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.

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 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.

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.

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.

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.

Structural condition-based maintenance for naval vessels combines onboard monitoring to sense and evaluate the current structural health of a vessel and make projections about the future state, plus a decision framework to determine the optimal moment when maintenance activities should be performed. This paper explores the implementation of structural condition-based maintenance aboard naval vessels in an end-to-end perspective, meaning from conceptualization to defining a baseline ship structural health monitoring sensor system and to linking with a decision framework for making informed maintenance decisions. Beginning with considering the motivations and necessities when operating naval vessels, possible maintenance strategies are defined. Competing motivations based on the relevant stakeholders are discussed, especially related to the desired outcomes of implementing a condition-based maintenance system for hull structural integrity. The major components of a condition-based maintenance system are outlined, focusing on structural damage due to fatigue, corrosion, and extreme loading. Special attention is paid to structural health monitoring and the different sensing techniques required, along with the state-of-the-art research supporting such techniques. Multiple monitoring concepts are explored, focusing on the different ways to monitor the wave environment exciting the vessel and the resulting structural damage. Three selected previous monitoring campaigns and resulting lessons learned offer guidance on a resulting baseline sensor system for structural condition-based maintenance for naval vessels. Specific areas of needed future research are pointed out to further advance structural condition-based maintenance onboard naval vessels.

Thanks to the availability of massive amounts of data, computing resources, and advanced algorithms, artificial intelligence (AI) has entered nearly every sector. This has sparked significant investment and interest, particularly in building data centers to develop and operate AI models. In this technical review article, we present energy consumption scenarios of data centers and their impact on GHG emissions, considering both near-term projections (up to 2030) and the long-term outlook (2035 and beyond). Through a scenario synthesis augmented by probabilistic uncertainty analysis, we decouple the analysis of AI’s physical energy footprint from its qualitative potential as a decarbonization enabler. In the near-term, the growing demand for AI will likely strain computing resources, increasing electricity consumption and associated CO2 emissions. However, the long-term outlook includes significant, albeit highly uncertain, promise. AI has the potential to fundamentally optimize processes across industries, from energy production to logistics, potentially decreasing the broader global carbon footprint. While establishing a definitive “net impact” requires complex macroeconomic tracking of rebound effects outside our current scope, this synthesis highlights the pathways required—including zero-carbon grids and algorithmic efficiency—to ensure AI’s systemic decarbonization benefits can realistically offset its substantial infrastructure footprint.

This work presents an end-to-end strategy for solving inverse problems constrained by Partial Differential Equations within a fully differentiable Machine Learning framework. The proposed formulation provides a unified and user-friendly methodology applicable to a wide range of problems, from data assimilation to closure modeling. Our approach combines a baseline differentiable PDE solver, which predicts the state $ \boldsymbol{w} $ from the nonlinear system $ \boldsymbol{R}\left(\boldsymbol{w}\right)=0 $, with a generic additive, parametrized, and differentiable correction $ {\boldsymbol{f}}_{\boldsymbol{\vartheta}}\left(\boldsymbol{w}\right) $, with trainable parameters $ \boldsymbol{\vartheta} $. We show how to optimize $ \boldsymbol{\vartheta} $ within a fully differentiable Python workflow by reformulating the PDE as an implicit layer, enabling its integration into arbitrary objective functions, while leveraging PyTorch’s automatic differentiation graph. The method is demonstrated on the Reynolds-averaged Navier–Stokes equations for compressible flows, where the closure term, or a portion of it, is modeled using trainable parameters or a Neural Network. The first application considers the 2D NASA Wall-Mounted Hump test case, where a production-term parameter is optimized against time-averaged LES data. A second application is carried out on the VKI LS-59 turbine blade, where the Spalart–Allmaras eddy viscosity field is reconstructed through the optimization of a trainable spatial field. A dataset is generated starting from the VKI LS-59 turbine blade geometry using the differentiable BROADCAST solver with the Spalart–Allmaras turbulence model. The results highlight the flexibility of the framework, showing its applicability beyond turbulence modeling to a broader class of physics-informed PDE-constrained problems with data-driven components.

Heart rate is one of the most commonly used metrics for human health. Measuring human heart rate typically involves direct body contact, whether from wearable devices or manual measurement. However, such devices can cause discomfort in some patients, particularly in sensitive populations where such monitoring is more critical. Other past work for noncontact or remote heart rate measurement (e.g., camera- or radio-based methods) is often limited by line-of-sight and privacy requirements, which inhibit application in real-world environments. This article presents FloorPulse, an indirect heart rate monitoring system for human beings using heartbeat-induced floor vibrations. The key insight is that the human body generates a small wave of pressure and sound with each heartbeat. These waves are propagated as vibration through the structures the person is in contact with (e.g., a chair), then into and through the floor. FloorPulse detects and interprets these small floor vibrations to monitor the person’s heart rate. We developed a highly sensitive vibration sensing system and heartbeat pattern modeling to identify these tiny vibrations among other body motions and ambient noise. We evaluated FloorPulse in a real home environment, demonstrating an average heart rate error similar to medical device standards on the floor near the participants’ chair, and on the order of 10 beats per minute (bpm) on the floor 2 m away from the subject.

This study presents a scene-based clustering methodology for underwater structural health monitoring (SHM), categorizing images by intrinsic scene attributes (visibility, color, and turbidity). Shifting focus from object detection to holistic scene understanding enhances automated condition assessment in underwater infrastructure inspection by prefiltering suboptimal images and optimizing downstream tasks such as image matching and alignment. Ensuring algorithms operate on images with consistent lighting, texture, and clarity reduces ambiguities and enhances feature correspondence. It integrates local and global feature extraction, correlation analysis, feature selection, dimensionality reduction, and outlier detection to improve clustering accuracy and pipeline robustness. Clustering uses hierarchical and centroid-based algorithms, evaluated by Silhouette Score, Calinski-Harabasz Index, F1-score, V-measure, Adjusted Mutual Information, and Adjusted Rand Index, applying the Hungarian algorithm for label mapping in pseudo-labeled cases. The methodology is validated on real and synthetic underwater datasets, including a bridge inspection video dataset with abovewater and underwater segments, and controlled laboratory experiments assessing turbidity effects on submerged structural elements. A key contribution is assessing feature matching performance across clustered and unclustered image sets, demonstrating that scene-based clustering significantly enhances keypoint detection, feature correspondence, and inlier ratios while reducing mismatches from illumination and viewpoint variations. Additionally, engineered features outperform pretrained deep learning features in this unsupervised setting, providing more reliable global scene representation and improved clustering and feature matching outcomes. These findings establish the proposed pipeline as a valuable tool for underwater SHM, supporting applications such as 3D reconstruction, infrastructure assessment, and autonomous underwater inspections.

This study develops a robust framework for estimating the compressive strength of self-compacting concrete (SCC) incorporating recycled aggregates using supervised machine learning (ML) techniques. A comprehensive experimental database comprising 582 concrete mix designs was used, encompassing diverse input variables including binder content, water, coarse and fine aggregates, recycled aggregate proportion, superplasticizer dosage, and curing time. Seven ML algorithms—XGBoost, CatBoost, AdaBoost, Extra Trees, Bagging Regressor, K-Nearest Neighbors, and Radius Neighbors—were systematically trained using a stratified 70/15/15 data split and optimized via grid search with five-fold cross-validation. Model performance was evaluated using coefficient of determination (R2), root mean squared error, and MAE across training, validation, and testing datasets. Among all models, XGBoost demonstrated the highest accuracy, achieving an average R2 of 0.9799, RMSE of 2.87 MPa, and mean absolute error of 1.97 MPa. The Permutation Feature Importance analysis revealed that binder content, water, and coarse aggregate were the most influential predictors of strength. This study confirms that ensemble ML models, particularly XGBoost, can reliably predict the compressive strength of SCC with recycled aggregates, while offering transparent insights into material behavior. The results provide a valuable tool for sustainable mix design optimization and practical implementation in eco-efficient concrete construction.

This work shows how adaptivity can enhance the value realization of digital twins (DTs) in civil engineering. We focus on adapting the state transition models within DTs represented through probabilistic graphical models. The bi-directional interaction between the physical and virtual domains is modeled using dynamic Bayesian networks. By treating state transition probabilities as random variables endowed with conjugate priors, we enable hierarchical online learning of transition dynamics from one state to another through effortless Bayesian updates. We provide the mathematical framework to account for a larger class of distributions with respect to the current literature on DTs. To compute dynamic policies with precision updates, we solve parametric Markov decision processes through reinforcement learning. The proposed adaptive DT framework enjoys enhanced personalization, increased robustness, and improved cost-effectiveness. We assess our approach on a case study involving structural health monitoring and maintenance planning of a railway bridge.

Three data-driven assimilation algorithms are compared in the flow around a surface mounted prism at $ \mathit{\operatorname{Re}}=1000 $. All algorithms employ proper orthogonal decomposition (POD) for dimensionality reduction and synthesize linear estimators (Kalman filters). Two estimators are new and exploit past historical patterns of the training data. They are constructed from the singular vectors of the time-delayed Hankel matrix assembled from the signals of the POD coefficients. The two estimators differ on the forcing term of the linear system and its statistics. They can reconstruct (and also forecast) the instantaneous velocity field from sparse data. The third algorithm is based on the n4sid system identification method. The performance of the algorithms is compared with respect to the number of sensor points, model order, computational time for synthesis, and accuracy at reproducing the statistics of the flow (Reynolds stresses) at design and off-design conditions. For all criteria, it is found that the two new estimators were more robust and accurate compared to n4sid. Between the two, the estimator with random noise forcing was slightly more accurate. The future evolution of the flow was also accurately forecast over long time horizons using only one sensor. Application of the model trained at the reference Reynolds number to an off-design condition (at the nearby $ \mathit{\operatorname{Re}}=800 $) showed that very satisfactory results can be obtained with only very few sensors. The new estimators are scalable, easy to construct, and physically interpretable and can provide flow reconstruction (and, if needed, forecasting over a rolling time window) in almost real time.

The optimal design of products is crucial in the manufacturing industry due to its significant impact on economic performance, resource efficiency, and environmental sustainability. This study addresses a critical challenge in tire manufacturing: determining optimal extrusion initializations to improve production efficiency and product quality. To tackle this problem, the research explores the use of Digital Twins, a technology that facilitates the simulation of various scenarios without working directly with the physical system. Specifically, a data-driven Digital Twin approach is employed, which has shown promising computational efficiency in similar contexts. Despite its potential, several challenges associated with Digital Twins have been identified in the literature, including issues related to human–machine interaction, model adaptability to dynamic changes, data quality, and overall precision. This study advances Digital Twin technology by developing a framework that enables real-time identification and control of crucial physical parameters. The proposed approach emphasizes real-time computation, seamless process integration, adaptability to production demands, and user-friendly interaction for operators. This approach, according to our results, could avoid the 99% failed extrusions and could decrease 82% the time required to stabilize product quality. These outcomes demonstrate the practicality and effectiveness of the Digital Twin in improving manufacturing operations. The study also underscores the importance of incorporating human-centric design principles, ensuring that the technology not only enhances operational efficiency but also aligns with the needs of the operators. Overall, the research highlights the significant advancements and practical benefits of applying Digital Twin technology in tire manufacturing.

In Fluid Mechanics, developing deep learning models for relevant engineering configurations using exclusively high-fidelity data is often impractical due to the large computational cost of the corresponding simulations. We introduce a Machine Learning procedure that combines three algorithms to construct a multi-fidelity autoencoder capable of providing real-time high-fidelity predictions with quantified uncertainties while substantially reducing the computational cost of database construction. We demonstrate the method on a problem of practical interest: the prediction of jet flow fields emanating from a family of parametric nozzle configurations. The proposed multi-fidelity dataset comprises a limited number of computationally expensive Large Eddy Simulations augmented by a larger ensemble of computationally cheap Reynolds-Averaged Navier–Stokes simulations. The trained model learned the underlying relation between nozzle geometry and jet properties from low-fidelity data, and used high-fidelity ones to construct a correction term from low to high fidelity, thus providing a high-fidelity reduced-order model in the full design space.

The cost of high-quality aerodynamics simulations for realistic automotive configurations makes comprehensive design studies unfeasible. Data-driven surrogates (learning from data) are an appealing alternative, and there is no shortage of approaches that target shape-to-aerodynamics predictions. However, there is a fundamental limitation (data insufficiency problem) in this context: owing to the proprietary nature of commercial automotive designs, training datasets are limited to a few freely-available geometries. In a previous work the authors, a strategy to construct datasets for training surrogates was introduced. It enables controlled generation of an arbitrary number of samples, by convex interpolation between a small number of basis geometries. In this work, we extend this strategy by introducing three features, namely size, density, and diversity that characterize more general datasets. These are important to assess how useful is a dataset for a specific prediction task (data for learning). A formal measure of diversity is developed and then, datasets of successively increasing diversity but constant size are constructed. We show that the dataset diversity has an impact on the predictive accuracy of machine learning surrogates. A power-law scaling, $ \varepsilon \hskip0.5em \propto \hskip0.5em {M}^{1/2}\hskip0.1em {m}^{-1/6} $, where $ \varepsilon $ is the prediction error, $ M $ is the diversity, and $ m $ the dataset size, collapses 23 controlled experiments onto a single curve, revealing that diversity dominates size in determining prediction error. The proposed framework allows for more rigorous a priori evaluation of models than is currently possible and can be applied readily to other shape optimization problems.