Advanced Applied Mathematics Seminar
Speaker: Arpita Mondal, IIT Bombay
Host: Manas Rachh
Title: Statistical Learning and Data Science for Climate Risk Assessment
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, August 13
Venue: Ramanujan Hall
Abstract: Risk of hydroclimatic extreme events informs engineering decision-making and sustainable environment management. This talk will highlight recent research efforts using advanced statistical frameworks, extreme value theory, unsupervised learning, predictive data-driven modeling and multi-criteria decision-making for attribution of hydroclimatic hazards in India to climate change, assessing their impact and quantifying their interactions with socio economic exposure and vulnerability. While the applied mathematical, statistical or data-driven methods are applicable to a class of extreme events, the talk will focus on the risk of hot extremes and heat waves in India and their interactions with other hazards such as droughts and air pollution.

Algebraic Groups Seminar
Speaker: Hariom Sharma, IIT Bombay, Mumbai
Host: Shripad M. Garge
Title: Iwahori Hecke algebras
Time, day and date: 5:00:00 PM - 7:00:00 PM, Thursday, August 13
Venue: Conference Room
Abstract: Hecke algebras

Deep Learning in Finance – Lecture 4
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Learning Stochastic Processes Part II: Ito Diffusion
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, August 13
Venue: Ramanujan Hall
Abstract: This presentation extends the learning of stochastic processes from parameter calibration to the more general problem of discovering stochastic differential equations directly from observed data. The objective is to learn the unknown drift and diffusion coefficients of Itô diffusions using neural networks trained on multiple sample trajectories. Separate learning strategies are developed for time-dependent, state-dependent, and fully general stochastic models, exploiting either explicit analytical solutions when available or Euler discretizations when closed-form solutions do not exist. The methodology estimates the local statistical moments of the process increment and uses them to train neural networks that provide smooth approximations of the drift and volatility functions, leading to the framework of Stochastically Informed Neural Networks (SINNs), a stochastic counterpart of Physics-Informed Neural Networks (PINNs). The approach is illustrated for generalized Brownian motion with drift, generalized geometric Brownian motion, and autonomous Itô diffusions, where suitable transformations, such as the logarithmic transformation for stock-price models, simplify the learning problem. The resulting framework enables the identification of stochastic models directly from data and provides flexible, data-driven representations of time-varying and state-dependent dynamics with applications in finance, physics, engineering, and other scientific disciplines.