The Inference Report

The robust treatment of environmental and operational variability (EOV) is an open challenge in population-based structural health monitoring (PBSHM). The difficulty is compounded in the case that the EOV signals are unmeasured. A common approach in conventional SHM is to apply \emph{projection-based} methods that discard subspaces of healthy feature data, reasoning that the EOV signal dominates the variance of the measured features. However, a common pitfall of projection-based approaches is that when damage acts close to the same variance-dominant direction, damage sensitivity is removed along with the EOV. An alternative identifying assumption for the removal of particular unmeasured EOVs is slowness; the latent EOV process is characterised by its long temporal correlation. In this paper, the latent EOV is cast as a state-space Gaussian process, enabling tractable $\mathcal{O}(T)$ inference via a Kalman filter. A robust hierarchical Bayesian identification framework is developed that enables population-level identification of latent EOVs and EOV-free residual features, using a Laplace approximation. The approach is first validated on a single laboratory-scale benchmark structure from the literature, subject to thermal EOVs, demonstrating robust damage detection and EOV recovery. The method is then applied to a simulated nine-turbine offshore wind farm with staggered deployment and damage, where it delivers a substantial true-positive uplift over projection and cointegration-based baselines at matched false-positive rates.

Power amplifier (PA) nonlinearity and memory effects significantly limit the spectral compliance, reliability, and energy efficiency of communication systems. To address this, we propose a transfer-learning-enabled, fully digital transceiver-cooperative method for amplitude-phase-time block modulation (APTBM)-based nonlinear single-carrier transmission under adjacent channel leakage ratio (ACLR) constraints. At the transmitter, iterative clipping and filtering (ICAF) and static digital pre-distortion (SDPD) act jointly to reduce signal peaks and suppress spectral regrowth without requiring wideband feedback. At the receiver, the inherent amplitude-phase constraints of APTBM provide weakly supervised prior knowledge for offline inverse-model pretraining, which is followed by the online few-shot adaptation of a lightweight digital post-distortion (DPoD) network. Subsequently, a cascaded DPoD and clipping-noise cancellation scheme systematically compensates for residual distortions induced by both the PA and ICAF. Simulation and measurement results demonstrate reliable transmission at an input back-off of approximately 2 dB under a 30-dBc ACLR constraint. Furthermore, the proposed DPoD approach significantly reduces online training time and computational overhead, delivering a performance gain of over 2 dB compared to conventional learning-based DPoD schemes.

Koopman theory offers a linear-operator view of nonlinear sequence dynamics by lifting observations into a space where evolution is governed by a linear time-invariant Koopman operator. While the Koopman operator provides a linear representation of nonlinear dynamics, it is generally infinite dimensional and defined under time-invariant assumptions. To model non-stationary signals with frequency-dependent behavior, a frequency-varying extension is required. In recent years, deep learning has been increasingly employed to exploit its powerful function-approximation ability for learning the Koopman operator. In this study, we propose a novel approach called neural decomposition Koopman (NDKoop), an end-to-end architecture that integrates a learnable signal decomposition module with both frequency-independent and frequency-dependent Koopman based networks for sequence forecasting. To the best of our knowledge, this is the first work to jointly realize end-to end Koopman modeling and signal decomposition within a unified neural framework. We demonstrate that decomposing a signal into a frequency-independent trend component and a frequency-dependent periodic component, each governed by a corresponding Koopman operator, improves prediction accuracy when perfect linearization is unattainable. Numerical experiments across several forecasting benchmarks indicate that the proposed NDKoop provides strong performance.

Cardiologists interpret electrocardiograms by localizing waveform components, measuring rhythm and interval patterns, and translating these structured observations into diagnostic evidence. Whether this expert reading process can serve as an effective prior for ECG agents remains unclear. To address this question, we introduce LuminaECG, a clinically structured ECG reasoning framework that reformulates ECG interpretation as measurement-grounded visual reading. ECG signals are rendered on standard electrocardiographic grid paper to preserve the spatial and scale cues used in clinical reading. P-wave, QRS-complex, and T-wave boundaries are explicitly delineated, and color-coded segmentation decomposes the waveform into discrete visual measurement primitives. A general 2B vision-language backbone is then trained with low-rank supervised fine-tuning to associate these primitives with diagnostic reasoning, without architectural modification. Across open, proprietary, and ECG-specialist zero-shot baselines, LuminaECG improves both waveform measurement and diagnostic recovery. It reaches a clinically meaningful reader tier on the CODE-test benchmark, transfers across geographically diverse ECG datasets without retraining, and generates reports whose structure contains an emergent prognostic signal. These findings suggest that effective ECG agents require not only larger models, but supervision that preserves the alignment between measurable waveform evidence and clinical knowledge.

Learning-based wireless localizers often fail to utilize geometric information about the propagation environment, limiting their ability to exploit non-line-of-sight (NLoS) propagation and generalize across scenes. To bridge this gap, we propose GLocFM, a Geometry-aware Localization Foundation Model, which jointly exploits WiFi measurements and scene geometry represented as a 3D point cloud. We formulate localization as a maximum-likelihood (ML) estimation problem, where the goal is to find a transmitter position that maximizes the likelihood of the wireless observations conditioned on the scene geometry. The likelihood of a candidate transmitter position is calculated by a learned scoring function that matches the observed delay--angle-of-arrival (AoA) spectrum against the spectrum predicted for that candidate. A hierarchical scene encoder extracts propagation-relevant features to produce geometric priors for LoS and one-bounce reflection paths. For scenarios with imperfect synchronization, we further introduce a time-of-flight (ToF)-robust GLocFM model to handle unknown ToF offsets. GLocFM is trained on a multi-modal synthetic indoor localization dataset comprising 221 diverse scenes whose associated wireless signals are generated using Sionna RT. On both synthetic and the NeRF$^{2}$ dataset based on real measurements, GLocFM reduces mean 3D localization error relative to one of the state-of-the-art localization baselines by 49.5\% and 48.8\%, respectively. Ablations across different number of receiver, bandwidths, and array sizes further demonstrate the effectiveness and robustness of the proposed framework.

Optimization theory is a widely used tool for intelligent decision-making. While classical optimization deals with fixed, time-invariant objective functions, many modern applications operate in dynamic environments where data arrive sequentially, and the learning objective evolves over time, often under decentralized data and communication constraints. Motivated by these trends, we study decentralized optimization from streaming data through a structured time-varying formulation in which the global objective is a temporally weighted average of losses observed across the network. We analyze multi-iteration decentralized first-order methods, including decentralized gradient descent. For strongly convex and smooth losses, we develop guarantees for the Euclidean-norm \emph{tracking error} through a contraction-mapping viewpoint. The resulting bounds decompose the tracking error into a fixed-point tracking component and a bias term induced by decentralization and data heterogeneity. We specialize our analysis to uniform and exponentially discounted weights, as well as their finite-memory \emph{windowed} counterparts. The bounds explicitly characterize the roles of the temporal weighting rule, per-step iteration budget, step size, and network connectivity. Uniform weighting yields a vanishing fixed-point tracking contribution of order $\mathcal O(1/t)$, whereas discounted and windowed strategies generally induce non-vanishing tracking floors governed by the discount factor and effective memory, respectively. In all cases, decentralization induces an additional non-zero bias floor under a constant step size. Numerical experiments illustrate the predicted trends.