提出cSVGD方法，实现神经网络参数的稀疏化、训练与不确定性量化同步完成。
Condensed Stein Variational Gradient Descent for Uncertainty Quantification of Neural Networks
- 通过图重构与参数凝聚降低模型复杂度，提升斯坦因集合相似性。
- 在固体力学表征问题中验证，可对参数本身提供不确定性估计，加速收敛。
- 适合需要高可信度参数估计的科学建模场景，如物理信息神经网络。
我们提出一种斯坦因变分梯度下降方法，能够同时对复杂参数化的模型（如神经网络）进行稀疏化、训练和不确定性量化。该方法采用图重构与凝聚过程，降低斯坦因参数集合的复杂度并增强其相似性。因此，所提出的凝聚斯坦因变分梯度（cSVGD）方法可对模型参数而非仅输出提供不确定性量化。此外，参数压缩通过对齐并区分参数敏感性，降低了组合复杂度，从而加快了斯坦因梯度下降的收敛速度。该方法在示例问题及固体力学中的表征任务中得到验证。
原文摘要 · Abstract (English)
We propose a Stein variational gradient descent method to concurrently sparsify, train, and provide uncertainty quantification of a complexly parameterized model such as a neural network. It employs a graph reconciliation and condensation process to reduce complexity and increase similarity in the Stein ensemble of parameterizations. Therefore, the proposed condensed Stein variational gradient (cSVGD) method provides uncertainty quantification on parameters, not just outputs. Furthermore, the parameter reduction speeds up the convergence of the Stein gradient descent as it reduces the combinatorial complexity by aligning and differentiating the sensitivity to parameters. These properties are demonstrated with an illustrative example and an application to a representation problem in solid mechanics.
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