Improving the performance of Stein variational inference through extreme sparsification of physically-constrained neural network models

However, the well-established methods for obtaining posterior distributions of likely parameters such as Markov chain Monte Carlo (MCMC) sampling [1] become infeasible with highly parameterized machine learning function representations, such as neural networks (NNs). The curse of dimensionality in this uncertainty quantification (UQ) setting is tied to the cost of sampling the posterior sufficiently to determine its covariance structure and generate representative push-forward realizations. In this work, our goal is to obtain a high-dimensional posterior distribution over a large number of random variables representing model parameters, which is particularly useful when limited amount of training data is available. One of the simplest ways to obtain the approximate posterior is to implement MCMC methods. However, this approach is challenged by the number of parameters typically present in NNs and it is difficult to converge samples to those representative of the posterior, even for models with moderate dimensionality. There has been enormous progress made to approximate high-dimensional posterior distributions using variational inference methods [2]. However, these methods restrict the approximate posterior to a certain parametric family and find the best approximate posterior through optimization. To surmount these issues, Liu and Wang [3] recently proposed a non-parametric variational inference method called Stein variational gradient descent (SVGD).