Self-supervised learning is a powerful approach for developing traversability models for off-road navigation, but these models often struggle with inputs unseen during training. Existing methods utilize techniques like evidential deep learning to quantify model uncertainty, helping to identify and avoid out-of-distribution terrain. However, always avoiding out-of-distribution terrain can be overly conservative, e.g., when novel terrain can be effectively analyzed using a physics-based model. To overcome this challenge, we introduce Physics-Informed Evidential Traversability (PIETRA), a self-supervised learning framework that integrates physics priors directly into the mathematical formulation of evidential neural networks and introduces physics knowledge implicitly through an uncertainty-aware, physics-informed training loss. Our evidential network seamlessly transitions between learned and physics-based predictions for out-of-distribution inputs. Additionally, the physics-informed loss regularizes the learned model, ensuring better alignment with the physics model. Extensive simulations and hardware experiments demonstrate that PIETRA improves both learning accuracy and navigation performance in environments with significant distribution shifts.

One of the main difficulties in facial age estimation is the lack of sufficient training data for many ages. Fortunately, the faces at close ages look similar since aging is a slow and smooth process. Inspired by this observation, in this paper, instead of considering each face image as an example with one label (age), we regard each face image as an example associated with a label distribution. The label distribution covers a number of class labels, representing the degree that each label describes the example. Through this way, in addition to the real age, one face image can also contribute to the learning of its adjacent ages. We propose an algorithm named IIS-LLD for learning from the label distributions, which is an iterative optimization process based on the maximum entropy model. Experimental results show the advantages of IIS-LLD over the traditional learning methods based on single-labeled data.