With the emergence of the low-altitude economy, radio maps have become essential for ensuring reliable wireless connectivity to aerial platforms. Autonomous aerial agents are commonly deployed for data collection using waypoint-based navigation; however, their limited battery capacity significantly constrains coverage and efficiency. To address this, we propose an uncertainty-aware radio map (URAM) reconstruction framework that explicitly leverages graph-based reasoning tailored for waypoint navigation. Our approach integrates two key deep learning components: (1) a Bayesian neural network that estimates spatial uncertainty in real time, and (2) an attention-based reinforcement learning policy that performs global reasoning over a probabilistic roadmap, using uncertainty estimates to plan informative and energy-efficient trajectories. This graph-based reasoning enables intelligent, non-myopic trajectory planning, guiding agents toward the most informative regions while satisfying safety constraints. Experimental results show that URAM improves reconstruction accuracy by up to 34% over existing baselines.

For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can we be about their predictions. In the present work, we propose a highly efficient deep-learning surrogate framework that is able to accurately predict the response of bodies undergoing large deformations in real-time. The surrogate model has a convolutional neural network architecture, called U-Net, which is trained with force-displacement data obtained with the finite element method. We propose deterministic and probabilistic versions of the framework. The probabilistic framework utilizes the Variational Bayes Inference approach and is able to capture all the uncertainties present in the data as well as in the deep-learning model. Based on several benchmark examples, we show the predictive capabilities of the framework and discuss its possible limitations