Abstract: It introduces two different kinds of function space, probability space and proper orthogonal space, both of which are used to describe the physics motions of Burgers equation. In order to discuss the distance between them, it proposed a problem involving the minimum average distance between probability space and proper orthogonal space. Here, simulated annealing was used to solve this problem. Besides,  by applying the minimum average distance, an approximate solution to Burgers equation was attained through the linear combination of basis functions of proper orthogonal space.

Key words: Burgers equation; probability space; proper orthogonal space; minimum average distance; simulated annealing