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In this work, we propose a method for efficient learning of amulti-dimensional function. This method combines the Bayesian neural networksand the query-by-committee method. A committee made of deep Bayesian neuralnetworks not only can provide uncertainty of the prediction but also canprovide the discrepancy between committee members. Both the uncertainty and thediscrepancy are large in the regions where the target function varies rapidly,and therefore, both quantities can be used to guide sampling data to suchregions. In this way, we can learn a function accurately with the number ofqueried data points much less than uniform sampling. Here we test our methodwith two examples. One example is to find a rare phase in a phase diagram,which is separated from other phases by a second-order phase transition. Inthis example, the target function is the susceptibility function, and since thedivergence of the susceptibility function locates the phase diagram, the taskof searching such a phase perfectly matches the advantage of our method.Another example is to learn the distribution function for Monte Carlointegration of a high-dimensional function. In both examples, we show that ourmethod performs significantly efficiently than uniform sampling. Our method canfind broad applications in computational scientific problems.

The Bayesian Committee Approach for Computational Physics Problems