Data Analytics for Scientists and Engineers
Learning Objective:This course provides an introduction to data analytics for individuals with no prior knowledge of data science or machine learning.
The course starts with an extensive review of probability theory as the language of uncertainty, discusses Monte Carlo sampling for uncertainty propagation, covers the basics of supervised (Bayesian generalized linear regression, logistic regression, Gaussian processes, deep neural networks, convolutional neural networks), unsupervised learning (k-means clustering, principal component analysis, Gaussian mixtures) and state space models (Kalman filters). The course also reviews the state-of-the-art in physics-informed deep learning and ends with a discussion of automated Bayesian inference using probabilistic programming (Markov chain Monte Carlo, sequential Monte Carlo, and variational inference). Throughout the course, the instructor follows a probabilistic perspective that highlights the first principles behind the presented methods with the ultimate goal of teaching the student how to create and fit their own models
Topics Covered:Introduction to predictive modeling. Review of probability theory. Uncertainty propagation using Monte Carlo. Principles of Bayesian inference. Supervised learning: linear and logistic regression. Unsupervised learning: clustering, density estimation, and dimensionality reduction. State-space models: Kalman filters. Gaussian process regression. Neural networks: regression, classification, physics-informed machine learning. Advanced methods for characterizing posteriors: Markov chain Monte Carlo, variational inference
- Working knowledge of multivariate calculus and basic linear algebra
- Basic Python knowledge
- Knowledge of probability and numerical methods for engineering would be helpful, but not required