  In large-scale computation of physics problems, one often encounters the
problem of determining a multi-dimensional function, which can be
time-consuming when computing each point in this multi-dimensional space is
already time-demanding. In the work, we propose that the active learning
algorithm can speed up such calculations. The basic idea is to fit a
multi-dimensional function by neural networks, and the key point is to make the
query of labeled data economically by using a stratagem called "query by
committee". We present the general protocol of this fitting scheme, as well as
the procedure of how to further compute physical observables with the fitted
functions. We show that this method can work well with two examples, which are
quantum three-body problem in atomic physics and the anomalous Hall
conductivity in condensed matter physics, respectively. In these examples, we
show that one reaches an accuracy of few percent error for computing physical
observables with less than $10\%$ of total data points compared with uniform
sampling. With these two examples, we also visualize that by using the active
learning algorithm, the required data are added mostly in the regime where the
function varies most rapidly, which explains the mechanism for the efficiency
of the algorithm. We expect broad applications of our method on various kind of
computational physics problems.
