].<ref name="mbv01">{{Cite book | last1 =Mazhdrakov | first1 =Metodi | last2 =Benov | first2 =Dobriyan |last3=Valkanov|first3=Nikolai | year =2018 | title =The Monte Carlo Method. Engineering Applications | publisher =ACMO Academic Press | volume = | pages = 250| isbn =978-619-90684-3-4 | doi =  |url=https://books.google.com/books?id=t0BqDwAAQBAJ&q=the+monte+carlo+method+engineering+applications+mazhdrakov}}</ref>

* In [[geostatistics]] and [[geometallurgy]], Monte Carlo methods underpin the design of [[mineral processing]] [[process flow diagram|flowsheets]] and contribute to [[quantitative risk analysis]].<ref name="mbv01">{{Cite book | last1 =Mazhdrakov | first1 =Metodi | last2 =Benov | first2 =Dobriyan |last3=Valkanov|first3=Nikolai | year =2018 | title =The Monte Carlo Method. Engineering Applications | publisher =ACMO Academic Press | volume = | pages = 250| isbn =978-619-90684-3-4 | doi =  |url=https://books.google.com/books?id=t0BqDwAAQBAJ&q=the+monte+carlo+method+engineering+applications+mazhdrakov}}</ref>

* 在地质统计学和地质冶金学中，蒙特卡罗方法是矿物处理流程设计的基础，并有助于定量风险分析。<ref name="mbv01" />

* 在'''地质统计学 Geostatistics'''和'''地质冶金学 Geometallurgy'''中，蒙特卡罗方法是矿物处理流程设计的基础，并有助于定量风险分析。<ref name="mbv01" />

* In [[wind energy]] yield analysis, the predicted energy output of a wind farm during its lifetime is calculated giving different levels of uncertainty ([[Percentile|P90]], P50, etc.)

* In [[wind energy]] yield analysis, the predicted energy output of a wind farm during its lifetime is calculated giving different levels of uncertainty ([[Percentile|P90]], P50, etc.)

* In [[fluid dynamics]], in particular [[gas dynamics|rarefied gas dynamics]], where the Boltzmann equation is solved for finite [[Knudsen number]] fluid flows using the [[direct simulation Monte Carlo]]<ref name=":33">G. A. Bird, Molecular Gas Dynamics, Clarendon, Oxford (1976)</ref> method in combination with highly efficient computational algorithms.<ref name=":34">{{cite journal | last1 = Dietrich | first1 = S. | last2 = Boyd | first2 = I. | year = 1996 | title = A Scalar optimized parallel implementation of the DSMC technique | url = | journal = Journal of Computational Physics | volume = 126 | issue = 2| pages = 328–42 | doi=10.1006/jcph.1996.0141|bibcode = 1996JCoPh.126..328D }}</ref>

* In [[fluid dynamics]], in particular [[gas dynamics|rarefied gas dynamics]], where the Boltzmann equation is solved for finite [[Knudsen number]] fluid flows using the [[direct simulation Monte Carlo]]<ref name=":33">G. A. Bird, Molecular Gas Dynamics, Clarendon, Oxford (1976)</ref> method in combination with highly efficient computational algorithms.<ref name=":34">{{cite journal | last1 = Dietrich | first1 = S. | last2 = Boyd | first2 = I. | year = 1996 | title = A Scalar optimized parallel implementation of the DSMC technique | url = | journal = Journal of Computational Physics | volume = 126 | issue = 2| pages = 328–42 | doi=10.1006/jcph.1996.0141|bibcode = 1996JCoPh.126..328D }}</ref>

* 在流体动力学，特别是稀薄气体动力学中，采用直接模拟蒙特卡罗方法<ref name=":33" /> 结合高效计算算法求解有限努森数流体的玻尔兹曼方程。<ref name=":34" />

* 在流体动力学，特别是'''稀薄气体动力学 Rarefied Gas Dynamics'''中，采用'''直接模拟蒙特卡罗方法  Direct Simulation Monte Carlo'''<ref name=":33" /> 结合高效计算算法求解有限'''努森数 Knudsen Number'''流体的玻尔兹曼方程。<ref name=":34" />

* In [[autonomous robotics]], [[Monte Carlo localization]] can determine the position of a robot. It is often applied to stochastic filters such as the [[Kalman filter]] or [[particle filter]] that forms the heart of the [[Simultaneous localization and mapping|SLAM]] (simultaneous localization and mapping) algorithm.

* In [[autonomous robotics]], [[Monte Carlo localization]] can determine the position of a robot. It is often applied to stochastic filters such as the [[Kalman filter]] or [[particle filter]] that forms the heart of the [[Simultaneous localization and mapping|SLAM]] (simultaneous localization and mapping) algorithm.

* 在自主机器人中，蒙特卡洛定位可以确定机器人的位置。它通常应用于随机滤波器，如卡尔曼滤波器或粒子滤波器，构成同步定位和映射算法的核心。

* 在自主机器人中，'''蒙特卡洛定位 Monte Carlo Localization'''可以确定机器人的位置。它通常应用于随机滤波器，如'''卡尔曼滤波器 Kalman Filter'''或'''粒子滤波器 Particle Filter'''，构成'''同步定位和映射算法 SLAM (Simultaneous Localization and Mapping)'''的核心。

* In [[telecommunications]], when planning a wireless network, design must be proved to work for a wide variety of scenarios that depend mainly on the number of users, their locations and the services they want to use. Monte Carlo methods are typically used to generate these users and their states. The network performance is then evaluated and, if results are not satisfactory, the network design goes through an optimization process.

* In [[telecommunications]], when planning a wireless network, design must be proved to work for a wide variety of scenarios that depend mainly on the number of users, their locations and the services they want to use. Monte Carlo methods are typically used to generate these users and their states. The network performance is then evaluated and, if results are not satisfactory, the network design goes through an optimization process.

* 在电信行业，在规划无线网络时，必须证明设计适用于各种主要取决于用户数量、他们的位置和他们想使用的服务的场景。蒙特卡罗方法通常用于生成这些用户及其状态。然后对网络性能进行评估，如果结果不令人满意，则进行网络设计优化。

* 在电信行业，在规划无线网络时，必须证明设计适用于各种不同用户数量、用户位置和他们想使用的服务的场景。蒙特卡罗方法通常用于生成这些用户及其状态。然后对网络性能进行评估，如果结果不能令人满意，则进行网络设计优化。

* In [[reliability engineering]], Monte Carlo simulation is used to compute system-level response given the component-level response. For example, for a transportation network subject to an earthquake event, Monte Carlo simulation can be used to assess the ''k''-terminal reliability of the network given the failure probability of its components, e.g. bridges, roadways, etc.<ref name=":35">Nabian, Mohammad Amin; Meidani, Hadi (2017-08-28). "Deep Learning for Accelerated Reliability Analysis of Infrastructure Networks". ''Computer-Aided Civil and Infrastructure Engineering''. '''33''' (6): 443–458. arXiv:1708.08551. Bibcode:2017arXiv170808551N. doi:10.1111/mice.12359. S2CID 36661983.</ref><ref name=":36">{{Cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2018|title=Accelerating Stochastic Assessment of Post-Earthquake Transportation Network Connectivity via Machine-Learning-Based Surrogates|url=https://trid.trb.org/view/1496617|journal=Transportation Research Board 97th Annual Meeting|volume=|pages=|via=}}</ref><ref name=":37">{{Cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2017|title=Uncertainty Quantification and PCA-Based Model Reduction for Parallel Monte Carlo Analysis of Infrastructure System Reliability|url=https://trid.trb.org/view/1439614|journal=Transportation Research Board 96th Annual Meeting|volume=|pages=|via=}}</ref> Another profound example is the application of the Monte Carlo method to solve the G-Renewal equation of the generalized renewal process.<ref name=":38">Krivtsov, V. V. (2000). ''Modeling and estimation of the generalized renewal process in repairable system reliability analysis'' (PhD). University of Maryland, College Park, ISBN/ISSN: 0599725877.</ref>

* In [[reliability engineering]], Monte Carlo simulation is used to compute system-level response given the component-level response. For example, for a transportation network subject to an earthquake event, Monte Carlo simulation can be used to assess the ''k''-terminal reliability of the network given the failure probability of its components, e.g. bridges, roadways, etc.<ref name=":35">Nabian, Mohammad Amin; Meidani, Hadi (2017-08-28). "Deep Learning for Accelerated Reliability Analysis of Infrastructure Networks". ''Computer-Aided Civil and Infrastructure Engineering''. '''33''' (6): 443–458. arXiv:1708.08551. Bibcode:2017arXiv170808551N. doi:10.1111/mice.12359. S2CID 36661983.</ref><ref name=":36">{{Cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2018|title=Accelerating Stochastic Assessment of Post-Earthquake Transportation Network Connectivity via Machine-Learning-Based Surrogates|url=https://trid.trb.org/view/1496617|journal=Transportation Research Board 97th Annual Meeting|volume=|pages=|via=}}</ref><ref name=":37">{{Cite journal|last1=Nabian|first1=Mohammad Amin|last2=Meidani|first2=Hadi|date=2017|title=Uncertainty Quantification and PCA-Based Model Reduction for Parallel Monte Carlo Analysis of Infrastructure System Reliability|url=https://trid.trb.org/view/1439614|journal=Transportation Research Board 96th Annual Meeting|volume=|pages=|via=}}</ref> Another profound example is the application of the Monte Carlo method to solve the G-Renewal equation of the generalized renewal process.<ref name=":38">Krivtsov, V. V. (2000). ''Modeling and estimation of the generalized renewal process in repairable system reliability analysis'' (PhD). University of Maryland, College Park, ISBN/ISSN: 0599725877.</ref>

* 在可靠性工程中，蒙特卡罗仿真被用来计算系统级响应给定的部件级响应。例如，对于一个受地震事件影响的交通网络，蒙特卡洛模拟可以用来评估网络的k终端可靠性，给定其组件，如桥梁、道路等的失效概率。<ref name=":35" /><ref name=":36" /><ref name=":37" /> 另一个意义深远的例子是应用蒙特卡罗方法求解广义更新过程的G-更新方程。<ref name=":38" />

* 在可靠性工程中，给定部件级响应，蒙特卡罗仿真用来计算系统级响应。例如，对于一个受地震事件影响的交通网络，给定其组件，如桥梁、道路等的失效概率，蒙特卡洛模拟可以用来评估网络的k-终端可靠性。<ref name=":35" /><ref name=":36" /><ref name=":37" /> 另一个意义深远的例子是应用蒙特卡罗方法求解'''广义更新过程 Generalized Renewal Process'''的G-更新方程。<ref name=":38" />

* In [[signal processing]] and [[Bayesian inference]], [[particle filter]]s and [[Sequential Monte Carlo method|sequential Monte Carlo techniques]] are a class of [[mean field particle methods]] for sampling and computing the posterior distribution of a signal process given some noisy and partial observations using interacting [[empirical measure]]s.

* In [[signal processing]] and [[Bayesian inference]], [[particle filter]]s and [[Sequential Monte Carlo method|sequential Monte Carlo techniques]] are a class of [[mean field particle methods]] for sampling and computing the posterior distribution of a signal process given some noisy and partial observations using interacting [[empirical measure]]s.