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Introduction to Uncertainty Quantification · LearnSpace
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Introduction to Uncertainty Quantification

Курс от Johns Hopkins University
Средний≈ 30 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

Uncertainty Quantification (UQ) is the science of mathematically quantifying and reducing uncertainty in systems of all types. Students will learn the nature and role of uncertainty in physical, mathematical, and engineering systems along with the basics of probability theory necessary to quantify uncertainty. The course provides an introduction to various sub-topics of UQ including uncertainty propagation, surrogate modeling, reliability analysis, random processes and random fields, and Bayesian inverse UQ methods.

Навыки, которые вы освоите

ProbabilityProbability DistributionProbability & StatisticsMathematical ModelingStatistical ModelingMarkov ModelSimulationsSampling (Statistics)Bayesian StatisticsReliabilitySimulation and Simulation SoftwareStatistical MethodsEstimationNumerical AnalysisStatistical InferenceApplied MathematicsStatistical AnalysisFailure Analysis

Программа курса

4 модулей · 109 учебных материалов

01Types of Uncertainty and Their Treatment21 материалов

Types of Uncertainty

Course IntroductionВидеоTypes of UncertaintyЧтениеWhat is Uncertainty?ВидеоAleatory UncertaintyВидео

Учитесь у экспертов

Michael Shields

Associate Professor

Introduction to Uncertainty Quantification
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Обучение на Coursera

≈ 30 ч

4 модулей

Язык: Английский

Субтитры: Казахский

Часть программы вашего университета
Epistemic UncertaintyВидео
Aleatory & Epistemic UncertaintyЗадание
Why is the distinction important?Обсуждение

Deciphering Aleatory and Epistemic Uncertainty

Deciphering Aleatory & Epistemic UncertaintyЧтениеChallenge of Deciphering Aleatory & Epistemic UncertaintyВидеоGeneral Model SettingВидеоSources of UncertaintyВидеоAleatory or Epistemic? Does it Matter?ВидеоDeciphering Aleatory and Epistemic UncertaintiesЗадание

Mathematical Tools for Aleatory and Epistemic Uncertainty

Mathematical Treatments for Aleatory and Epistemic UncertaintyЧтениеFrequentist Interpretation of ProbabilityВидеоBayesian Interpretation of ProbabilityВидеоBayesian Fair DieЛабораторнаяBayesian and Frequentist InterpretationsОбсуждениеMathematical Treatment of Uncertainty: Part I - Aleatory UncertaintyВидеоMathematical Treatment of Uncertainty: Part II - Epistemic UncertaintyВидеоMathematical Treatment of UncertaintyЗадание
02Basic Probability for UQ30 материалов

Probability Concepts

Elements of Set Theory and ProbabilityЧтениеElements of Set TheoryВидеоSample Spaces, Events, and Venn DiagramsЗаданиеDefine your own experimentОбсуждениеAxioms of ProbabilityВидеоElements of ProbabilityЗаданиеConditional Probability ВидеоLaw of Total ProbabilityВидеоBayes' RuleВидеоConditional Probability & Bayes' RuleЗаданиеPractice ProblemsЗадание

Random Variables

Random VariablesЧтениеRandom VariablesВидеоRandom VariablesЗаданиеMoments of Random VariablesВидеоMoments of Random VariablesЗаданиеImportant Probability DistributionsЧтениеGaussian Random Variables

Random Vectors & Random Processes

Random Vectors & Random ProcessesЧтениеRandom VectorsВидеоMoments of Random VectorsВидеоRandom Vectors and Their MomentsЗаданиеRandom ProcessesВидеоMoments of Random ProcessesВидеоStationary Random Processes
03Introduction to Uncertainty Propagation33 материалов

Change of Variables

Uncertainty PropagationЧтениеFunctions of Random VariablesЧтениеUncertainty PropagationВидеоUncertainty PropagationЗаданиеChange of Variables TheoremВидеоMultivariate Change of Variables TheoremВидеоFunctions of Multiple Random VariablesВидеоFunctions of Random Variables Задание

Expansion Methods

Taylor Series ExpansionsЧтениеTaylor Series ExpansionsВидеоTaylor Series for Functions of Random VariablesВидеоTaylor Series for Functions of Random VectorsВидеоTaylor Series ExpansionsЗаданиеSecond-Order Taylor Series ExpansionЗадание

Monte Carlo Methods

Monte Carlo MethodsЧтениеLaw of Large NumbersВидеоDemo: Law of Large NumbersЛабораторнаяMonte Carlo SimulationВидеоSimulation of Random VariablesВидеоDemo: Psuedo Random Number GeneratorЛабораторнаяDemo: Inverse Transform

Surrogate Modeling

Surrogate ModelingЧтениеSurrogate Modeling ConceptВидеоGaussian Process Regression SurrogatesВидеоDemo: Gaussian Process RegressionЛабораторнаяPolynomial Chaos Expansion SurrogatesВидеоDemo: Polynomial Chaos ExpansionsЛабораторная
04Advanced Topics: Reliability, Sensitivity, Inference, and More 25 материалов

Numerical Methods for Uncertainty Propagation

Numerical MethodsЧтениеIntro to Numerical Methods for Uncertainty PropagationВидеоStochastic Galerkin MethodВидеоStochastic Collocation MethodВидеоNumerical Methods for Uncertainty PropagationЗадание

Reliability Analysis

Reliability AnalysisЧтениеReliability Analysis: Problem FormulationВидеоFirst Order Reliability Method (FORM)ВидеоFORMЛабораторнаяVariance Reduction Methods - Subset Simulation ВидеоSubset SimulationЛабораторнаяVariance Reduction Methods - Importance SamplingВидеоReliability AnalysisЗадание

Global Sensitivity Analysis

Global Sensitivity AnalysisЧтениеGlobal vs. Local Sensitivity AnalysisВидеоVariance-based GSAВидеоMonte Carlo Methods for GSAВидеоSobol SensitivitiesЛабораторнаяSurrogate Models for GSAВидеоGlobal Sensitivity Analysis

Bayesian Inference and Course Conclusion

Bayes' Rule RevisitedВидеоBayesian Parameter EstimationВидеоInference with MCMCВидеоBayesian InferenceЗаданиеBayesian Inference Лабораторная
Видео
Gaussian and Uniform Random VariablesЗадание
Видео
Random Process and Their MomentsЗадание
Random Process and Their Moments - Challenge ProblemsЗадание
Markov ChainsВидео
Markov ChainsЗадание
Taylor Series Expansions for Moment EstimationЗадание
Лабораторная
Markov Chain Monte CarloВидео
Markov Chain Monte CarloЛабораторная
Variance Reduction TechniquesВидео
Monte Carlo MethodsЗадание
Surrogate ModelsЗадание
Задание