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About the Lectures

This four-lecture seminar series introduces the basic concept of machine learning and its applications. The following topics will be covered: a) machine learning approaches (supervised learning, unsupervisedÌýlearning, and reinforcement learning); b) deep neural networks (from biological neurons to artificial neurons, neural networks for supervised learning, and neural network training via empirical risk minimization); c) more advanced topics on neural networks (universal approximation theorem, stochastic gradient descent with backpropagation, and exploding and vanishing issues); and d) recent personal research on scientific deep learning approaches for learning forward and inverse solutions of PDEs.

Tan Bui-Thanh's Bio

Tan Bui-Thanh is an Associate Professor, and the endowed William J Murray Jr. Fellow in Engineering No. 4, of the Oden Institute for Computational Engineering & Sciences, and the Department of Aerospace Engineering & Engineering Mechanics at the University of Texas at Austin. Bui-Thanh obtained his PhD from the Massachusetts Institute of Technology in 2007, Master of Sciences from the Singapore MIT-Alliance in 2003, and Bachelor of Engineering from the Ho Chi Minh City University of Technology (DHBK) in 2001.

He has decades of experience and expertise on multidisciplinary research across the boundaries of different branches of computational science, engineering, and mathematics. Bui-Thanh is currently a Co-director of the Center for Scientific Machine Learning at the Oden Institute. He is a former elected vice president of the SIAM Texas-Louisiana Section, and the former elected secretary of the SIAM SIAG/CSE. Bui-Thanh was an NSF (OAC/DMS)Ìýearly CAREER recipient, the Oden Institute distinguished research award, and a two-time winner of the Moncrief Faculty Challenging Award.

Detailed Information About the Lectures

Lecture 1. What is machine learning?Ìý

This talk provides an introduction to the field of machine learning, in particular:

• ÌýWhat is the difference between traditional programming and machine learning?
• Supervised learning (regression, classification, and neural networks)
• Unsupervised learning (density approximation, clustering, and dimensionality reduction)
• Reinforcement learning

Lecture 2. Deep Neural NetworksÌý

Topics covered:

• Biological neurons versus artificial neurons, McCulloch-Pitts neurons
• (Artificial) deep neural networks (notations, architecture, and mathematical descriptions)
• Neural networks for supervised learning
• Neural network training problems with optimization

Lecture 3. Additional topics on neural networksÌý

Topics covered:

• Is neural network that good (universal approximation theorem)?
• Training neural network with stochastic gradient descent via backpropagation
• Exploding and vanishing issues (if time permits)

Lecture 4. Some applications of deep learning in researchÌý

Topics covered:

• A deep learning approach for learning solution of PDEs (forward problems)Ìý
• A deep learning approach for solutions of PDE-constrained optimization (inverse problems)

RegistrationÌý