论文标题
贝叶斯深度学习框架，用于高维度的不确定性定量
Bayesian deep learning framework for uncertainty quantification in high dimensions
论文作者
论文摘要
我们开发了一种新型的深度学习方法，用于基于贝叶斯神经网络（BNN）和汉密尔顿蒙特卡洛（HMC）的随机部分微分方程的不确定性定量。 BNN通过对网络参数进行贝叶斯推断，有效地了解深神经网络中参数的后验分布。使用HMC有效地采样后验分布来量化系统中的不确定性。在高维度的前进和反问题显示了几个数值示例，以证明提出的不确定性定量方法的有效性。这些还表明了令人鼓舞的结果，即计算成本几乎与问题的维度无关，证明了该方法应对所谓的维度诅咒的潜力。
We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior distribution of the parameters in deep neural networks by performing Bayesian inference on the network parameters. The posterior distribution is efficiently sampled using HMC to quantify uncertainties in the system. Several numerical examples are shown for both forward and inverse problems in high dimension to demonstrate the effectiveness of the proposed method for uncertainty quantification. These also show promising results that the computational cost is almost independent of the dimension of the problem demonstrating the potential of the method for tackling the so-called curse of dimensionality.
