The nonlinear and non-unique relationship between unit-cell topology and bandgap properties motivates the development of complementary data-driven approaches for metamaterial inverse design. This work presents a conditional denoising diffusion probabilistic model (DDPM)-based framework for the on-demand generation of two-dimensional metamaterial unit cells conditioned on prescribed bandgap properties. We employ a conditional DDPM because its non-adversarial denoising objective enables stable training and stochastic generation of diverse candidate topologies, although it requires iterative sampling and does not provide the explicit low-dimensional latent representation available in variational autoencoders. The model learns a probabilistic mapping from Gaussian noise, conditioned on the prescribed bandgap width and mid-frequency, to binary unit-cell topologies. The results show that the proposed framework generates structurally diverse candidate topologies with low surrogate-predicted errors relative to the prescribed targets. The proposed approach provides a flexible framework for conditional one-to-many metamaterial inverse design and a basis for future extension to broader classes of periodic structures.
In this work, a surrogate modeling approach based on graph neural networks (GNNs) is presented to rapidly predict the homogenized stress-strain response of polycrystalline microstructure volume elements (MVEs). Each grain is represented as a node in a graph, with features such as crystallographic orientation, grain size, and aspect ratio, while grain boundaries are encoded as edges. This graph-based representation enables the GNN to capture both local and long-range interactions that govern the macroscopic mechanical response. A synthetic dataset of MVEs was generated using DREAM.3D, covering a wide range of microstructural variations in grain size distributions, morphological anisotropy, and four crystallographic texture classes. Full-field crystal plasticity (CP) simulations performed on these MVEs provided the ground-truth stress-strain data used to train and validate the GNN model. The results demonstrate high correlation between GNN predictions and CP simulations, with strong agreement across different loading conditions and an inference-time speedup of approximately 55,000 × relative to full-field CP, achieved up to the reported accuracies and excluding the one-time training and data-generation overhead. The trained surrogate is then subjected to a comprehensive explainability analysis using integrated gradients, providing grain-level attribution maps that identify the microstructural features most influential to the predicted stress response. Population-level attribution statistics, together with cross-validation against GradientShap, trace the dominant attribution to the statistical representativity of each volume element, whose response dispersion scales inversely with the square root of its grain count. Overall, the proposed framework offers an accurate, efficient, and interpretable tool for microstructure-informed mechanical property prediction in heterogeneous polycrystalline materials.
We present EVA-PINN, an emergency-aware physics-constrained neural surrogate for multiscale crowd evacuation. The contribution is not the generic combination of neural prediction and physical constraints, which is established in prior physics-infused crowd simulation, but a pedestrian-level allocation of ten data and physics objectives conditioned on emergency risk and geometry. The reference dynamics combine a social-force law, contact interactions, a reaction–diffusion field, and bounded individual activation. We evaluate the surrogate on controlled synthetic benchmarks and by zero-shot transfer to 100 Jülich and 39 MADRAS real-world sequences. A new matched weighting experiment compares fixed weights, an SA-PINN-style loss-adaptive baseline, and the proposed risk-conditioned weighting on 20 paired scenarios spanning four geometries and five density levels. Relative to SA-style weighting, EVA-PINN increases evacuated fraction by 0.111 (95 p=1.7× 10^-5 ), reduces T_50 by 11.72 s (95 p=0.00117 ), and reduces cumulative contact duration by 18,092 pair · s (95 · s reduction; adjusted p=6.7× 10^-5 ). EVA-PINN also reproduces density-dependent speed reduction, preserves evacuation-time sensitivity to the reaction–diffusion coefficient over the tested range, and achieves approximately 15 × lower CPU rollout time than the reference simulator.
Atomic vacancies introduce uncertainty into the response of single-walled-carbon nanotube (SWCNT)-reinforced polymer nanocomposites, making probabilistic characterization essential for design. This study presents a multiscale framework for evaluating the distributions of Young’s modulus and yield strength in SWCNT-reinforced polyphenylsulfone (PPSU) nanocomposites with SWCNT volume fraction and vacancy level. The novelty is combining representative-volume-element (RVE) modeling, Monte Carlo simulation (MCS), and artificial neural networks (ANNs) to describe defect-driven variability without imposing a probability distribution. Four configurations combined SWCNT volume fractions of 2.5
Mixing-based data augmentation methods have demonstrated significant improvements in the generalisation of deep convolutional neural networks for image classification. Although saliency-guided methods such as SnapMix have demonstrated that using training-model class activation maps (CAMs) with semantically weighted labels outperforms area-proportional baselines, two distinct limitations remain unaddressed across this family: the absence of temporal smoothing for per-batch CAM estimates, and the lack of a progressive schedule that adapts CAM influence to the evolving reliability of the network’s representations during training. We propose ProCAMMix, which addresses these two limitations simultaneously. ProCAMMix accumulates stable per-class attention representations through an exponential moving average (EMA) buffer, and introduces a progressive annealing schedule that interpolates from standard CutMix behaviour in early training epochs—when CAMs are noisy and background-biased—to fully CAM-guided mixing in later epochs—when CAMs are discriminative. Label assignment is further corrected by replacing area-proportional mixing ratios with CAM-mass-weighted ratios. Experiments on CIFAR-100 with ResNet-50, repeated over three independent random seeds, show that ProCAMMix achieves 80.86 ± 0.21
Deploying machine learning surrogates in scientific simulations faces multifaceted challenges, primary among which is the lack of Continual Learning (CL) capabilities—specifically, the inability to adapt to new physical regimes without significantly degrading performance on prior ones. This is particularly problematic for autoregressive surrogates of time-dependent Partial Differential Equations (PDEs), where small prediction errors can accumulate over long rollouts and new physical regimes overwrite previously learned dynamics. We formulate this adaptation as a CL problem, demonstrating that while standard Experience Replay (ER) is a robust baseline across Advection-Diffusion, Burgers’, and Navier-Stokes equations, storing full high-resolution rollouts can be memory-inefficient. To address this, we introduce Replay-TS, a temporal-slicing replay strategy that stores compact autoregressive windows sampled across past simulations. Through empirical analysis, we show that Replay-TS exploits the low-frequency spectral redundancy of physical systems to enable sparse supervision for rollout steps. By preserving the contiguous historical context and sparsely penalizing the autoregressive target steps, Replay-TS improves retention performance under a fixed memory budget by leveraging higher sample diversity. Replay-TS consistently outperforms standard ER methods across standard 1D and 2D streams, achieving over a 30
This paper presents a Fourier-enhanced operator autoencoder (F-OAE) for decoder-free reconstruction and latent learning of dynamical systems. Conventional autoencoder-based reduced-order models compress high-dimensional fields into compact latent variables but recover the full physical fields via a nonlinear neural decoder, thereby introducing an additional reconstruction stage during prediction and deployment. In contrast, the proposed framework reformulates the reconstruction using the branch-trunk architecture. The branch network encodes each field snapshot or response sample into latent coefficients, while the trunk network learns shared spatial basis functions on a fixed coordinate grid. The full field is reconstructed through explicit linear superposition of the coefficients and learned basis functions. Fourier layers are introduced into the trunk network to improve the expressiveness of the learned basis functions for complex spatiotemporal fields. The proposed framework is evaluated through four representative dynamic case studies. The results show that F-OAE achieves accuracy comparable to or better than classical AE-based reduced-order models while providing a more efficient latent-to-field reconstruction path. In the cylinder wake case, F-OAE decreases the total inference time from 0.991 s to 0.559 s. In the physics-augmented Navier–Stokes benchmark, the training-epoch time is reduced from 54.10 ms to 24.00 ms compared with the AE baseline.
Physics-Informed Neural Networks (PINNs) are sensitive to how collocation and labeled points are distributed, especially in unsteady flows with localized high-gradient dynamics. Existing sampling strategies are mainly uniform or residual-driven and may underutilize physically critical regions while oversampling low-information areas. We propose a process-oriented sampling framework that jointly optimizes collocation and labeled-data placement by prioritizing feature-rich regions. The framework supports two region definitions: (i) empirical regions identified by domain knowledge, such as the Karman vortex street, and (ii) automatically detected feature-dominant regions obtained through KDTree-based neighborhood search and vorticity-divergence analysis. The framework is evaluated using a two-dimensional cylinder wake at Re = 3900 and a high-Reynolds-number wind-flow case at Re = 4.8 × 10⁷. In the cylinder-wake case, increasing collocation density in feature-rich regions reduces reconstruction errors by up to one order of magnitude. For labeled data, a “fewer but better” effect is observed: strategically placing fewer labels in feature-rich regions outperforms placing more labels in non-feature regions. In the high-Re case, feature-dominant sampling improves prediction accuracy for u, v, and p, reducing errors by 14.7
High-fidelity numerical models are widely used in civil engineering design and assessment, but their computational cost hinders extensive parametric studies and optimisation. Machine learning-based surrogate models offer a promising alternative by learning fast input–output mappings from limited simulation or experimental data. This work presents a systematic comparative study of three widely used surrogate techniques—artificial neural networks (ANN), Kriging metamodels and support vector machines (SVM)—applied to three representative civil engineering problems: (i) structural optimisation of an overhead travelling crane, (ii) assessment of the liquefaction potential of sandy soils and (iii) back-calculation of flexible pavement layer responses under different loading levels. For each case, a designed set of simulations or measurements is used to train the surrogates, and their predictive performance is evaluated using error-based metrics and computational efficiency indicators. The results provide a clear quantitative picture of model performance: Kriging and SVM consistently achieve the best classification accuracies for small to moderate datasets, with SVM and Kriging reaching top classification accuracies of 99.0
Zinc oxide (ZnO) is a widely studied metal oxide known for its excellent properties in applications such as antimicrobial activity and photocatalysis. These properties are strongly influenced by the particle size and shape which depend on controlled synthesis. However, due to the complexity of the synthesis process and limited mechanistic understanding, optimization is often guided by trial and error. Machine learning offers a data-driven approach to predict and control synthesis outcomes. In this study, various ZnO synthesis methods, experimental conditions, and their resulting particle sizes and shapes were analyzed. Random Forest emerged as the best-performing model for both regression and classification, achieving a mean R2 of 0.6043 (range = -0.4526 – 0.9414, std dev = 0.2708)) and RMSE of 776.87 (range = 387.34 – 1971.15, std dev = 392.14) and mean accuracy of 0.7520 (range = 0.6821 – 0.8092, std dev = 0.0284) and F1-score of 0.7428 (range = 0.6590 – 0.8075, std dev = 0.0305), respectively for particle shape dimensionality classification. These results demonstrate the potential of machine learning, particularly Random Forest, to guide the synthesis of ZnO. This approach reduces the need for extensive experimental trials which enables more precise control over material properties and improves both efficiency and accuracy in the synthesis. The codes and data for this work can be found on: https://github.com/SN-Matussin/ML-ZnO-particle-size-and-particle-shape-dimensionality
Adaptive metaheuristics are optimization algorithms that dynamically adjust their search behavior to improve performance during an optimization run. Adaptive strategies are among the techniques developed to improve the search performance of metaheuristics. This study proposes a Reinforcement Learning-based Dhole Optimization Algorithm with Population-Based Incremental Learning (RL-DOA-PBIL) to improve search performance in real-world constrained optimization problems. The proposed adaptive strategy is based on a probabilistic learning mechanism that guides search dynamics through self-adjusted learning and mutation parameters. By embedding distribution-guided learning into the dhole-hunting mechanism, RL-DOA-PBIL strengthens search diversity in the early stages while promoting more refined convergence toward promising feasible regions. The performance of RL-DOA-PBIL is validated on the IEEE Congress on Evolutionary Computation (CEC2020) benchmark suite for real-world constrained optimization, comprising 57 challenging problems across six engineering domains. For fair assessment, 25 independent runs of all algorithms are executed with the same maximum number of function evaluations. Statistical results, including mean fitness values, standard deviations, and Friedman ranks, are collected to measure algorithm performance. The obtained results demonstrate that RL-DOA-PBIL achieves the best overall Friedman rank of 2.41, outperforming its predecessor, Dhole Optimization Algorithm (DOA), and all other competitors across most benchmark categories. These findings indicate that the proposed algorithm can serve as an effective optimization tool for solving complex constrained engineering design problems, supporting improved decision-making, resource utilization, and system performance in real-world applications.
Thermoelectric materials enable direct conversion of waste heat into electricity, but their rational design is hindered by the intrinsic coupling among the Seebeck coefficient ( S ), electrical conductivity ( σ ), thermal conductivity ( κ ), and figure of merit ( ZT ). Here, we develop a unified, composition-driven machine-learning framework for the simultaneous prediction of all four transport properties. A curated dataset of 4,251 samples, containing experimental data, was represented using 246 composition-based descriptors (215 elemental statistics and 31 physically informed proxies). Systematic benchmarking identifies ExtraTrees as optimal for S , σ , and ZT , and XGBoost for κ , achieving high predictive accuracy ( R^2 = 0.953 , 0.918 , 0.963 , and 0.927 ) with minimal overfitting ( Δ R^2 < 0.08 ). SHAP-based interpretability reveals strong agreement with established thermoelectric physics, highlighting the roles of temperature, compositional complexity, electronic structure, and phonon-scattering descriptors in governing transport behaviour. High-throughput screening of 98,787 Materials Project compounds successfully recovers known high-performance thermoelectrics and identifies promising candidates for both near-room- and high-temperature applications. The proposed framework offers a physically interpretable and computationally efficient alternative to conventional first-principles approaches, enabling rapid and scalable discovery of advanced thermoelectric materials.
Physics-informed neural networks (PINNs) offer a promising mesh-free alternative to conventional computational fluid dynamics (CFD), but their practical use is limited by high training cost and poor generalization across different geometric configurations. This work proposes a geometry-conditioned hypernetwork PINN (GCH-PINN) framework that combines a convolutional neural network (CNN) HyperNet with a PINN MainNet to predict steady, incompressible laminar flow around two-dimensional obstacles over a family of shapes and locations. The HyperNet processes a signed distance function (SDF) map of the obstacle to extract spatial features and dynamically generates the weights and biases of the MainNet’s first hidden layer, enabling the solver to adapt its internal representation to each geometry without retraining. The MainNet, implemented as a multilayer perceptron, is trained using a hybrid loss that enforces the continuity and Navier–Stokes equations via automatic differentiation while leveraging full-field CFD solutions as supervision. The GCH-PINN is evaluated on two scenarios: single-factor variation (fixed location, varying shape) and two-factor variation (varying both shape and location) in a square domain. Across both settings, the network achieves Mean Absolute Errors (MAE) on the order of 10-6–10-4 and mean relative L₂ errors 3.86—8.02
The growing complexity and operational requirements of modern power plants demand advanced monitoring and maintenance strategies to maintain system re- liability, efficiency, and safety. Conventional maintenance methods, including re- active and scheduled maintenance, often result in unexpected equipment failures, higher operational expenses, and decreased system availability. In recent years, artificial intelligence (AI) has gained significant attention as an effective approach for intelligent fault detection and predictive maintenance in power generation sys- tems. This review provides a comprehensive analysis of AI-based techniques used for fault diagnosis and predictive maintenance in power plants. The paper explores a range of machine learning and deep learning methods—such as artificial neural networks, support vector machines, decision trees, random forests, and deep neural networks—that are applied to analyze operational data and identify anomalies in critical components, including turbines, boilers, generators, and transformers. Moreover, the study discusses data-driven predictive maintenance frameworks that integrate sensor data, Internet of Things (IoT) technologies, and advanced analytical techniques to predict potential failures before they occur. The advan- tages, limitations, and effectiveness of various AI-based approaches reported in re- cent studies are critically reviewed. In addition, the paper addresses several impor- tant challenges, including data quality issues, model interpretability, computational complexity, and the integration of AI systems with existing industrial infrastruc- tures. Finally, the review outlines potential future research directions aimed at im- proving the robustness and real-world implementation of AI-driven maintenance solutions in power plants. Overall, this study seeks to provide researchers and in- dustry professionals with a comprehensive understanding of recent advancements and emerging opportunities in applying artificial intelligence for intelligent fault detection and predictive maintenance in power generation systems.
Large language model (LLM)-based frameworks extend beyond agents; they also enable the on-demand creation of specialized scientific and engineering tools. We demonstrate this concept in the field of solid mechanics. There, so-called constitutive models describe the relationship between body deformation and mechanical stress. They are essential for both the scientific understanding and industrial application of materials. However, even recent data-driven methods of constitutive modeling, such as constitutive artificial neural networks (CANNs), still require substantial expert knowledge and human labor. We present a framework in which an LLM generates a CANN on demand, tailored to a given material class and dataset provided by the user. The framework covers LLM-based architecture selection, integration of physical constraints, and complete implementation. Evaluation on three benchmark problems demonstrates that LLM-generated CANNs achieve accuracy and generalization comparable to or greater than manually engineered counterparts, while substantially reducing the expertise required for constitutive modeling.
Multifidelity modeling aims to combine abundant but approximate low-fidelity data with sparse and expensive high-fidelity data to construct accurate surrogate representations of complex systems. While many existing approaches focus on statistical fusion or purely data-driven correction, they often struggle when the discrepancy between low- and high-fidelity responses becomes structured, nonlinear, or difficult to learn from limited high-fidelity samples. In this work, we present a knowledge-informed machine learning framework for bi-fidelity discrepancy learning within multifidelity modeling, in which prior structural insight is embedded through an ansatz-guided discrepancy representation. The proposed framework is assessed against four benchmark settings of increasing difficulty, ranging from simple linear scaling to divergent fidelity relationships, using five comparative methods: Standard Gaussian Process, Joint Gaussian Process, Standard Neural Network, Ansatz-Informed Neural Network, and Bayesian Ansatz-Informed Neural Network. The results show that purely data-driven neural discrepancy learning remains unreliable across all cases, even as the number of high-fidelity samples increases. In contrast, the ansatz-informed models consistently provide substantially improved accuracy by introducing a structured correction mechanism that reflects prior knowledge of the fidelity relationship. The Bayesian ansatz extension further delivers predictive uncertainty estimates while maintaining strong performance under both noiseless and noisy conditions. Gaussian-process methods become highly competitive when the high-fidelity sample count is sufficiently large, but are less reliable in the sparse-data regime. Overall, the study demonstrates that embedding problem-specific knowledge into the discrepancy model yields a robust and interpretable route for knowledge-informed multifidelity surrogate construction, especially when high-fidelity data are limited, and uncertainty quantification is required.
Bayesian model updating is widely used in engineering for the identification of unknown parameters of computational models based on noisy experimental measurements. In practical applications, however, the repeated evaluation of computational models may be demanding, which renders direct Bayesian inference prohibitive as it relies often on extensive sampling procedures. Surrogate models, particularly Gaussian process regression, are therefore frequently employed due to their capability to provide both predictions of the model response and a probabilistic characterization of the approximation uncertainty. Nevertheless, the uncertainty introduced by the surrogate model is not always treated consistently within the Bayesian inference procedure. This contribution proposes a framework for Bayesian model updating that explicitly propagates the predictive uncertainty induced by Gaussian process surrogates into the likelihood function via analytical marginalization. In addition, the proposed framework allows the simultaneous identification of the measurement noise characteristics. Moreover, an active learning strategy is developed in order to adaptively refine the surrogate model while controlling the uncertainty in the estimation of the model evidence. The resulting formulation provides a unified framework in which surrogate uncertainty, measurement noise, and adaptive learning are treated in a consistent probabilistic manner within Bayesian inference. The approach is illustrated by means of a simple dynamical system.
Domain-decomposed variants of physics-informed neural networks (PINNs) such as finite basis PINNs (FBPINNs) mitigate some of PINNs’ issues like slow convergence and spectral bias through localisation, but still rely on iterative nonlinear optimisation within each subdomain. In this work, we propose a hybrid approach that combines multilevel domain decomposition and partition-of-unity constructions with random feature models, yielding a method referred to as multilevel ELM-FBPINN. By replacing trainable subdomain networks with extreme learning machines, the resulting formulation eliminates backpropagation entirely and reduces training to a structured linear least-squares problem. We provide a systematic numerical study comparing ELM-FBPINNs and multilevel ELM-FBPINNs with standard PINNs and FBPINNs on representative benchmark problems, demonstrating that ELM-FBPINNs and multilevel ELM-FBPINNs achieve competitive errors while significantly accelerating convergence and improving robustness with respect to architectural and optimisation parameters. Through ablation studies, we further clarify the distinct roles of domain decomposition and random feature enrichment in controlling expressivity, conditioning, and scalability.
Accurate evaluation of the mechanical properties of aerospace-grade fiber composites is critical for ensuring structural integrity, certification compliance, and operational performance of aircraft and spacecraft. However, significant variability in reported mechanical properties arises from differences in fabrication techniques, process parameters, and testing conditions, necessitating efficient predictive methodologies. While previous machine learning studies have focused predominantly on single property prediction using homogeneous datasets, comprehensive comparative analyses across multiple algorithms utilizing heterogeneous data sources remain limited. This study presents a systematic comparative analysis of machine learning models; Linear Regression (LR), Support Vector Regression (SVR), Multilayer Perceptron (MLP), and Instance-based K-Nearest Neighbors (IBK) for predicting both tensile and flexural strength of fiber-reinforced composites. Models were trained using two distinct datasets: in-house laboratory experimental data (28–45 instances) and an expanded dataset combining laboratory results with published literature (98–102 instances). Input attributes encompassed reinforcement type, matrix composition, ply orientation, fiber content, stacking sequence, and specimen dimensions. Statistical evaluation revealed that LR and SVR achieved superior accuracy for smaller datasets (R2 = 0.998 and 0.996, respectively), attributed to their effectiveness in low-dimensional feature spaces. Conversely, MLP demonstrated robust predictive capability for larger, more heterogeneous datasets (R2 = 0.9538 for flexural; R2 = 0.9445 for tensile strength), owing to its capacity for capturing non-linear relationships. These findings establish that appropriately selected ML-based models can effectively predict FRC mechanical properties, providing designers and manufacturers with reliable, data-driven approaches to accelerate material qualification while reducing dependence on extensive experimental testing.
Solving stiff ordinary differential equations (StODEs) requires sophisticated numerical solvers, which are often computationally expensive. In general, traditional explicit time integration schemes with restricted time step sizes are not suitable for StODEs, and one must resort to costly implicit methods to compute solutions. On the other hand, state-of-the-art machine learning (ML) based methods such as Neural ODE (NODE) poorly handle the timescale separation of various elements of the solutions to StODEs, while still requiring expensive implicit/explicit integration at inference time. In this work, we propose a linear latent network (LiLaN) approach in which the dynamics in the latent space can be integrated analytically, and thus numerical integration is completely avoided. At the heart of LiLaNs are the following key ideas: i) two encoder networks to encode initial condition together with parameters of the ODE to the slope and the initial condition for the latent dynamics, respectively. Since the latent dynamics, by design, are linear, the solution can be evaluated analytically; ii) a neural network to map the initial condition, parameters, and the physical time to latent times, one for each latent variable. Intuitively, this allows for the "stretching/squeezing" of time in the latent space, thereby allowing for varying levels of attention to different temporal scales in the solution. Finally, iii) a decoder network to decode the latent solutions into the physical solution at the corresponding physical time. LiLaN is thus a solution operator approach that instantly provides an approximate flow map solution of a system of nonlinear ODEs at any time. We provide a universal approximation theorem for the proposed LiLaN approach, showing that it can approximate the solution of any stiff nonlinear system on a compact set to any degree of accuracy ϵ . We also show an interesting fact that the dimension of the latent dynamical system in LiLaNs is independent of ϵ . Numerical results on "Robertson Stiff Chemical Kinetics Model" (Anantharaman et al. 2021) and "Plasma Collisional-Radiative Model" (Chung et al. High Energy Density Phys. 2005;1) suggest that LiLaNs outperformed state-of-the-art machine learning approaches for handling StODEs. Numerically, we also show that LiLaNs outperformed other machine learning methods on multiple partial differential equations (PDEs) with known stiff behaviors, such as the "Allen-Cahn" and "Cahn-Hilliard" PDEs (Montanelli and Bootland 2020). Furthermore, we show that LiLaNs is equally well-suited for non-stiff differential equations such as the 2D Navier-Stokes equation. Our numerical experiments on the 2D Navier-Stokes equation demonstrate that LiLaN achieves remarkable speedup and accuracy compared to state-of-the-art machine learning methods, further highlighting its versatility as a solution operator for complex fluid dynamics problems.
