Active operator learning with predictive uncertainty quantification for partial differential equations

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.

CT-GAN: Conditional Transformation Generative Adversarial Network for Image Attribute Modification

We propose a novel, fully-convolutional conditional generative model capable of learning image transformations using a light-weight network suited for real-time applications. We introduce the conditional transformation unit (CTU) designed to produce specified attribute modifications and an adaptive discriminator used to stabilize the learning procedure. We show that the network is capable of accurately modeling several discrete modifications simultaneously and can produce seamless continuous attribute modification via piece-wise interpolation. We also propose a task-divided decoder that incorporates a refinement map, designed to improve the network's coarse pixel estimation, along with RGB color balance parameters. We exceed state-of-the-art results on synthetic face and chair datasets and demonstrate the model's robustness using real hand pose datasets. Moreover, the proposed fully-convolutional model requires significantly fewer weights than conventional alternatives and is shown to provide an effective framework for producing a diverse range of real-time image attribute modifications.