Nick Winovich

Nick Winovich, Mitchell Daneker, Lu Lu et al.

In this work, we develop a method for uncertainty quantification in deep operator networks (DeepONets) using predictive uncertainty estimates calibrated to model errors observed during training. The uncertainty framework operates using a single network, in contrast to existing ensemble approaches, and introduces minimal overhead during training and inference. We also introduce an optimized implementation for DeepONet inference (reducing evaluation times by a factor of five) to provide models well-suited for real-time applications. We evaluate the uncertainty-equipped models on a series of partial differential equation (PDE) problems, and show that the model predictions are unbiased, non-skewed, and accurately reproduce solutions to the PDEs. To assess how well the models generalize, we evaluate the network predictions and uncertainty estimates on in-distribution and out-of-distribution test datasets. We find the predictive uncertainties accurately reflect the observed model errors over a range of problems with varying complexity; simpler out-of-distribution examples are assigned low uncertainty estimates, consistent with the observed errors, while more complex out-of-distribution examples are properly assigned higher uncertainties. We also provide a statistical analysis of the predictive uncertainties and verify that these estimates are well-aligned with the observed error distributions at the tail-end of training. Finally, we demonstrate how predictive uncertainties can be used within an active learning framework to yield improvements in accuracy and data-efficiency for outer-loop optimization procedures.

Sangpil Kim, Nick Winovich, Guang Lin et al.

We propose a fully-convolutional conditional generative model, the latent transformation neural network (LTNN), capable of view synthesis using a light-weight neural network suited for real-time applications. In contrast to existing conditional generative models which incorporate conditioning information via concatenation, we introduce a dedicated network component, the conditional transformation unit (CTU), designed to learn the latent space transformations corresponding to specified target views. In addition, a consistency loss term is defined to guide the network toward learning the desired latent space mappings, a task-divided decoder is constructed to refine the quality of generated views, and an adaptive discriminator is introduced to improve the adversarial training process. The generality of the proposed methodology is demonstrated on a collection of three diverse tasks: multi-view reconstruction on real hand depth images, view synthesis of real and synthetic faces, and the rotation of rigid objects. The proposed model is shown to exceed state-of-the-art results in each category while simultaneously achieving a reduction in the computational demand required for inference by 30% on average.