Sampling Methods for Uncertainty Quantification

CAP 6938 (Spring 2026)

Department of Computer Science
University of Central Florida
Orlando, FL, USA

Instructor and TA information

Email: alisk@ucf.edu
Office hours: TBA

TAs:

Description

This special topics course introduces modern computational sampling methods for uncertainty quantification in scientific computing and engineering applications. Topics include mathematical and computational principles of classical and contemporary sampling approaches with emphasis on understanding the inner workings of deep generative models, variational inference, and simulation-based inference methods. Students implement sampling algorithms and apply them to uncertainty quantification problems through hands-on programming assignments.

Why take this course?

AI models have recently driven significant advances in various science and engineering domains, yet critical reliability concerns remain: models produce unreliable predictions, lack quantifiable safety guarantees, and their theoretical foundations remain opaque to many practitioners. Current approaches focused on scaling and post-hoc validation cannot systematically address these issues. In this course, you will learn modern uncertainty quantification techniques that not only can be applied widely in various science and engineering domains but also hold the key to designing more reliable AI models. You will go beyond treating generative models, which are key components of modern sampling and uncertainty quantification techniques, as black boxes, understanding and implementing the core mathematical principles that make them work. Through five hands-on programming assignments, you will build these algorithms from the ground up, gaining the deep foundational expertise needed to adapt, debug, and innovate in this rapidly evolving field.

Prerequisites

Students should have background in probability theory, linear algebra, and programming. Familiarity with deep learning basics is recommended but not required.

Textbooks

There is no required textbook for the class. A list of recommended papers will be provided during the course.

Grading

Programming assignments 75% (5 assignments × 15% each)
Paper presentation 25%
There will be 2% extra credit for submitting teaching evaluation, if more than 80% of students submitted the evaluation

Tentative schedule

Course material will be posted on the website before each lecture. The instructor reserves the right to alter this schedule as needed.

Week	Module	Lecture Topics	Assignments/Notes
Week 1-2	Module 1: Foundations	Uncertainty quantification in scientific computing Review of probability, linear algebra, and deep learning background Monte Carlo methods and importance sampling Markov Chain Monte Carlo (Metropolis-Hastings, Gibbs sampling) Convergence diagnostics and effective sample size	Assignment 1
Week 3-4	Module 2: Modern MCMC	Gradient-based MCMC: Langevin dynamics and MALA Hamiltonian Monte Carlo fundamentals No-U-Turn Sampler (NUTS) Adaptive MCMC methods Practical considerations and debugging strategies	Assignment 2 Assignment 1 due
Week 5-7	Module 3: Variational Inference	Variational inference and the Evidence Lower Bound (ELBO) Variational autoencoders for uncertainty representation Amortized inference and reparameterization trick Stein Variational Gradient Descent (SVGD) and particle-based methods VI vs MCMC tradeoffs and diagnostics	Assignment 3 Assignment 2 due
Week 8-9	Module 4: Deep Generative Models	Normalizing flows for exact density modeling Coupling layers and autoregressive flows Invertible neural networks Diffusion models and score-based generative models Maximum likelihood perspective on flow and diffusion models	Assignment 4 Assignment 3 due
Week 10-11	Module 5: Simulation-Based Inference	Likelihood-free inference and Approximate Bayesian Computation (ABC) Neural posterior estimation and neural likelihood estimation Sequential methods and active learning Practical implementation and diagnostic tools	Assignment 5 Assignment 4 due
Week 12-13	Instructor-Guided Paper Discussions	Instructor curates and leads discussions on 4-6 recent research papers	Assignment 5 due
Week 14-15	Student Paper Presentations	Student presentations on research papers (selected from curated list or instructor-approved) Critical analysis and discussion of recent developments Advanced topics and cutting-edge developments in sampling methodology	Paper presentations