基于神经网络的高维committer函数的半群方法
A semigroup method for high dimensional committor functions based on neural network
摘要：
本文提出了一种基于神经网络计算满足Fokker-Planck方程的高维committor函数的新方法。该方法不使用偏微分方程，而是使用基于微分算子半群的积分公式。新配方的变分形式，然后解决了参数化的提交函数作为一个神经网络。这种新方法有两个主要好处。首先，随机梯度下降型算法可以应用于提交者函数的训练，而不需要计算任何混合二阶导数。此外，与以前的方法，通过惩罚项强制边界条件，新的方法自动考虑边界条件。数值结果证明了所提出的方法的性能。
英文摘要：
This paper proposes a new method based on neural networks for computing the high-dimensional committor functions that satisfy Fokker-Planck equations. Instead of working with partial differential equations, the new method works with an integral formulation based on the semigroup of the differential operator. The variational form of the new formulation is then solved by parameterizing the committor function as a neural network. There are two major benefits of this new approach. First, stochastic gradient descent type algorithms can be applied in the training of the committor function without the need of computing any mixed second-order derivatives. Moreover, unlike the previous methods that enforce the boundary conditions through penalty terms, the new method takes into account the boundary conditions automatically. Numerical results are provided to demonstrate the performance of the proposed method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
