An innovative coupling numerical algorithm is proposed in the current paper, the front-tracking method–lattice Boltzmann method–machine learning (FTM-LBM-ML) method, to precisely capture fluid flow phase interfaces at the mesoscale and accurately simulate dynamic processes. This method combines the distinctive abilities of the FTM to accurately capture phase interfaces and the advantages of the LBM for easy handling of mesoscopic multi-component flow fields. Taking a single vacuole rising as an example, the input and output sets of the machine learning model are constructed using the FTM’s flow field, such as the velocity and position data from phase interface markers. Such datasets are used to train the Bayesian-Regularized Back Propagation Neural Network (BRBPNN) machine learning model to establish the corresponding relationship between the phase interface velocity and the position. Finally, the trained BRBPNN neural network is utilized within the multi-relaxation LBM pseudo potential model flow field to predict the phase interface position, which is compared with the FTM simulation. It was observed that the BRBPNN-predicted interface within the LBM exhibits a high degree of consistency with the FTM-predicted interface position, showing that the BRBPNN model is feasible and satisfies the accuracy requirements of the FT-LB coupling model.

In the field of intelligent manufacturing, image anomaly detection plays a pivotal role in automated product quality inspection. Most existing anomaly detection methods are adept at capturing local features of images, achieving high detection accuracy for structural anomalies such as cracks and scratches. However, logical anomalies typically appear normal within local regions of an image and are difficult to represent well by the anomaly score map, requiring the model to possess the capability to extract global context features. To address this challenge while balancing the detection of both structural and logical anomalies, this paper proposes a lightweight anomaly detection framework built upon EfficientAD. This framework integrates the reconstruction difference constraint (RDC) and a logical anomaly detection module. Specifically, the original EfficientAD relies on the coarse-grained reconstruction difference between the student and the autoencoder to detect logical anomalies; but, false detection may be caused by the local fine-grained reconstruction difference between the two models. RDC can promote the consistency of the fine-grained reconstruction between the student and the autoencoder, thereby effectively alleviating this problem. Furthermore, in order to detect anomalies that are difficult to represent by feature maps more effectively, the proposed logical anomaly detection module extracts and aggregates the context features of the image, and combines the feature-based method to calculate the overall anomaly score. Extensive experiments demonstrate our method’s significant improvement in logical anomaly detection, achieving 94.2 AU-ROC on MVTec LOCO, while maintaining strong structural anomaly detection performance at 98.4 AU-ROC on MVTec AD. Compared to the baseline, like EfficientAD, our framework achieves a state-of-the-art balance between both anomaly types.

This paper presents a case study demonstrating the use of the moving least square method (MLS) for modeling the mechanical response of an electrothermal microactuator. Under the MLS framework, the governing equations for heat transfer and structural mechanics are discretized across the computational domain. The resulting discrete electrothermal system is solved accurately through an incremental load and Newton–Raphson iterative method to determine the temperature field. Subsequently, the displacement field is obtained by solving the discrete mechanical equation, which includes contributions from natural boundary conditions. Convergence of the temperature solution is rigorously evaluated across different iterative schemes. The accuracy of the MLS solutions is validated against experimental temperature data and finite element method (FEM) simulations. Results indicate that the temperature distribution obtained from the MLS aligns well with both experimental and FEM results, even under idealized boundary conditions. Additionally, a similarly favorable comparison is observed between the displacement fields predicted by the MLS, polynomial point interpolation collocation method (PPCM), and FEM.