Computational Inverse Problems is a Master’s level course introducing the statistical and computational foundations of inverse problems within the Bayesian framework. The course focuses on formulating inverse problems as problems of probabilistic inference, modeling uncertainty through appropriate prior distributions, and computing posterior distributions using modern sampling algorithms.
Students will study multivariate Gaussian models, covariance operators, and the Karhunen–Loève expansion, and learn how to formulate both finite- and infinite-dimensional inverse problems. Computational methods include maximum a posteriori (MAP) estimation, the Metropolis–Hastings algorithm, and Hamiltonian Monte Carlo. The course also provides an introduction to Bayesian optimal experimental design.
Emphasis is placed on combining mathematical rigor with practical implementation in Python. Through collaborative problem-solving, weekly assignments, and a final project, students develop the ability to analyze, approximate, and interpret posterior distributions, and to quantify uncertainty in complex inverse problems.
- Opettaja: Lam Duong
- Opettaja: Babak Maboudi Afkham
- Opettaja: Hassan Yazdanian