# MoRF-AST: Calibrated Probabilistic Virtual Sensing for Structural Monitoring under Changing Operating Conditions

arXiv: https://arxiv.org/abs/2608.24531 · HTML: https://mlsanity.com/paper/2608.24531/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 58 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 22 of 22)

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- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
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- [The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problems](https://mlsanity.com/paper/2202.07773/) (2022)
- [Semi Conditional Variational Auto-Encoder for Flow Reconstruction and Uncertainty Quantification from Limited Observations](https://mlsanity.com/paper/2007.09644/) (2020)
- [Conditional diffusions for amortized neural posterior estimation](https://mlsanity.com/paper/2410.19105/) (2024)
- [A Statistical Benchmark for Diffusion Posterior Sampling Algorithms](https://mlsanity.com/paper/2509.12821/) (2025)
- [Learning to solve Bayesian inverse problems: An amortized variational inference approach using Gaussian and Flow guides](https://mlsanity.com/paper/2305.20004/) (2023)
- [Conditional Flow Matching for Bayesian Posterior Inference](https://mlsanity.com/paper/2510.09534/) (2025)
- [Data Fusion for Full-Range Response Reconstruction via Diffusion Models](https://mlsanity.com/paper/2502.00795/) (2025)

## Abstract (arXiv)

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.