论文标题
贝叶斯委员会的计算物理问题方法
The Bayesian Committee Approach for Computational Physics Problems
论文作者
论文摘要
在这项工作中，我们提出了一种有效学习多维功能的方法。该方法结合了贝叶斯神经网络和逐委员会的方法。由深贝叶斯神经网络组成的委员会不仅可以提供预测的不确定性，而且还可以提供委员会成员之间的差异。在目标函数迅速变化的区域中，不确定性和差异都很大，因此，这两个量都可用于将数据引导到此类区域。这样，我们可以准确地学习一个功能，而查询数据点的数量远小于均匀的采样。在这里，我们用两个示例测试我们的方法。一个例子是在相图中找到罕见的相位，该相位通过二阶相变与其他阶段分开。在此示例中，目标函数是敏感性函数，并且由于敏感性函数的差异定位了相图，因此搜索此相位的任务与我们方法的优势完全匹配。另一个例子是学习高维函数的蒙特卡洛整合的分布函数。在这两个示例中，我们都表明我们的方法的性能高于均匀抽样。我们的方法可以在计算科学问题中找到广泛的应用。
In this work, we propose a method for efficient learning of a multi-dimensional function. This method combines the Bayesian neural networks and the query-by-committee method. A committee made of deep Bayesian neural networks not only can provide uncertainty of the prediction but also can provide the discrepancy between committee members. Both the uncertainty and the discrepancy are large in the regions where the target function varies rapidly, and therefore, both quantities can be used to guide sampling data to such regions. In this way, we can learn a function accurately with the number of queried data points much less than uniform sampling. Here we test our method with 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. In this example, the target function is the susceptibility function, and since the divergence of the susceptibility function locates the phase diagram, the task of searching such a phase perfectly matches the advantage of our method. Another example is to learn the distribution function for Monte Carlo integration of a high-dimensional function. In both examples, we show that our method performs significantly efficiently than uniform sampling. Our method can find broad applications in computational scientific problems.
