A Physics-informed Deep Learning Approach for Minimum Effort Stochastic Control of Colloidal Self-Assembly [article]

Iman Nodozi, Jared O'Leary, Ali Mesbah, Abhishek Halder
2022 arXiv   pre-print
We propose formulating the finite-horizon stochastic optimal control problem for colloidal self-assembly in the space of probability density functions (PDFs) of the underlying state variables (namely, order parameters). The control objective is formulated in terms of steering the state PDFs from a prescribed initial probability measure towards a prescribed terminal probability measure with minimum control effort. For specificity, we use a univariate stochastic state model from the literature.
more » ... th the analysis and the computational steps for control synthesis as developed in this paper generalize for multivariate stochastic state dynamics given by generic nonlinear in state and non-affine in control models. We derive the conditions of optimality for the associated optimal control problem. This derivation yields a system of three coupled partial differential equations together with the boundary conditions at the initial and terminal times. The resulting system is a generalized instance of the so-called Schrödinger bridge problem. We then determine the optimal control policy by training a physics-informed deep neural network, where the "physics" are the derived conditions of optimality. The performance of the proposed solution is demonstrated via numerical simulations on a benchmark colloidal self-assembly problem.
arXiv:2208.09182v2 fatcat:ftfcw7kwurektmcefa7xvjah3y