Transfer learning via interpolating structures

This paper presents a methodology-centered transfer learning framework for fragility adaptation under domain shift, class imbalance, and scarce target labels while preserving engineering interpretability and supporting decision-making under uncertainty. Four transfer learning strategies (instance-based, parameter-based, hierarchical Bayesian, and multi-source) are demonstrated through three complementary case studies: (i) instance-based transfer learning via importance weighting, demonstrated on coastal bridge fragility using Hurricane Katrina observations; (ii) parameter-based transfer learning together with hierarchical Bayesian transfer learning, enabling partial pooling across strata and posterior uncertainty quantification, demonstrated on residential building fragility using Hurricane Ian observations; and (iii) multi-source transfer learning that fuses multiple analytical fragility models with learned source weights and regularized target-domain adaptation, demonstrated on seismic bridge fragility using observations from the 2001 Nisqually earthquake. Across these case studies, direct transfer of source models (i.e. using existing state-of-the-art models) fails under domain shift and severe class imbalance, while targeted adaptation substantially improves failure detection and predictive stability in low-data regimes. These findings highlight the need for systematic guidance on diagnostics, strategy selection, and uncertainty reporting when developing and adapting fragility models.

Transfer learning is a natural strategy when a target population has limited data but multiple related auxiliary sources are available. A central difficulty is source heterogeneity: auxiliary sources may not be equally useful, and their usefulness may vary in a structured, cluster-like fashion. Existing transfer-learning methods often reduce source selection to a binary informative/non-informative decision, overlooking subgroups of sources with differential transferability. Motivated by a suicide-risk study using data from the Connecticut Hospital Information Management Exchange (CHIME), comprising 636,758 patients across 27 hospitals, we propose Trans-GLMC, a cluster-structured transfer-learning procedure for generalized linear models. The CHIME setting illustrates the core challenge: hospital-specific risk models are unstable because suicide attempts are rare at any single facility, whereas indiscriminate pooling across hospitals can obscure facility-level differences in patient mix and risk profiles. Trans-GLMC first constructs a coefficient-based distance among the target and candidate sources to recover latent source clusters. It then combines global fusion, within-cluster refinement, and target debiasing to produce an estimator that adapts to the detected structure. We establish a non-asymptotic error bound that improves over its unclustered counterpart whenever a meaningful target cluster exists and matches the unclustered rate up to constants otherwise. In simulations and in the CHIME study, Trans-GLMC improves facility-specific prediction, identifies interpretable communities of hospitals with mutual transferability, and recovers clinically coherent suicide-risk factors.

A natural strategy for inverse problems with scarce labelled data is to transfer relational structure learned from abundant forward-simulation data. We show this strategy fails systematically, even when it satisfies the standard theoretical justification for why structure should help. We prove that approximate structure provides estimation-error benefits whenever the edge error satisfies $Δ< n^2 - kn$, reducing sample complexity from $O(n^2)$ to $O(kn+Δ)$. Structure learned via Neural Relational Inference (NRI) from dynamics prediction satisfies this condition, yet on a source-localisation task across 180 CFD-simulated hydrogen-leak scenarios and 180 acoustic scenarios, it degrades performance by 116% and 201% relative to a flexible, task-optimised attention baseline, while a physics-based prior (Green's function) degrades by only 69-72%. Four independent lines of evidence show this is not a tuning failure: NRI improves only 0.5% when given 18x more training data (versus 16.6% for the task-optimised baseline, $p<0.001$); performance is insensitive to the NRI edge threshold across a wide range; the dynamics-learned graph overlaps the task-optimal graph on only 6% of edges; and two further dynamics-derived structure estimators (correlation- and mutual-information-based) show no measurable benefit over a structure-free baseline, with the correlation-based estimator performing markedly worse. We formalise this gap as a statement about approximation error that the edge-accuracy condition cannot control, and we provide a lightweight transferability test (Jaccard similarity against a partially-observed target-task graph) that separates successful from failed transfer in all four domain/structure pairs we evaluate, using under an hour of computation and 15-20% of target-domain data; we present this as a heuristic calibrated on few cases, not a validated general threshold.