  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.
