Title: AI in Materials Science
Abstract: Materials informatics is an emerging area fusing aspects of computer science and machine learning with statistical inference and materials science. I will start by briefly providing a historical perspective on the value of information in the sciences and review some of the early work in materials science using older versions of tools we use today. Guiding materials discovery is essentially making smart or optimal decisions of what experiments or calculations to do next so that one can minimize the number needed to discover materials with desired properties. I will show how algorithms employed to train ALPHAGO, that has beaten GO grandmasters, are beginning to help us find materials with target response. Finally, in contrast to merely learning from data, I will show how physics based models can be employed to guide the discovery process.
Title: An Introduction to Topological Data Analysis (TDA)
Abstract: Topological Data Analysis is an emerging area which has been the center of attraction for many researchers in Mathematics and related to the field of Data Analysis, for more than two decades. TDA uses tools from algebraic topology to extract the topological information from data and understand the ‘shape’ of data. One of the main tools from TDA is persistent homology, which extracts the information related to the birth and death of multi-scale topological features of the data. TDA has many applications in Data clustering, Network analysis, Signal processing, Finance and Economics, Image Classification etc.
In these lectures, we will be focusing on the basics required to give an introduction to TDA and then give an overview of the TDA pipeline for Data Analysis.
Title: Supervised and Unsupervised Learning in Finance
Abstract: In this presentation, we will explore the use of machine learning for option pricing, focusing specifically on vanilla options (both European and American). We'll cover the use of feedforward neural networks and physics-informed neural networks (PINNs) for this purpose. The discussion will include an overview of the network architectures and their application to option valuation. We’ll evaluate and compare the efficiency of these approaches, considering both their accuracy and computational time. Finally, we'll highlight how these methods can be extended to more complex option pricing models, where alternative approaches might be computationally prohibitive.