FastPivot: An Algorithm for Inverse Problems

Yuling Guan, Ang Li, Sven Koenig, Stephan Haas, T. K. Satish Kumar

Abstract: The laws of physics are usually stated using mathematical equations, allowing us to accurately map a given physical system to its response. However, when building systems, we are often faced with the inverse problem: How should we design a physical system that produces a target response? In this paper, we present a novel algorithm, called FastPivot, for solving such inverse problems. FastPivot starts with a system state and invokes alternating forward and backward passes through the system variables. In a forward pass, it leads the current state of the system to its response. In the subsequent backward pass, a small amount of information is allowed to percolate from the target response back to the system variables. FastPivot produces good quality solutions efficiently. We demonstrate the promise of FastPivot on the inverse problem of placing atoms in a bounded region using a scanning tunneling microscope to achieve target responses in the density of states. We also compare FastPivot to Monte Carlo methods and analyze various empirical observations.