in which f (x) is the speed function, and u(x) is the time function, ∂Ω is the boundary of the surface Ω. As the gradient of the time decreases with the increase in speed, u(x) can be treated as the shortest time to reach ∂Ω from a point x on the surface. In the context of using this method to find the MFEP, if a starting point and an end point are specified, one then wishes to find the path that costs the least amount of 'time' from the start to the end, while the 'speed' should be inversely proportional to the energy, U(q).