  Complex systems may be subject to various uncertainties. A great effort has
been concentrated on predicting the dynamics under uncertainty in initial
conditions. In the present work, we consider the well-known Burgers equation
with random boundary forcing or with random body forcing. Our goal is to
attempt to understand the stochastic Burgers dynamics by predicting or
estimating the solution processes in various diagnostic metrics, such as mean
length scale, correlation function and mean energy. First, for the linearized
model, we observe that the important statistical quantities like mean energy or
correlation functions are the same for the two types of random forcing, even
though the solutions behave very differently. Second, for the full nonlinear
model, we estimate the mean energy for various types of random body forcing,
highlighting the different impact on the overall dynamics of space-time white
noises, trace class white-in-time and colored-in-space noises, point noises,
additive noises or multiplicative noises.
