DMS Graduate Student Seminar

Speaker: Mr.  Somak Das

Title: Adaptive Gradient Descent Method in Optimal Control of Partial Differential Equation with Random Parameters.

Abstract: Most of our contemporary mathematical models are based on partial differential equations. However, the varied levels of randomness pose difficulties for such systems to be accurately modeled using deterministic partial differential equations. In such settings we use stochastic partial differential equations to incorporate the randomness. To determine the optimal control for the stochastic system, we adopt the stochastic gradient descent algorithm. With vast data sets being customary for training of most machine learning algorithms, the stochastic gradient descent method is one of the efficient ways to obtain the optimal control. Another class of algorithms, adaptive gradient, also has widespread applications in large scale stochastic optimization. The algorithm is robust and adjusts its step size at every iteration depending on the current gradient value unlike stochastic gradient where we need to retune the step-size manually. In this talk, we show the results obtained from these algorithms.