{"componentChunkName":"component---src-templates-course-unit-page-tsx","path":"/en/courseunit/802661s/","result":{"data":{"translations":{"edges":[{"node":{"context":{"locale":"fi","code":"802661S","title":"Computational Inverse Problems"},"path":"/fi/opintojakso/802661s/"}},{"node":{"context":{"locale":"en","code":"802661S","title":"Computational Inverse Problems"},"path":"/en/courseunit/802661s/"}}]},"SISU":{"courseUnit":[{"id":"otm-235ce05d-e41d-323e-b5e9-7ef34f9df084","code":"802661S","name":{"en":"Computational Inverse Problems","fi":"Computational Inverse Problems","sv":"Computational Inverse Problems"},"credits":{"max":5,"min":5},"studyLevel":null,"possibleAttainmentLanguages":[{"name":{"en":"English","fi":"englanti","sv":"engelska"}}],"responsibleOrganisations":[],"coordinatingOrganisations":[],"curriculumPeriods":[],"cooperationNetworkDirection":"INBOUND","cooperationNetworks":[{"targetGroups":[{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["jy-DP-15471","jy-DP-21321","jy-DP-13215","otm-157daa3c-6f87-4d1d-86e2-5f2ed9872b58","jy-DP-13221","jy-DP-21280","jy-DP-30241"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":null,"phase2OptionGroupIds":["jy-DP-15471","jy-DP-13215","jy-DP-30241"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null}],"description":{"en":"

This course is offered through the Network for Inverse Problems. These studies are available for the following degree students:

","fi":"

Tämä opintojakso on tarjolla Inversio-ongelmien verkostossa. Verkoston opinnot ovat tarjolla seuraavien tutkinto-ohjelmien opiskelijoille:

"},"cooperationNetwork":{"abbreviation":"inversio","name":{"en":"Education network on Inverse Problems","fi":"Inversio-ongelmien koulutusverkosto"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"Upon successful completion of this course, students will be able to:\r\n-Formulate inverse problems within a rigorous statistical framework.\r\n-Select and justify appropriate Bayesian prior models for both discrete and infinite-dimensional unknown parameters.\r\n-Distinguish between and implement sampling strategies suitable for linear and nonlinear inverse problems.\r\n-Generate discrete samples from posterior distributions using Markov chain Monte Carlo (MCMC) methods.\r\n-Assess the quality and convergence of posterior samples in approximating the target distribution.\r\n-Summarize, visualize, and interpret uncertainty for posterior distributions using key statistical summaries, including posterior mean, maximum a posteriori (MAP) estimates, posterior standard deviation, and credibility intervals.","fi":"Upon successful completion of this course, students will be able to:\r\n-Formulate inverse problems within a rigorous statistical framework.\r\n-Select and justify appropriate Bayesian prior models for both discrete and infinite-dimensional unknown parameters.\r\n-Distinguish between and implement sampling strategies suitable for linear and nonlinear inverse problems.\r\n-Generate discrete samples from posterior distributions using Markov chain Monte Carlo (MCMC) methods.\r\n-Assess the quality and convergence of posterior samples in approximating the target distribution.\r\n-Summarize, visualize, and interpret uncertainty for posterior distributions using key statistical summaries, including posterior mean, maximum a posteriori (MAP) estimates, posterior standard deviation, and credibility intervals."},"tweetText":null,"content":{"en":"-Multivariate Gaussian random variables\r\n-Gaussian covariance operators and Karhunen–Loève expansion\r\n-Bayesian formulation of inverse problems: prior, likelihood, and posterior distributions\r\n-Introduction to continuous (infinite-dimensional) inverse problems\r\n-Maximum a posteriori (MAP) estimation\r\n-Markov chain Monte Carlo methods, including the Metropolis–Hastings algorithm\r\n-Hamiltonian Monte Carlo (HMC) methods\r\n-Introduction to Bayesian optimal experimental design","fi":"-Multivariate Gaussian random variables\r\n-Gaussian covariance operators and Karhunen–Loève expansion\r\n-Bayesian formulation of inverse problems: prior, likelihood, and posterior distributions\r\n-Introduction to continuous (infinite-dimensional) inverse problems\r\n-Maximum a posteriori (MAP) estimation\r\n-Markov chain Monte Carlo methods, including the Metropolis–Hastings algorithm\r\n-Hamiltonian Monte Carlo (HMC) methods\r\n-Introduction to Bayesian optimal experimental design"},"additional":{"en":"Required Background\r\nStudents enrolling in this course are expected to have the following background knowledge and skills:\r\n-Linear Algebra: Familiarity with eigenvalue decomposition, matrix–vector operations, and core concepts in finite-dimensional vector spaces.\r\n-Functional Analysis: Basic understanding of function spaces, norms, and inner products.\r\n-Python Programming: A solid working knowledge of Python is required. However, the computational components of the course begin with structured and accessible coding tasks and progressively advance to more sophisticated implementations.\r\n-Teamwork and Collaboration: Since the course is built around structured group activities and collaborative problem-solving, students must be prepared to actively participate in teamwork, contribute responsibly to group tasks, and engage in constructive mathematical discussion.\r\nStudents should be comfortable working with mathematical abstractions, implementing numerical algorithms, and collaborating effectively with peers.","fi":"Required Background\r\nStudents enrolling in this course are expected to have the following background knowledge and skills:\r\n-Linear Algebra: Familiarity with eigenvalue decomposition, matrix–vector operations, and core concepts in finite-dimensional vector spaces.\r\n-Functional Analysis: Basic understanding of function spaces, norms, and inner products.\r\n-Python Programming: A solid working knowledge of Python is required. However, the computational components of the course begin with structured and accessible coding tasks and progressively advance to more sophisticated implementations.\r\n-Teamwork and Collaboration: Since the course is built around structured group activities and collaborative problem-solving, students must be prepared to actively participate in teamwork, contribute responsibly to group tasks, and engage in constructive mathematical discussion.\r\nStudents should be comfortable working with mathematical abstractions, implementing numerical algorithms, and collaborating effectively with peers."},"prerequisites":{"en":"Prerequisites and co-requisites\r\nIntroduction to Inverse Problems, Core courses in the B.Sc curriculum of mathematical sciences, Numerical Analysis, Fourier analysis (recommended), Functional analysis (beneficial, but not necessary).","fi":"Esitietovaatimukset\r\nIntroduction to Inverse Problems, Core courses in the B.Sc curriculum of mathematical sciences, Numerical Analysis, Fourier analysis (recommended), Functional analysis (beneficial, but not necessary)."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Computational Inverse Problems","id":"otm-235ce05d-e41d-323e-b5e9-7ef34f9df084","code":"802661S","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-71fd8cc0-9fb4-38e1-bbb0-d1d63f911ddf"],"organisations":[],"attainmentLanguages":["en"],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}