Operator learning has been increasingly adopted in scientific and engineering applications, many of which require calibrated uncertainty quantification. Since the output of operator learning is a continuous function, quantifying uncertainty simultaneously at all points in the domain is challenging. Current methods consider calibration at a single point or over one scalar function or make strong assumptions such as Gaussianity. We propose a risk-controlling quantile neural operator, a distribution-free, finite-sample functional calibration conformal prediction method. We provide a theoretical calibration guarantee on the coverage rate, defined as the expected percentage of points on the function domain whose true value lies within the predicted uncertainty ball. Empirical results on a 2D Darcy flow and a 3D car surface pressure prediction task validate our theoretical results, demonstrating calibrated coverage and efficient uncertainty bands outperforming baseline methods. In particular, on the 3D problem, our method is the only one that meets the target calibration percentage (percentage of test samples for which the uncertainty estimates are calibrated) of 98%.

This early-stage research work aims to improve online human-robot imitation by translating sequences of joint positions from the domain of human motions to a domain of motions achievable by a given robot, thus constrained by its embodiment. Leveraging the generalization capabilities of deep learning methods, we address this problem by proposing an encoder-decoder neural network model performing domain-to-domain translation. In order to train such a model, one could use pairs of associated robot and human motions. Though, such paired data is extremely rare in practice, and tedious to collect. Therefore, we turn towards deep learning methods for unpaired domain-to-domain translation, that we adapt in order to perform human-robot imitation.