In this paper, we investigate the application of Physics-Informed Neural Networks (PINNs) to open-loop optimal control problems under limited information, such as sparse boundary or initial data and partially unknown system parameters. Using a Lagrangian multiplier framework, we derive the necessary optimality conditions and employ PINNs to jointly approximate the state, adjoint, and control variables, enabling effective learning even under severe data scarcity. Furthermore, we consider scenarios in which parts of the governing equations are not fully known and certain parameters must be identified during training. To address this challenge, we introduce a two-stage PINN framework. In the first stage, the uncontrolled dynamics are reconstructed from scattered data while simultaneously identifying multiple unknown parameters. In the second stage, the full optimal control problem is solved using the recovered dynamics. Numerical experiments on several cases of the Gardner equation show that the proposed methodology achieves high accuracy and robustness, even when the available data are extremely limited.
Automated segmentation of metallographic images can support quantitative microstructural characterisation while reducing the manual effort associated with conventional image analysis. This study evaluated a ResNet34-U-Net workflow for five-class semantic segmentation of steel microstructures using the publicly available MetalDAM scanning electron microscopy (SEM) dataset. Forty-two expert-annotated source micrographs were partitioned into training (29), validation (6), and test (7) subsets before extraction of 378 non-overlapping 256 × 256-pixel patches (260, 55, and 63 patches, respectively), preventing source-image overlap between subsets. The model incorporated an ImageNet-pretrained ResNet34 encoder and was trained using multiclass Dice loss. Three independent training runs were performed to assess reproducibility. On the held-out test subset, the initial pretrained model achieved a five-class macro Dice similarity coefficient (DSC) of 0.5950, macro intersection over union (IoU) of 0.4972, and pixel accuracy of 0.8015. Across three independent runs, validation macro DSC was 0.6018 ± 0.0190 and macro IoU was 0.4965 ± 0.0252 (mean ± standard deviation). For a separately defined binary Matrix-versus-non-Matrix task, the model achieved a DSC of 0.8647, compared with 0.8233 for Otsu thresholding and 0.8232 for adaptive thresholding. Class-specific analysis identified substantial limitations in Precipitate and Martensite/Austenite segmentation. Connected-component analysis further demonstrated discrepancies between predicted and reference morphological measurements. Mean inference latency was 18.902 ms per 256 × 256-pixel patch on an NVIDIA Tesla T4 GPU. The findings demonstrate the feasibility of integrating established deep learning architectures with quantitative metallographic image analysis while highlighting the importance of source-image-level evaluation, minority-class performance, and validation of downstream morphological descriptors. Further investigation using larger and independently acquired datasets is required before industrial application.
Diabetes mellitus is a chronic disease that continues to pose significant global health pressure, affecting a considerable proportion of the world’s population, with an estimated 537 million people affected worldwide in 2021, with an expected increase of 46
Machine-learning models for the compressive strength of coconut fiber reinforced concrete (CFRC) are usually fitted to minimise prediction error alone and evaluated on random splits of data pooled from many studies. This can hide physically inconsistent behaviour and overstate accuracy. This study proposes a physics-guided neural network (PGNN) that computes five physics-engineered features inside the network: a normalised ACI 209 hydration factor, an Abrams factor, a fiber reinforcing index, an RCA reduction factor and an aggregate packing factor. It also imposes four directional laws (for curing age, water-to-cement ratio, cement content and recycled aggregate replacement) as soft derivative penalties at collocation points that extend beyond the data. The model was trained on 586 source-verified records from 30 studies and evaluated with repeated random splits, leave-one-study-out (LOSO) validation, an ablation study, one-factor-at-a-time compliance tests and extrapolation tests. Under random splits, the PGNN reached R2 = 0.914 ± 0.033 (RMSE 4.63 MPa), below unconstrained gradient boosting (R2 = 0.957). Under LOSO, every machine-learning model lost most of its accuracy (R2 ≤ 0.33; PGNN 0.19) and a four-coefficient physics-only model did no worse (R2 = 0.40), showing that unrecorded between-study differences dominate prediction for a new study. The physics loss reduced the share of test mixes violating the four laws from 23–100
The structural application of composite materials has intensified in high-performance engineering sectors; however, interlaminar delamination remains one of the most critical damage mechanisms due to its low detectability and complex effects on dynamic response. This work investigates the influence of multiple internal delaminations on the vibration behavior of Carbon Fiber Reinforced Polymer (CFRP) laminated plates and evaluates the feasibility of using Convolutional Neural Networks (CNN) for damage identification from modal data. A ply-level finite element model was developed to generate 1,000 damage scenarios, spanning delaminated areas from 0.004% to 3.10% , producing 40, 000 modal field images. As a theoretical innovation, this work establishes via the Courant-Fischer theorem that constraint-release delamination models cannot physically increase natural frequencies; any observed positive shifts strictly represent discretisation errors, thereby defining a numerical noise floor. Statistical analysis reveals that mean modal curvature and frequency shifts exhibit statistically indistinguishable correlations with damage severity ( r = 0.50 and 0.46, respectively). Furthermore, CNN performance is rigorously benchmarked against novel analytical reference predictors derived from the sampling design. The networks achieved accuracies below 0.20 and R^2 < 0.054 , outperforming a baseline majority-class predictor by at most four percentage points. The hold-out predictions exclude overfitting as the cause: in 37 of the 40 classification models the retained network assigns a single class to every test image. The results demonstrate that the CNN’s predictive limitations arise not merely from the physical subtlety of the damage, but because the damage signature is fundamentally eclipsed by the model’s discretisation noise, establishing critical numerical resolution limits for deep learning datasets in structural health monitoring.
