CTRL-FM: Inference-Time Structural Control for Flow-Based Virtual Sensing under Long-Horizon Node Outages

Flow matching has emerged as a powerful alternative to diffusion models for generative modeling, but standard conditional flow matching is fundamentally misaligned with partially observed time series: starting from an uninformed Gaussian source forces the model to transport even already-observed entries from noise to the target, wasting capacity on trivially known regions. We propose MissPath-FM, a partial-observation-aware flow matching framework that redesigns the source prior and probability path for incomplete time series. MissPath-FM employs structured source priors (interpolation priors and Gaussian process posterior priors) to initialize the flow close to the observed signal, paired with a missingness-aware smooth path that allocates transport asymmetrically between observed and missing regions. We evaluate systematically across four datasets, four missingness mechanisms (MCAR, block, MNAR, irregular), two missing ratios, and three sequence lengths (T in {24, 48, 96}), totaling 48 settings against eight baselines. MissPath-FM wins 29 of 32 settings at T=48 and 45 of 48 overall (93.8%). Our ablations reveal a regime-dependent design hierarchy in which no single component suffices: under random missingness the source prior yields a large initial gain, but under structured block missingness it can fail entirely and the learned flow becomes indispensable; the missingness-aware path contributes a further 12%-26% across all regimes. Mechanistically, structured priors shorten observed-region transport by up to 15x, concentrating the velocity field on genuinely uncertain entries. Project page: https://zgp110.github.io/misspath-fm/

Probabilistic full-field reconstruction provides uncertainty-aware response evidence for structural reliability assessment, yet inference from sparse and noisy measurements remains underdetermined. Most existing methods overlook shifts between offline training and operational distributions. Under such shifts, posterior intervals may become miscalibrated, causing the reported uncertainty to lose its probabilistic meaning. This study proposes Modal Residual Flow Matching with Context-Conditioned Affine Spread Transport (MoRF-AST) for calibrated structural virtual sensing under changing operating conditions. MoRF constructs an analytic Gaussian reference posterior in normalized modal coordinates and trains a conditional flow only on posterior-whitened residuals. At deployment, AST estimates response scale from historical measurements at installed sensors and uses gated, mean-preserving Bures-Wasserstein transport to adjust posterior spread. On a bridge-deck benchmark, MoRF achieves a posterior-mean normalized root-mean-square error (NRMSE) of 7.20%, compared with 16.1% and 17.9% for two direct conditional flows. Across eight shifted traffic domains, AST reduces MoRF's cross-domain average coverage error from 0.0535 to 0.0236, a 55.9% reduction, while preserving posterior-mean accuracy. The same transport does not improve the tested alternatives in aggregate, showing that calibration gains require its direction to match the base posterior's dispersion bias. MoRF-AST provides a data-efficient framework for probabilistic full-field reconstruction whose uncertainty remains interpretable under scale-dominated operational distribution shifts. More broadly, this work highlights the need to calibrate uncertainty under changing operational distributions, thereby supporting trustworthy probabilistic modeling and reliability-informed decision-making in civil and infrastructure engineering.

Traffic sensor data exhibit strong temporal and cross-sensor dependencies, yet long gaps erase both a sensor's local history and the joint observations needed to learn its relationships with other sensors. We introduce MoHL, a mixture of hypergraph Laplacians that learns group-wise relational structure directly from incomplete spatiotemporal data. MoHL discovers overlapping sensor groups from observed co-variation, constructs a Laplacian component for each interaction order, and learns their mixture through holdouts that mimic the missingness pattern. By sharing weights across group-induced couplings, MoHL pools scattered evidence instead of estimating each coupling independently. We characterize the induced weight-sharing structure and analyze the conditions under which sharing reduces estimation risk. Experiments on three traffic networks show that higher-order groups are most beneficial under long gaps, while support-matched comparisons demonstrate the advantage of shared weights when relational evidence is scarce. MoHL achieves the lowest error among the evaluated baseline methods under day-long gaps, with orders of magnitude fewer learned parameters than deep imputers. These results show how group-wise sharing can sustain reliable reconstruction precisely when missingness depletes the evidence needed to learn cross-sensor dependence.