Data-driven methods have demonstrated strong predictive capabilities in fluid mechanics, yet most current applications still focus on simplified configurations, often characterized by statistical stationarity or limited temporal variability. This work proposes a methodology that combines data assimilation (DA) and machine learning (ML) to numerically predict the flow around immersed bodies moving in oscillatory motion. Starting from limited, sparse high-fidelity measurements and a low-fidelity numerical model, the DA approach performs data fusion to obtain complete and accurate flow state estimations in time. This complete dataset is used to train multiple ML tools, which are applied across different phases of the body motion to augment the model’s predictions when high-fidelity data might not be available for the DA application. The methodology is applied to the analysis of an oscillating cylinder in a laminar regime using a sliding-window approach, in which separate models are trained for specific flow conditions to ensure each model specializes in flow dynamics representative of a phase of the oscillation period. This phase-resolved learning enables the efficient capture of transient features that would be challenging for a single global model. The results highlight the potential of this method to study complex flow configurations due to body motion, where neither the flow nor the cycle is known a priori, particularly by exploiting real-time training and updates, as is commonly done in digital twins, which require continuous model correction and adaptation.

Structural health monitoring plays a crucial role in ensuring the safety, reliability, and longevity of bridge infrastructures through early damage detection. Although recent advances in deep learning-based models have enabled automated event detection, their performance is often limited by data scarcity, environmental noise, and class imbalance. To address these challenges, this study introduces a customized generative adversarial network (GAN) model, STFTSynth, designed particularly for generating short-time Fourier transform spectrograms derived from acoustic-event signals. In contrast to augmentation techniques such as MixUp, GANs can synthesize spectrograms that visually and statistically resemble real event representations, providing a basis for representation-level dataset enrichment. The proposed model integrates dense residual blocks for spatial consistency with bidirectional gated recurrent units for temporal dependency modeling. Model performance is evaluated against three baseline generative models using qualitative inspection and quantitative metrics, including structural similarity index measure, peak signal-to-noise ratio, and Fréchet inception distance. Results show that STFTSynth outperforms baseline models, producing high-resolution, temporally consistent spectrograms that align closely with real-world data. These findings highlight the potential of GAN-based spectrogram synthesis for representation-level enrichment of rare acoustic-event datasets in bridge monitoring, particularly when real examples such as prestressing wire breakage are limited.

The synthesis of turbulence dynamics using machine learning, statistical, and dynamical system-based models has become an emerging research direction. Validation of synthetic turbulence time series is often based on marginal and second-order statistics, which may overlook whether the underlying interaction structure is preserved. In this work, we apply a set of linear and information-theoretic measures to evaluate interactions between pairs of turbulence time series obtained from a turbulent channel flow at various wall distances, as well as between their synthetic counterparts. To demonstrate the applicability of these measures, we assess synthetic time series generated from a high-order vector autoregressive (VAR) model. The results show that the VAR-generated time series preserve the linear interactions measured by auto- and cross-covariance functions, even for long-memory dynamics. However, when assessed by information-theoretic measures, such as time-delayed mutual information and transfer entropy, the agreement deteriorates. Despite under-predicting the magnitude of transfer entropy, the VAR-generated time series correctly capture the dominant direction of net information transfer in most of the pairs. Furthermore, when the time series embedding is optimally constructed, the interpretation of net transfer entropy is shown to be consistent with relevant physical interpretations of causal interactions reported in the turbulence literature. Future research should consider applying this framework to multivariate turbulence time series generated by other data-driven techniques to ensure more comprehensive validation.

Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often constitute an obstacle to physical interpretability. This work introduces Hierarchical Fourier Neural Operators (HFNOs), a novel FNO-based architecture tailored to the reduced-order modeling of turbulent fluid flows and designed to enhance interpretability by explicitly separating fluid behavior across scales. The proposed architecture processes wavenumber bins in parallel, enabling the approximation of dispersion relations and nonlinear interactions. Inputs are lifted to a higher-dimensional space, Fourier-transformed, and partitioned into wavenumber bins. Each bin is processed by a Fully Connected Neural Network (FCNN), with outputs subsequently padded, summed, and inverse-transformed back into physical space. A final transformation refines the output in physical space as a correction model, by means of one of the following architectures: a Convolutional Neural Network (CNN) or an Echo State Network (ESN). We evaluate the proposed model on a series of increasingly complex dynamical systems: first on the one-dimensional Kuramoto–Sivashinsky equation, then on two-dimensional Kolmogorov flow, and finally, on the prediction of the wall shear stress in turbulent channel flow, given the near-wall velocity field. In all test cases, the model demonstrates its ability to decompose turbulent flows across various scales, opening up the possibility of increased interpretability and multiscale modeling of such flows.

This study develops a Bayesian, uncertainty-aware framework for tendon breakage localization in prestressed concrete members using high-resolution data from distributed fiber-optic sensors (DFOS). DFOS enables full-field monitoring of strain changes on the surface of prestressed concrete members due to such failure. A finite element model (FEM) of an experimental tendon-breakage test is constructed, and model parameters are calibrated probabilistically against DFOS measurements. To capture model-form uncertainty (MFU), stochastic perturbations are embedded directly into material parameters, enabling the joint inference of physical properties and MFU within a unified probabilistic framework. Gaussian Process surrogates are employed to efficiently emulate the nonlinear FEM response, supporting computationally tractable Bayesian inference. A $ \phi $-divergence-based influence analysis identifies the DFOS measurements that most strongly shape the posterior distributions, providing interpretable diagnostics of sensor informativeness and model adequacy. The calibrated parameters and embedded uncertainties are then transferred to a FEM of a full-scale structural configuration, enabling prediction of tendon breakage localization under realistic conditions. A separability analysis of the predictive strain distributions quantifies the identifiability of tendon breakage at varying depths, assessing the confidence with which different damage scenarios can be distinguished given the propagated uncertainties. Results demonstrate that the framework achieves robust parameter calibration, interpretable diagnostics, and uncertainty-informed damage detection, integrating experimental data, embedded MFU, and probabilistic modeling. By systematically propagating both experimental and model uncertainties, the approach supports reliable tendon breakage localization, informed decision-making, and optimal DFOS placement.

Reinforced concrete shear walls are essential components of seismic-resistant structures, yet accurately predicting their drift capacity remains challenging due to the nonlinear interaction among geometric, material, and loading parameters. Traditional empirical or analytical models often fail to capture these complexities, motivating the use of machine learning (ML) as a data-driven alternative. In this study, a dedicated experimental database of 208 reinforced concrete shear walls with rectangular and I-shaped cross-sections was derived from the ACI 445B Shear Wall Database. The selected input parameters include the wall length-to-thickness ratio, normalized shear coefficient, axial load ratio, transverse reinforcement spacing-to-diameter ratio, ultimate-to-yield strength ratio of boundary reinforcement, longitudinal reinforcement ratio in boundary and web regions, and transverse reinforcement ratio. Three tree-based machine learning regressors were optimized using nested cross-validation. To improve predictive accuracy, their outputs were combined into a stacking ensemble. The dataset was divided into a development subset and an independent hold-out test subset, with model development and hyperparameter optimization performed exclusively within the development data. In addition, the predictive capability of the machine learning models was compared with the empirical formulation proposed by Abdullah and Wallace. The results show that the ML-based approaches provide strong predictive performance on independent test data. Among the considered models, the Stacking Ensemble achieved the best overall results, highlighting the potential of ensemble learning to capture the complex nonlinear relationships governing the drift capacity of reinforced concrete shear walls. The findings support the use of data-driven models as complementary tools to traditional empirical approaches for deformation-capacity prediction.

This paper investigates the computational relevance of the Energy-Conserving Sampling and Weighting (ECSW) method for hyper-reduction in reduced-order models (ROMs), with particular attention to modern Graphical Processing Unit (GPU)-accelerated and deep-learning-based frameworks. While hyper-reduction techniques such as ECSW are traditionally introduced to enable tractable evaluation of nonlinear terms in Galerkin ROMs, their actual benefit for computable nonlinearities with traditional Proper Orthogonal Decomposition (POD)–Galerkin ROMs combined with deep learning and on deep-learning GPU hardware remains a question. We provide a full ECSW implementation for finite element Navier–Stokes solvers, compatible with automatic differentiation and batched tensor operations, and derive exact operation counts for both standard tensorial and hyper-reduced formulations. Theoretical analysis shows that the computational complexity scales as $ \mathcal{O}\left({r}^3\right) $ for tensorial ROMs and $ \mathcal{O}(rm) $ for ECSW, where $ r $ is the reduced dimension and $ m $ the number of retained quadrature points. Extensive CPU and GPU benchmarks are conducted on the fluidic pinball configuration to assess asymptotic scaling, memory effects, and hardware bottlenecks. Results confirm the linear complexity and efficiency of ECSW on CPUs but reveal that, on GPUs, the regular tensorial formulation can outperform hyper-reduction for common reduction dimensions due to highly optimized batched matrix kernels and limited bandwidth constraints. Overall, the study clarifies when hyper-reduction remains advantageous in practice and provides concrete guidelines for integrating ECSW within deep-learning-augmented ROM frameworks.