Speaker
Description
We study optimal control problems arising from partial differential equations. More specifically, we look at the optimal control of Allen-Cahn Equation (ACE) with a source term. ACE is well known for modeling phase transitions and thus, has many applications, apart from physics (semiconductors), in biological systems, material science and image processing. ACE models cellular membranes which are vital in transporting vesicles, viral budding and dynamical sorting and signaling.
Through the dynamic programming principle, optimal control problem are reformulated into the Hamilton-Jacobi-Bellman (HJB) Equations. It is well known that the computational cost is prohibitively expensive when standard methods are implemented in solving the HJB Equations. Thus we obtain reduced order models, using tensor decomposition techniques for reduced order basis. Sparse optimization and flexible hybrid methods are used for low rank canonical polyadic tensor decomposition. The reduced optimal control problem leads to reduced state-dependent Riccati Equations which can be solved efficiently.