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Shallow neural networks process the features directly, while deep networks extract features automatically along with the training. Both models suffer from overfitting or poor generalization in many cases. Deep networks include more hyper-parameters than shallow ones that increase the overfitting probability. This paper states a systematic review of the overfit controlling methods and categorizes them into passive, active, and semi-active subsets. A passive method designs a neural network before training, while an active method adapts a neural network along with the training process. A semi-active method redesigns a neural network when the training performance is poor. This review includes the theoretical and experimental backgrounds of these methods, their strengths and weaknesses, and the emerging techniques for overfitting detection. The adaptation of model complexity to the data complexity is another point in this review. The relation between overfitting control, regularization, network compression, and network simplification is also stated. The paper ends with some concluding lessons from the literature.

Single-cell RNA sequencing data have complex features such as dropout events, overdispersion, and high-magnitude outliers, resulting in complicated probability distributions of mRNA abundances that are statistically characterized in terms of a zero-inflated negative binomial (ZINB) model. Here we provide a mesoscopic kinetic foundation for the widely used ZINB model based on the biochemical reaction kinetics underlying transcription. Using multiscale modeling and simplification techniques, we show that the ZINB distribution of mRNA abundance and the related phenomenon of transcriptional bursting naturally emerge from a three-state stochastic transcription model. We further reveal a nontrivial quantitative relationship between dropout events and transcriptional bursting, which provides novel insights into how the burst size and burst frequency affect the dropout rate. Two different biophysical origins of overdispersion are also clarified at the single-cell level.

Computational Fluids Dynamics (CFD) simulations are essential for optimizing the design of a cockpit’s internal environment, but the complex geometric models consume a significant amount of computational resources and time. Arbitrary simplification of geometric models may result in inaccurate calculations of physical fields. To address this issue, this study establishes a geometric model simplification strategy and successfully applies it to a cockpit. The implementation of the whole approach is divided into three steps, summarized in three methods, namely Sensitivity Analysis Method (SAM), Detail Suppression Method (DSM), and Evaluation Standards Method (ESM). Sensitivity analysis of the detailed features of the geometric model is performed using the adjoint method. The details of the geometric model are suppressed based on the principle of curvature continuity. After evaluation, the suppression degrees of detailed features with different sensitivity levels are obtained. The results demonstrate that this strategy can be employed to achieve precise simplification standards, thereby avoiding excessive deviations caused by arbitrary simplification and reducing the significant costs associated with trial-and-error simplification.

The dynamic behavior of a compliant rolling-sliding contact system is theoretically analyzed using a cam-follower mechanism. The mechanism consists of a rigid cam (which provides a known periodic motion input) and a flexible follower with kinematic, contact, and friction non-linearities. A comprehensive kinematic and dynamic model of the system is developed using a combination of analytical and numerical formulations. To obtain the dynamic response of the system, the model simultaneously solves the kinematic and dynamic equations of the system, which involves computationally expensive steps. Alternatively, three simplified models are developed based on several approximations to reduce the computational effort. The best among the simplified models is identified by comparing the static and dynamic responses of the simplified models with those of the comprehensive model. Then, the non-linear dynamic response of the system is studied using frequency response plots and phase portraits, where the higher period and chaotic behavior are observed for the compliant system. Further, the contribution of the follower’s compliance to its dynamics is evaluated by comparing its response to that of a similar rigid system. Finally, the effects of varying the mean load, alternating load, and material damping on the dynamic response of the flexible system are analyzed. The work has presented a novel comprehensive dynamic model for the compliant mechanism integrating the complex geometry. In addition, a computationally simpler yet accurate alternative model has been identified. It is envisaged that the modeling framework devised in this article can be extended to more complicated systems to aid the evolution of faster and more robust digital twins.

Recent advances in measurement technologies have significantly improved the accuracy of multi-scale 3D reconstruction, yet the resulting large-scale data with inherent redundancy pose challenges for storage and real-time rendering. This paper proposes a systematic framework for efficient lightweight processing of 3D real-scene mesh model, integrating planar feature extraction, point cloud classification, and semantics-driven simplification. The key scientific contributions include: (1) A preprocessing process for the reality 3D model is added for the plane segmentation algorithm; (2) A training-free point cloud classification method employing 9 complementary geometric-semantic features and probabilistic smoothing to achieve computationally efficient classification without the need for deep learning or annotated data; and (3) An innovative semantic-driven simplification strategy that dynamically adjusts processing priorities based on feature importance. Experimental results demonstrate the framework's effectiveness in preserving critical architectural features (e.g., façades and roofs) while aggressively compressing less significant elements (e.g., terrain and clutter), achieving balanced data reduction and information retention. At equivalent simplification ratios, our algorithm achieves a 23% improvement in model accuracy compared to the baseline method, with a 31% accuracy enhancement specifically for critical geometric features. When maintaining equivalent accuracy levels, the proposed method reduces face count by 23% relative to the baseline approach. The proposed methods advance 3D urban modeling by addressing both technical and practical challenges in large-scale scene processing.

Efficient simplification of 3D models is essential for mobile and other resource-constrained application scenarios. Industrial 3D assemblies, typically composed of numerous components and dense triangular meshes, often pose significant challenges in rendering and transmission due to their large scale and high complexity. The Quadric Error Metrics (QEM) algorithm offers a practical balance between simplification accuracy and computational efficiency. However, its application to large-scale industrial models remain limited by performance bottlenecks, especially when combined with curvature-based optimization techniques that improve fidelity at the cost of increased computation. Therefore, this paper presents a parallel implementation of the QEM algorithm and its curvature-optimized variant using the OpenMP framework. By identifying key bottlenecks in the serial workflow, this research parallelizes critical processes such as curvature estimation, error metric computation, and data structure manipulation. Experiments on large industrial assembly models at a simplification ratio of 0.3, 0.5, and 0.7 demonstrate that the proposed parallel algorithms achieve significant speedups, with a maximum observed speedup of 5.5×, while maintaining geometric quality and topological consistency. The proposed approach significantly improves model processing efficiency, particularly for medium- to large-scale industrial models, and provides a scalable and practical solution for real-time loading and interaction in engineering applications.

Transjugular intrahepatic portosystemic shunt (TIPS) is a widely used surgery for portal hypertensive patients, whose potential postoperative complications are closely related to the hemodynamic condition of the portal venous system. The selection of shunt position in the surgery may affect the postoperative hemodynamics; however, it is difficult for clinical studies to investigate the influence. Therefore, this study aims to employ the computational model simulating TIPS to compare the hemodynamic differences resulting from different shunt positions, and also to investigate the influences of different geometrical model simplification strategies used in the TIPS simulation. For this purpose, the clinical data of two representative patients were retrospectively collected, based on which, the computational hemodynamic models of the portal venous systems after TIPS were constructed, incorporating three typical shunt positions (i.e. shunt at the left/main/right portal vein) and three types of geometrical model simplification. Results showed that among the models with different shunt positions, the area-averaged flow velocity magnitudes in the shunts were very similar, while the model with shunt at the main portal vein showed the lowest postoperative portal pressure and the smallest area of high wall shear stress near the portal venous bifurcation. Among the models using different geometrical model simplification strategies, the simulated blood pressures at the main portal veins were very similar, but showed marked differences near the shunt inlets. Moreover, the area-averaged flow velocity magnitudes in the shunts were almost the same, while the velocity distributions differed a lot, leading to the different spatial distributions of wall shear stress near the portal venous bifurcations and shunt walls. These results on one hand suggested that placing the shunt at the main portal vein is more beneficial for the patient; on the other hand, they proved the feasibility of utilizing simplified model to save computational cost without losing the accuracy when the pressure at the main portal vein is mainly focused on. These findings would assist clinical decision-making and promote more accurate and efficient TIPS simulations.

Natural porous media are generally heterogeneous and anisotropic. The structure of porous media plays a vital role and is often the source of their heterogeneity and anisotropy. In physical processes such as fluid flow in porous media, a small number of dominant features, here referred to as wide channels, are responsible for the majority of the flow. The thickness and orientation of these channels often determine the permeability characteristics of the media. Typically, identifying such dominant features requires extensive and costly simulations. Here, we propose a prompt approach based on geometric properties derived from three‐dimensional (3D) images. The size or radius of the dominant features is obtained via distance maps, and their orientations are determined using Principal Component Analysis. Subsequently, we visualize these dominant features with color and color brightness according to their orientation and size, together with their location and distribution in 3D space. The combined visualization of anisotropy (orientation) and heterogeneity (size) in a single plot provides a straightforward way to enhance our understanding of pore structure characteristics. Besides, we propose a refined stereographic projection method to statistically illustrate both heterogeneity and anisotropy. Based on these insights, we further present a potential approach to reduce model size in numerical simulations, significantly reducing computational costs while preserving essential characteristics. Plain Language Summary Natural porous media, such as soil or rock, have uneven structures that result in distinctive behavior depending on their specific location or orientation. While this understanding is widely acknowledged, conventional approaches to predict these behaviors rely on extensive and costly methods, such as field investigations, laboratory experiments, or numerical simulations. Although imaging techniques such as X‐ray computed tomography (CT) can provide three‐dimensional structures, there is still no visualization technique that directly depicts both heterogeneity and anisotropy. Here, we propose a novel method that uses color and color brightness to simultaneously visualize the size (heterogeneity) and orientation (anisotropy) of targeted objects. We introduce a refined stereographic projection to statistically display both heterogeneity and anisotropy in a single plot. To demonstrate the effectiveness of our method, we present examples of coral pore structures, rock fractures, and ice crystals. The derived geometric features show a strong correlation with numerical simulation results of fluid flow, validating the accuracy and value of our approach in enhancing our comprehension of the heterogeneity and anisotropy of porous media. Based on these findings, we propose a potential approach to simplify geometric models in numerical simulations, significantly reducing computational costs while preserving essential characteristics. Key Points A novel method for visualizing the heterogeneity and anisotropy of porous media is proposed by deriving geometric properties from 3D images Stereographic projection is refined to statistically demonstrate heterogeneity and anisotropy in a single plot Enhanced understanding of heterogeneity and anisotropy leads to a potential approach for simplifying geometric models in numerical simulations

As the integration of electronic-interfaced devices have increased, microgrid models have become too complex to perform a stability analysis. Thus, an effective model simplification method keeping most dynamics of the system becomes very essential. Singular perturbation is a common way for model simplification. However, its accuracy is insufficient when nonlinear properties dominate. This is caused by the “Quasi-Steady State Assumption” that traditional singular perturbation holds. By assuming that microgrid can only be stabilized when fast variables stop variating, the traditional method ignores some common phenomena before a stabilization occurs, leading to a loss of dynamics. To improve the accuracy, this paper proposes a “second-order singular perturbation”. Here, the traditional “Quasi-Steady State” is updated to a scenario that third-order derivatives of fast variables become zero before the microgrid stabilizes. The updated assumption covers more common phenomena before a stabilization occurs. This leads to a more precise simplification. Simulation results indicate that the proposed method outperforms traditional singular perturbation in accuracy.

Energy storage systems play a vital role in balancing solar- and wind-generated power. However, the uncertainty of their lifespan is a key factor limiting their large-scale applications. While currently reported battery aging models, empirical or semi-empirical, are capable of accurately assessing battery decay under specific operating conditions, they cannot reliably predict the battery lifespan beyond the measured data. Moreover, these models generally require a tedious procedure to determine model parameters, reducing their value for onsite applications. This paper, based on Newman’s pseudo-2D performance model and incorporating microparameters obtained from cell disassembly, developed a mechanistic model accounting for three major aging mechanisms of lithium iron phosphate/graphite cells, i.e., solid electrolyte interphase growth, lithium plating, and gas generation. The prediction of this mechanistic model agrees with the experimental results within an average error of ±1%. The mechanistic model was further simplified into an engineering model consisting of only two core parameters, loss of active lithium and loss of active material, and was more suitable for large-scale applications. The accuracy of the engineering model was validated in a 100 MW/200 MWh energy storage project. When the actual State of Health (SOH) of the battery degraded to 89.78%, the simplified model exhibited an error of −0.17%, and the computation time decreased from 8.12 h to 10 s compared to the mechanistic model.