DMS Applied Mathematics Seminar

Speaker: Somak Das

Title: Stochastic gradient descent and adaptive gradient descent methods in control of stochastic partial differential equations

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 in this project, 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, has also widespread applications in large scale stochastic optimizations. The algorithm adjusts its step-size at every iteration depending on the current gradient value unlike stochastic gradient where we need to re-tune the step-size manually. In this talk we show the results obtained from these algorithms.