用贝叶斯方法提升PINN在逆问题中的不确定性估计能力
Bayesian PINNs for uncertainty-aware inverse problems (BPINN-IP)
- 构建分层贝叶斯框架，融合先验知识与网络权重信息
- 通过后验分布实现图像重建的不确定性量化
- 适用于需可信度评估的图像恢复任务，如去卷积与超分辨率
本文提出一种用于线性逆问题的分层贝叶斯物理信息神经网络（BPINN-IP）。该方法将先验知识引入神经网络输出及权重，利用变分推断和蒙特卡洛丢弃法获得重建图像的预测均值与方差，从而自然地量化不确定性。以去卷积和超分辨为例，详细说明了实现步骤并展示了初步结果。
原文摘要 · Abstract (English)
The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the expected NN output, as well as its weights. Also, as we can have access to the posterior probability distributions, naturally uncertainties can be quantified. Also, variational inference and Monte Carlo dropout are employed to provide predictive means and variances for reconstructed images. Un example of applications to deconvolution and super-resolution is considered, details of the different steps of implementations are given, and some preliminary results are presented.
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