A multimodal system may begin inference while holding only some of its inputs and may acquire the rest at a cost. With adaptive acquisition, the policy determines which inputs are ultimately observed, so we state risk control conditional on that terminal input pattern. Conditional calibration typically assumes that the grouping map is fixed independently of the calibration sample, a condition that policy-induced grouping does not satisfy. We characterize when pattern-conditional risk control remains valid and give two finite-sample constructions: threshold-free routing with calibration applied at the terminal pattern, and simultaneous validation of complete policy-pattern pairs, which lets calibration data select the deployed policy. A counterexample shows that validity proved for a calibration-independent grouping map need not transfer once the policy makes the terminal group calibration-dependent. We call the resulting method RouteCert. On a clinical electrocardiogram task with a staged, cost-ordered lead protocol, the deployed policy answers 71.2% of held-out patients, with an observed 7.4% disagreement with the cardiologist's diagnosis at 48.8% of the prespecified ordinal cost of acquiring each stage, and all three acquisition stages are validated separately. On masked multimodal benchmarks, validating pointwise at each terminal pattern holds observed worst-pattern selective risk, measured against the full-information reference decision rather than the true label, at 0.034, where a pooled design reaches 0.145 against a 0.10 cap, at a comparable answered fraction (0.350 vs 0.342); under the budget-matched simultaneous comparison, the answered fraction falls to 0.305.
Many-query applications such as design optimization, uncertainty quantification and digital twins call for repeated full-field predictions from expensive partial differential equation (PDE) simulations. Grassmannian reduced-order models interpolate parameter-dependent subspaces but commonly vectorize the spatial field, and the ambient dimension then grows with the product of the grid sizes. Tensor-based models preserve the multiway structure but often use shared mode-wise bases or a fixed core across parameters. We propose a Tucker-based surrogate that keeps the spatial directions and time as separate modes. The factor subspaces are interpolated on a product Grassmann manifold, Procrustes alignment places the Tucker cores in one coordinate system, and a truncated singular value decomposition models their variation. Across five PDE benchmarks in two and three spatial dimensions, including public computational fluid dynamics data, the interpolation size is reduced by factors of 13 to 482 and the stored model by factors of 13 to 464 relative to a single-subspace Grassmannian surrogate with the same local interpolation. Cached queries run 3.3 to 8.5 times faster, the mean errors over ten resampled splits differ by at most 0.22 percentage points (0.36 when every model choice is re-selected inside each split), and the prediction-error terms of the two methods differ by less than 0.1 percentage points. The remaining accuracy differences are consistent with the larger representation error of the Tucker format. In a three-dimensional grid study the interpolation-size ratio rises to 2,260 and the query speedup to 11.9 at 64^3.
High-fidelity simulations such as computational fluid dynamics and finite element analysis are essential for modelling complex engineering systems but remain prohibitively expensive for tasks including parametric studies, optimisation and real-time control. Projection-based reduced-order models (ROMs) alleviate this cost by projecting full-order dynamics onto low-dimensional subspaces. On the other hand, projection-based ROMs can become less robust under parameter variation, and one approach is to adapt the projection basis (that is, the subspace) as the parameters change. We propose constrained extreme gradient boosting (cXGBoost) for predicting the proper orthogonal decomposition (POD) basis at given parameter settings. In particular, given the observed parameter-subspace pairs, we map the subspaces from the Grassmann manifold to a Euclidean space. Then, cXGBoost is trained in this Euclidean space with a constraint that the norm of the predicted vectors is bounded to ensure the injectivity of the mapping between the Euclidean space and the Grassmann manifold. On four parametric problems, a cylinder wake, Kolmogorov flow, the Kuramoto-Sivashinsky equation and a forced beam, cXGBoost has lower mean reconstruction errors than existing approaches, namely the projected Gaussian process and Grassmann interpolation.
Hospitals that serve medical tourists alongside local patients share beds, specialists, and appointment slots between two groups for whom waiting has different consequences. Operations research models are widely used for hospital capacity and scheduling, but often do not explicitly capture patient behavior; agent-based simulation can represent such behavior alongside discrete-event patient flow, while medical-tourism research still mainly treats traveling patients as cases to be scheduled. We develop a hybrid simulation that represents channel choice, physician switching, treatment abandonment, and medication-related deterioration in a multi-specialty international patient department. A 256-run fractional factorial experiment screens 16 controllable factors across six performance measures, followed by a replicated comparison with a discrete-event-only version without these behaviors. At a bed-constrained configuration, mean inpatient admission waiting time is 42% lower in the hybrid model (14.8 versus 25.8 days in the discrete-event-only model, p < 0.001) and 25% to 64% lower under two further conditions. Lacking these behaviors, the simpler model shows no abandonment and fewer emergency escalations. The comparison shows how results depend on model structure; neither variant is validated against observed waiting times. A bed-sharing routine in both variants adds no beds as implemented, so bed sharing is not evaluated. The screening identifies bed capacity as the most consistent driver of waiting; priority rules, channel design, and appointment timing also matter, while specialist capacity has less effect on waiting. Managers should review bed capacity and admission rules before adding specialists or tightening schedules.