Most scientific machine learning (SciML) applications of neural networks involve hundreds to thousands of parameters, and hence, uncertainty quantification for such models is plagued by the curse of dimensionality. Using physical applications, we show that $L_0$ sparsification prior to Stein variational gradient descent ($L_0$+SVGD) is a more robust and efficient means of uncertainty quantification, in terms of computational cost and performance than the direct application of SGVD or projected SGVD methods. Specifically, $L_0$+SVGD demonstrates superior resilience to noise, the ability to perform well in extrapolated regions, and a faster convergence rate to an optimal solution.

翻译：大多数科学机器学习（SciML）的神经网络应用涉及数百至数千个参数，因此此类模型的不确定性量化深受维度灾难的困扰。通过物理应用案例，我们证明在Stein变分梯度下降（SVGD）前进行$L_0$稀疏化（$L_0$+SVGD）是一种比直接应用SVGD或投影SVGD方法更具鲁棒性和效率的不确定性量化手段，其优势体现在计算成本与性能两方面。具体而言，$L_0$+SVGD展现出更强的噪声抵抗能力、在外推区域保持良好性能的特性，以及更快的收敛速度至最优解。