One often makes trade-offs between these goals, as a result of practical considerations (e.g., computational efficiency); see Table S1 in the Supplementary Material (SUPP) for a brief summary.

We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need for data-driven correction. Moreover, non-autonomous dynamics are governed by time-dependent control inputs, which pose challenges in learning predictive models directly from temporal snapshot data. To address these, we reformulate the vehicle dynamics via a local parameterization of the time-dependent inputs, yielding a modified system composed of a sequence of local parametric dynamical systems. We approximate these parametric systems using two complementary approaches. First, we employ the DRIPS (dimension reduction and interpolation in parameter space) methodology to construct efficient linear surrogate models, equipped with lifted observable spaces and manifold-based operator interpolation. This enables data-efficient learning of vehicle models whose dynamics admit accurate linear representations in the lifted spaces. Second, for more strongly nonlinear systems, we employ FML (Flow Map Learning), a deep neural network approach that approximates the parametric evolution map without requiring special treatment of nonlinearities. We further extend FML with a transfer-learning-based model correction procedure, enabling the correction of misspecified prior models using only a sparse set of high-fidelity or experimental measurements, without assuming a prescribed form for the correction term. Through a suite of numerical experiments on unicycle, simplified bicycle, and slip-based bicycle models, we demonstrate that DRIPS offers robust and highly data-efficient learning of non-autonomous vehicle dynamics, while FML provides expressive nonlinear modeling and effective correction of model-form errors under severe data scarcity.

Balancing resource efficiency and fairness is critical in networked systems that support modern learning applications. We introduce the Fair Minimum Labeling (FML) problem: the task of designing a minimum-cost temporal edge activation plan that ensures each group of nodes in a network has sufficient access to a designated target set, according to specified coverage requirements. FML captures key trade-offs in systems where edge activations incur resource costs and equitable access is essential, such as distributed data collection, update dissemination in edge-cloud systems, and fair service restoration in critical infrastructure. We show that FML is NP-hard and $Ω(\log |V|)$-hard to approximate, where $V$ is the set of nodes, and we present probabilistic approximation algorithms that match this bound, achieving the best possible guarantee for the activation cost. We demonstrate the practical utility of FML in a fair multi-source data aggregation task for training a shared model. Empirical results show that FML enforces group-level fairness with substantially lower activation cost than baseline heuristics, underscoring its potential for building resource-efficient, equitable temporal reachability in learning-integrated networks.

In practice, this integral is approximated with averaging over a finite number of Monte Carlo samples.

The provision of social care applications is crucial for elderly people to improve their quality of life and enables operators to provide early interventions. Accurate predictions of user dropouts in healthy ageing applications are essential since they are directly related to individual health statuses. Machine Learning (ML) algorithms have enabled highly accurate predictions, outperforming traditional statistical methods that struggle to cope with individual patterns. However, ML requires a substantial amount of data for training, which is challenging due to the presence of personal identifiable information (PII) and the fragmentation posed by regulations. In this paper, we present a federated machine learning (FML) approach that minimizes privacy concerns and enables distributed training, without transferring individual data. We employ collaborative training by considering individuals and organizations under FML, which models both cross-device and cross-silo learning scenarios. Our approach is evaluated on a real-world dataset with non-independent and identically distributed (non-iid) data among clients, class imbalance and label ambiguity. Our results show that data selection and class imbalance handling techniques significantly improve the predictive accuracy of models trained under FML, demonstrating comparable or superior predictive performance than traditional ML models.