Uncertainty Quantification of Graph Convolution Neural Network Models of Evolving Processes
This work addresses the need for reliable uncertainty quantification in neural network models for scientific machine learning, though it appears incremental as it compares existing methods on specific architectures.
The paper tackled the problem of quantifying uncertainty in neural network models of complex spatial-temporal processes, specifically comparing Hamiltonian Monte Carlo and Stein variational gradient descent methods on graph convolutional neural networks, showing that Stein variational inference provides similar uncertainty profiles with generally more generous variance.
The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural network models have proved to be adept at modeling processes with spatial-temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial-temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance.Projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.