Scientific Machine Learning

Course content

Intended learning outcome:

In this course students will get a comprehensive introduction to the machine learning techniques and will gain the ability to formulate and solve complex probabilistic models by using the sum and product rules of probability. Through the machine learning techniques acquired in this course, students will gain the ability to generate models in engineering design optimization, which enable them to explore the solutions automatically and efficiently by exploiting the uncertainties obtained in the learning process. Besides, preprocessing such as feature extraction, which is often used in image recognition technology, can also be performed by the machine learning techniques acquired in this course. These contribute to the simplification of problems and cost efficiency in engineering problems in general, and also enable automatic sample generation, so to say, constructing new images in the above example. Furthermore, in scientific problems, it is used as a key technology to reveal essential physical quantities. Overall by viewing globally and unifying the theory of probability from Bayesian perspectives, students will be able to formulate probabilistic models actively and to acquire proper machine learning approaches on each problem setting. The course includes practical tutorials using computer programs.

Module content:

• Introduction to machine learning
• Theory of probability
• Linear regression models
• Regularization
• Extension to Bayesian approaches
• Dual representation (Kernel methods)
• Gaussian processes (Kriging)
• Neural networks
• Extension to unsupervised learning
• Sampling, optimization and efficient numerical methods for the Bayesian approaches
• Graphical models
• Global perspective of the methods via the Bayesian statistics