Deepanshu Verma, Emory University
2023 AWM Research Symposium
Recent Developments in Control, Optimization, and the Analysis of Partial Differential Equations [Organized by Lorena Bociu and Pelin Guven Geredeli]

This talk will focus on the applications of DNNs in high-dimensional optimal control problems. Traditional methods for solving these problems often suffer from the Curse-of-Dimensionality, where computational complexity increases exponentially with the dimension of the problem. Utilizing DNNs to approximate the value function of control problems can effectively tackle this issue. One of the key challenges in training is to discover the relevant parts of the state space. To address this, techniques from control theory will be employed to devise an unsupervised training algorithm. Several numerical experiments, including applications to PDE constrained optimization, will be presented.

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