A Stochastic Gradient Descent Method for Computational Design of Random Rough Surfaces in Solar Cells (Communications in Computational Physics, 2023)
In this work, we develop a stochastic gradient descent method for the computational optimal design of random rough surfaces in thin-film solar cells. We formulate the design problems as random PDE-constrained optimization problems and seekthe optimal statistical parameters for the random surfaces. The optimizations at fixedfrequency as well as at multiple frequencies and multiple incident angles are investigated. To evaluate the gradient of the objective function, we derive the shape derivatives for the interfaces and apply the adjoint state method to perform the computation.The stochastic gradient descent method evaluates the gradient of the objective functiononly at a few samples for each iteration, which reduces the computational cost significantly. Various numerical experiments are conducted to illustrate the efficiency of themethod and significant increases of the absorptance for the optimal random structures.We also examine the convergence of the stochastic gradient descent algorithm theoretically and prove that the numerical method is convergent under certain assumptionsfor the random interfaces.
Keywords: Optimal design; random rough surface; solar cell; Helmholtz equation; stochastic gradient descent method.