This online course introduces students to relevant paradigms, mathematical foundations and numerical techniques in Uncertainty Quantification (UQ), which is a research area of growing importance. The surveyed numerical techniques include Monte Carlo, Markov chain Monte Carlo, multilevel sampling, statistical inference, surrogate-based computation, Gaussian process, Polynomial Chaos expansion, probabilistic machine learning, etc. The course will cover forward predictive analysis, model calibration, validation, and also model selection under uncertainties. Examples will be drawn from structural and mechanical (solid and fluid) systems, seismic models, and flow in porous media. Source codes for these models will be provided and students will apply the learned subjects by developing codes and applying them to the engineering problems. The course tries to strike a balance between the fundamental knowledge and computational implementation, and can equip students with a unique skill set needed for future success in industry or academic positions (in data science and scientific computing).
Schedule and location:
Lectures are online,
Credit: 4 hours
Prerequisites:
Background knowledge and experience in probability theory and statistics (at 400 level), numerical methods, and good programming skills.
Syllabus:
- Goals and applications of uncertainty quantification
- Brief review of important concepts from probability theory
- Monte Carlo methods
- Advanced sampling techniques, variance reduction
- Markov chain Monte Carlo (MCMC)
- Statistical inference, model calibration
- Random fields, Karhunen-Loève expansion
- Gaussian processes
- Infinite-dimensional polynomial chaos expansions
- Probabilistic machine learning: least square, compressed sensing.
- Sparse grid
- Surrogate-based Bayesian inference
- Model error and model validation
- Bayesian model averaging
Fall 2016 & Spring 2017: CEE 598-UQ: Uncertainty Quantification
Fall 2014 and Fall 2015: CEE 201 Systems Engineering and Economics
Introduction to the formulation and solution of civil engineering problems. Major topics: engineering economy, mathematical modeling, and optimization. Application of techniques, including classical optimization, linear and nonlinear programming, network theory, critical path methods, simulation, decision theory, and dynamic programming to a variety of civil engineering problems.
Textbook: Civil and Environmental Systems Engineering, by ReVelle et al., 2004, 2nd Edition.
Spring 2015: CEE 460 Steel Structures I
Introduction to the design of metal structures; behavior of members and their connections; theoretical, experimental, and practical bases for proportioning members and their connections.
Textbook: Structural Steel Design, by McCormac & Csernak, 2012, 5th Edition.
