Local Minima Research Articles

A Gastrointestinal Image Classification Method Based on Improved Adam Algorithm

In this study, a gastrointestinal image classification method based on the improved Adam algorithm is proposed. Gastrointestinal image classification is of great significance in the field of medical image analysis, but it presents numerous challenges, including slow convergence, susceptibility to local minima, and the complexity and imbalance of medical image data. Although the Adam algorithm is widely used in stochastic gradient descent, it tends to suffer from overfitting and gradient explosion issues when dealing with complex data. To address these problems, this paper proposes an improved Adam algorithm, AdamW_AGC, which combines the weight decay and Adaptive Gradient Clipping (AGC) strategies. Weight decay is a common regularization technique used to prevent machine learning models from overfitting. Adaptive gradient clipping avoids the gradient explosion problem by restricting the gradient to a suitable range and helps accelerate the convergence of the optimization process. In order to verify the effectiveness of the proposed algorithm, we conducted experiments on the HyperKvasir dataset and validation experiments on the MNIST and CIFAR10 standard datasets. Experimental results on the HyperKvasir dataset demonstrate that the improved algorithm achieved a classification accuracy of 75.8%, compared to 74.2% for the traditional Adam algorithm, representing an improvement of 1.6%. Furthermore, validation experiments on the MNIST and CIFAR10 datasets resulted in classification accuracies of 98.69% and 71.7%, respectively. These results indicate that the AdamW_AGC algorithm has advantages in handling complex, high-dimensional medical image classification tasks, effectively improving both classification accuracy and training stability. This study provides new ideas and expansions for future optimizer research.

Revisiting Possibilistic Fuzzy C-Means Clustering Using the Majorization-Minimization Method.

Possibilistic fuzzy c-means (PFCM) clustering is a kind of hybrid clustering method based on fuzzy c-means (FCM) and possibilistic c-means (PCM), which not only has the stability of FCM but also partly inherits the robustness of PCM. However, as an extension of FCM on the objective function, PFCM tends to find a suboptimal local minimum, which affects its performance. In this paper, we rederive PFCM using the majorization-minimization (MM) method, which is a new derivation approach not seen in other studies. In addition, we propose an effective optimization method to solve the above problem, called MMPFCM. Firstly, by eliminating the variable V∈Rp×c, the original optimization problem is transformed into a simplified model with fewer variables but a proportional term. Therefore, we introduce a new intermediate variable s∈Rc to convert the model with the proportional term into an easily solvable equivalent form. Subsequently, we design an iterative sub-problem using the MM method. The complexity analysis indicates that MMPFCM and PFCM share the same computational complexity. However, MMPFCM requires less memory per iteration. Extensive experiments, including objective function value comparison and clustering performance comparison, demonstrate that MMPFCM converges to a better local minimum compared to PFCM.

Optimization of methanol yield and carbon dioxide utilization in methanol synthesis process

The method of CO2 hydrogenation to methanol can effectively reduce carbon emission and has wide application prospects in chemical industry and environment. Therefore, methanol synthesis is an important way to save energy, reduce emission and transform energy utilization. In this paper, the mathematical model of methanol synthesis reactor is established. Under the condition of controllable cooling temperature, the optimization is carried out with maximum methanol yield and CO2 utilization rate. The results show that the methanol yield can be increased by 6.57% and CO2 utilization rate can be increased to 39.1% by adjusting the cooling temperature control strategy. The comparative study found that the optimal cooling temperatures all show up and down variations, with local minima and maxima. In addition, an industrial application method of methanol yield maximization cooling strategy is proposed. When the stage cooling at different temperatures is adopted, the methanol yield could be increased by 5.38%.

Implicit Sharpness-Aware Minimization for Domain Generalization

Domain generalization (DG) aims to learn knowledge from multiple related domains to achieve a robust generalization performance in unseen target domains, which is an effective approach to mitigate domain shift in remote sensing image classification. Although the sharpness-aware minimization (SAM) method enhances DG capability and improves remote sensing image classification performance by promoting the convergence of the loss minimum to a flatter loss surface, the perturbation loss (maximum loss within the neighborhood of a local minimum) of SAM fails to accurately measure the true sharpness of the loss landscape. Furthermore, its variants often overlook gradient conflicts, thereby limiting further improvement in DG performance. In this paper, we introduce implicit sharpness-aware minimization (ISAM), a novel method that addresses the deficiencies of SAM and mitigates gradient conflicts. Specifically, we demonstrate that the discrepancy in training loss during gradient ascent or descent serves as an equivalent measure of the dominant eigenvalue of the Hessian matrix. This discrepancy provides a reliable measure for sharpness. ISAM effectively reduces sharpness and mitigates potential conflicts between gradients by implicitly minimizing the discrepancy between training losses while ensuring a sufficiently low minimum through minimizing perturbation loss. Extensive experiments and analyses demonstrate that ISAM significantly enhances the model’s generalization ability on remote sensing and DG datasets, outperforming existing state-of-the-art methods.

EOFA: An Extended Version of the Optimal Foraging Algorithm for Global Optimization Problems

The problem of finding the global minimum of a function is applicable to a multitude of real-world problems and, hence, a variety of computational techniques have been developed to efficiently locate it. Among these techniques, evolutionary techniques, which seek, through the imitation of natural processes, to efficiently obtain the global minimum of multidimensional functions, play a central role. An evolutionary technique that has recently been introduced is the Optimal Foraging Algorithm, which is a swarm-based algorithm, and it is notable for its reliability in locating the global minimum. In this work, a series of modifications are proposed that aim to improve the reliability and speed of the above technique, such as a termination technique based on stochastic observations, an innovative sampling method and a technique to improve the generation of offspring. The new method was tested on a series of problems from the relevant literature and a comparative study was conducted against other global optimization techniques with promising results.

An Efficient Modified Black Widow Optimized Node Localization in Wireless Sensor Network

Wireless Sensor Network (WSN) is an encouraging technology in various applications like atmosphere monitoring, vehicular systems, and targeting devices. Localization in WSN is performed to identify the current position or coordinates of sensor nodes. The crucial task of localization is to find coordinates without manual configuration and expensive hardware like GPS. This work proposes a new localization algorithm using Modified Black Widow Optimization (MBWO). The proposed method involves an optimal selection of anchor nodes to reduce localization errors. Black Widow Optimization (BWO) is a naturally inspired optimization algorithm encouraged by the unique coupling behaviour of black widow spiders. The performance of black widow optimization is improved by levy flight distribution to escape from local minima. Experimental results show that the proposed MBWO-optimized localization achieves a higher localized node count with minimized localized error compared to other optimization algorithms.

The path planning algorithm for UUV based on the fusion of grid obstacles of artificial potential field

The artificial potential field approach (APFA) has the advantages of short computation time and easy implementation, widely used in path planning. The problems of local oscillation and susceptibility to local minima for APFA are considered in three dimensions (3D) path planning application of unmanned underwater vehicle (UUV), and the artificial potential field grid method (APFG) is proposed. The core principles of APFG include three key methods: firstly, obstacles are rasterized in a 3D map, and repulsive points are attached to the grid surface to alter the range of repulsive influence, thereby compensating for the issue of longer planned paths caused by the idealized modeling in traditional APFA; secondly, the repulsion function of the grid surface is modified to ensure that the potential field is parallel to the grid surface, thus addressing the problem of local oscillation in UUV path planning. Additionally, the introduction of virtual target points helps prevent the UUV from getting trapped in local optima, effectively overcoming the drawbacks of local oscillation and convergence to local minima in 3D path planning for UUV. The simulations show that APFG effectively overcomes the shortcomings of local oscillations and the tendency to fall into local minima for UUV in 3D path planning, and the path planning is smooth and efficient.

Interference mechanism of plasma self-organization in transparent dielectrics under the intense femtosecond laser pulse exposure

A new mechanism of plasma self-organization in transparent dielectrics with wide bandgap exposed to the intense tightly focused laser radiation was revealed, which causes the generation of 3D periodic ring structures with subwavelength period both along the laser pulse propagation and in the radial direction. The mechanism involves formation of dense plasma burst in the pre-focal region that provides efficient scattering of the incident wave. The interference of a plane incident laser wave in the focal region and a divergent reflected one will form the standing wave pattern with local minima and maxima of laser field both in the direction of the incident wave propagation and perpendicular to it producing the ring patterns of effective ionization regions in the dielectric volume. Analytical and numerical simulations of the process of laser wave scattering on a near-spherical plasma object with dimensions both smaller and larger than the laser radiation wavelength are performed to verify the proposed model.

Understanding two-dimensional tractor magnets: Theory and realizations

We present a comparative investigation of two-dimensional tractor magnet configurations, analyzing both theoretical predictions and experimental results with a focus on the minimal tractor magnet. The minimal tractor magnet consists of a rigid assembly of one attracting magnet (attractor), two repelling magnets (repulsors), and a fourth magnet (follower) that is magnetically stabilized in a local energy minimum. The theoretical framework relies on magnetostatics and stability analysis of stationary equilibria. To calculate the magnetostatic force and energy, we use a multipole method. In a first approximation, we derive analytical results from the point dipole approximation. The point dipole analysis defines an upper bound criterion for the magnetic moment ratio and provides analytical expressions for stability bounds in relation to geometry parameters. Our experimental results are consistent with the predictions from the fourth-order multipole expansion. Beyond the minimal tractor magnet, we introduce a more advanced configuration that allows for a higher magnetic binding energy and follower capture at larger distances.

An Automated Approach to Estimating Convective Boundary Layer Depth from Dual-Polarization WSR-88D Radar Observations

Abstract Convective boundary layer (CBL) depth can be estimated from dual-polarization WSR-88D radars using the product differential reflectivity ZDR because the CBL top is collocated with a local ZDR minimum produced by Bragg scatter at the interface of the CBL and the free troposphere. Quasi-vertical profiles (QVPs) of ZDR are produced for each radar volume scan and profiles from successive times are stitched together to form a time–height plot of ZDR from sunrise to sunset. QVPs of ZDR often show a low-ZDR channel that starts near the ground and rises during the morning and early afternoon, identifying the CBL top. Unfortunately, results show that this channel within the QVP can occasionally be misleading. This motivated creation of a new variable DVar, which combines ZDR with its azimuthal variance and is particularly helpful at identifying the CBL top during the morning hours. Two methods are developed to track the CBL top from QVPs of ZDR and DVar. Although each method has strengths and weaknesses, the best results are found when the two methods are combined using inverse variance weighting. The ability to detect CBL depth from routine WSR-88D radar scans rather than from rawinsondes or lidar instruments would vastly improve our understanding of CBL depth variations in the daytime by increasing the temporal and spatial frequencies of the observations. Significance Statement The daytime convective boundary layer (CBL) can increase in depth from a few hundred to a few thousand meters between sunrise and sunset and is strongly connected to temperature changes at Earth’s surface. Unfortunately, current observations of CBL depth primarily consist of measurements from twice daily rawinsonde launches at 97 locations across the United States. As a result, CBL depth observations lack fine spatial and temporal resolution and miss the daily cycle of CBL growth. This study seeks to fill the gaps in CBL depth observations by developing an automated method to estimate CBL depth from dual-polarization WSR-88D radar observations with a temporal resolution as fine as 5–10 min. These observations will greatly enhance our ability to observe and monitor CBL depth in real time.

AUTOMATED SYNTHESIS OF OPTIMAL SCHEMES LOCATION OF PRODUCTION FACILITIES ON RUGGED TERRAIN

An automated method has been developed to synthesize layouts of industrial facilities on rugged terrains, aimed at minimizing costs associated with utilities routes development (construction and operation). Additional conditions of optimization synthesis include constraints on the regulatory minimum permissible clear distances between facilities and requirements that prevent facilities from being placed in restricted zones. Three characteristic types of terrain surface relief sufficient to solve the optimization problem presented under automated design conditions have been identified. The terrain allocated for enterprise placement is specified in the conditions of the optimization problem being solved by a regular grid created based on Delaunay triangulation. To calculate the elevation (applicate) of the center of the geometric image of the facility’s base at any position, a secondary approximation of a local small area is applied using a second-order Lagrange interpolation polynomial. Due to the multimodal nature of the objective function, partly caused by the complexity of the topography of the territory designated for facility location, the use of one of the stochastic population methods, specifically the modified method of differential evolution, is proposed to ensure a search for the global minimum of the objective function. A numerical example of synthesizing facilities layouts is provided, assuming their location on different slopes of a depression. The results of the numerical experiment confirmed the possibility of using the method presented in the paper for automated search of optimal (close to optimal) layouts for facilities on rugged terrains.

Energetic Electrons Accelerated and Trapped in a Magnetic Bottle above a Solar Flare Arcade

Where and how flares efficiently accelerate charged particles remains an unresolved question. Recent studies revealed that a “magnetic bottle” structure, which forms near the bottom of a large-scale reconnection current sheet above the flare arcade, is an excellent candidate for confining and accelerating charged particles. However, further understanding its role requires linking the various observational signatures to the underlying coupled plasma and particle processes. Here we present the first study combining multiwavelength observations with data-informed macroscopic magnetohydrodynamics and particle modeling in a realistic eruptive flare geometry. The presence of an above-the-loop-top magnetic bottle structure is strongly supported by the observations, which feature not only a local minimum of magnetic field strength but also abruptly slowing plasma downflows. It also coincides with a compact above-the-loop-top hard X-ray source and an extended microwave source that bestrides the flare arcade. Spatially resolved spectral analysis suggests that nonthermal electrons are highly concentrated in this region. Our model returns synthetic emission signatures that are well matched to the observations. The results suggest that the energetic electrons are strongly trapped in the magnetic bottle region due to turbulence, with only a small fraction managing to escape. The electrons are primarily accelerated by plasma compression and facilitated by a fast-mode termination shock via the Fermi mechanism. Our results provide concrete support for the magnetic bottle as the primary electron acceleration site in eruptive solar flares. They also offer new insights into understanding the previously reported small population of flare-accelerated electrons entering interplanetary space.

New type of solutions for Schrödinger equations with critical growth

We consider the following nonlinear Schrödinger equations with critical growth: −Δu+V(|y|)u=uN+2N−2,u>0inRN, where V(|y|) is a bounded positive radial function in C1, N ≥ 5. By using a finite reduction argument, we show that if r2V(r) has either an isolated local maximum or an isolated local minimum at r0 > 0 with V(r0) > 0, there exists infinitely many non-radial large energy solutions which are invariant under some sub-groups of O(3).

Decentralized H2 Control for Discrete-Time Networked Systems With Positivity Constraint.

In this brief, we study the decentralized H2 state-feedback control problem for networked discrete-time systems with positivity constraint. This problem (for a single positive system), raised recently in the area of positive systems theory, is known to be challenging due to its inherent nonconvexity. In contrast to most works, which only provide sufficient synthesis conditions for a single positive system, we study this problem within a primal-dual scheme, in which necessary and sufficient synthesis conditions are proposed for networked positive systems. Based on the equivalent conditions, we develop a primal-dual iterative algorithm for solution, which helps prevent from converging to a local minimum. In the simulation, two illustrative examples are employed for verification of our proposed results.

Enhanced Multimodal Nonparametric Probabilistic Method for Model-Form Uncertainty Quantification and Digital Twinning

The nonparametric probabilistic method (NPM) is a physics-based machine learning approach for model-form (MF) uncertainty quantification (UQ), model updating, and digital twinning. It extracts from reference data information not captured by a real-time computational model and infuses it into a “hyperparameterized,” stochastic version of this model by solving an inverse statistical problem formulated using a loss function and a few hyperparameters. The loss function is designed such that the mean value and statistical fluctuations of some quantities of interest predicted using the real-time stochastic model match target values obtained from the reference data. NPM’s performance hinges upon the efficient minimization of the loss function, which is unfortunately stochastic and nonconvex and thus prone to getting the optimization procedure trapped in suboptimal local minima. The latter scenario is exacerbated when the reference data is scarce. The paper addresses these issues by adopting the squared quadratic Wasserstein distance as the measure of dissimilarity between two different sets of data and by reformulating NPM’s inverse statistical problem as a multimodal data-assimilation problem. The potential of the resulting enhanced NPM for MF-UQ, model updating, and digital twinning is demonstrated using numerical simulations relevant to applications in structural dynamics, including structural health monitoring.

Functional Medium Entropy Alloys for Joint Replacement: An Atomistic Perspective of Material Deformation and a Correlation to Wear, Corrosion, and Biocompatibility

The present study adopts a muti-facet approach to design bio inspired concentrated alloys for potential application as articulating surfaces in joint replacements. A series of equiatomic, Nb rich and Ti rich TiMoNbZr based medium entropy alloys (MEAs) were processed via arc melting and their mechanical, in-vitro corrosion, wear, and in vitro and in vivo biocompatibility were investigated. Equiatomic MEA had primarily bcc with minor hcp phases where the single bcc was achieved with the addition of Nb. The single bcc Nb rich alloy resulted in 13% elongation, much higher than equiatomic or Ti rich alloy. All the MEAs showed comparatively higher yield strength due to the climb of edge dislocations which is the main rate limiting mechanism at 300 K, as evident molecular dynamics (MD) simulation. The locally fluctuating energy landscape promotes kinks on edge dislocation, and at local minima nanoscale segments gets pinned. Upon yielding the entangled kink leaves a trail of vacancies/interstitials and escapes via climb motion to render high yield strength. The higher corrosion and pitting resistance of Nb enriched alloys can be attributed to the stable ZrO2, Nb2O5, TiO2, and MoO3 oxides, high polarization resistance (106-105 Ωcm−2), and low defect densities (1016-1018). In vitro cell-materials interaction using MC3T3-E1 showed bioinert but cytocompatible nature of the MEAs. The wear rate of the MEAs was in the range of 7-9×10−5 mm3N−1m−1. The wear debris did not show any tissue necrosis when implanted in rabbit femur rather new bone regeneration can be seen around the particles. Statement of SignificanceIn the present work, a noble Nb enriched MEAs with superior mechanical, in vitro wear, corrosion and cytocompatibility properties was designed for articulating surfaces in joint replacement.•Single bcc in Nb enriched MEAs resulted in 13 % elongation with high hardness and yield strength.•Climb of entangled edge segment is the rate limiting mechanism in controlling high yield strength of MEAs at 300 K.•High polarization resistance (106-105 Ωcm−2), and low defect densities (1016-1018) attributes to ZrO2, Nb2O5, TiO2, and MoO3 oxides enriched passive film.•Wet sliding wear rate ranged in order 7-9×10−5 mm3N−1m−1. In-situ generated wear debris when implanted in rabbit femur did not show any tissue necrosis rather new bone regeneration was observed around debris.

DynGAN: Solving Mode Collapse in GANs With Dynamic Clustering.

Generative Adversarial Networks (GANs) are widely-used generative models for synthesizing complex and realistic data. However, mode collapse, where the diversity of generated samples is significantly lower than that of real samples, poses a major challenge for further applications. Our theoretical analysis demonstrates that the generator loss function is non-convex with respect to its parameters when there are multiple modes in real data. In particular, parameters that result in generated distributions with perfect partial mode coverage of the real distribution are the local minima of the generator loss function. To address mode collapse, we propose a unified framework called Dynamic GAN. This method detects collapsed samples in the generator by thresholding on observable discriminator outputs, divides the training set based on these collapsed samples, and trains a dynamic conditional model on the partitions. The theoretical outcome ensures progressive mode coverage and experiments on synthetic and real-world data sets demonstrate that our method surpasses several GAN variants. In conclusion, we examine the root cause of mode collapse and offer a novel approach to quantitatively detect and resolve it in GANs.

A novel prediction model of total drag coefficient of an MPV vehicle based on LSA optimization

Abstract Environmental degradation and energy scarcity are caused by the ongoing rise in the number of automobiles. The most efficient way to lower air resistance while driving is to boost vehicle energy efficiency and reduce energy consumption. In this case, a specific MPV model serves as the study subject in this work, and we use CFD simulation to estimate the drag coefficient along with the selection of important factors. Furthermore, to increase prediction accuracy, a lightning search algorithm (LSA)-based BP-neural-network prediction model is created and developed. The results show that the average relative error reduction of 2.83% in the drag resistance model optimized by the lightning search method represents a significant improvement in accuracy. This phenomenon can be explained by the LSA’s ability to resolve the BP neural network’s initial weight and threshold uncertainty as well as the issue of local minima being quickly reached. The high prediction accuracy drag prediction model, obtained herein, is useful for creating and producing automobile shapes with low drag coefficients.

Regularization in space–time topology optimization for additive manufacturing

In additive manufacturing, the fabrication sequence has a large influence on the quality of manufactured components. While planning of the fabrication sequence is typically performed after the component has been designed, recent developments have demonstrated the possibility and benefits of simultaneous optimization of both the structural layout and the corresponding fabrication sequence. This is particularly relevant in multi-axis additive manufacturing, where rotational motion offers enhanced flexibility compared to planar fabrication. The simultaneous optimization approach, called space–time topology optimization, introduces a pseudo-time field to encode the manufacturing process order, alongside a pseudo-density field representing the structural layout. To comply with manufacturing principles, the pseudo-time field needs to be monotonic, i.e., free of local minima. However, explicitly formulated constraints proposed in prior work are not always effective, particularly for complex structural layouts that commonly result from topology optimization.In this paper, we introduce a novel method to regularize the pseudo-time field in space–time topology optimization. We conceptualize the monotonic additive manufacturing process as a virtual heat conduction process starting from the surface upon which a component is constructed layer by layer. The virtual temperature field, which shall not be confused with the actual temperature field during manufacturing, serves as an analogy for encoding the fabrication sequence. In this new formulation, we use local virtual heat conductivity coefficients as optimization variables to steer the temperature field and, consequently, the fabrication sequence. The virtual temperature field is inherently free of local minima due to the physics it resembles. We numerically validate the effectiveness of this regularization in space–time topology optimization under process-dependent loads, including gravity and thermomechanical loads.

Geometric and Electronic Properties of P Atom-Doped Al Nanoclusters: Alkaline-like Superatom of P@Al12.

The geometric and electronic characteristics of phosphorus-atom doped aluminum nanoclusters, AlnPm (n = 7-17, m = 1 and 2), were investigated through a combination of experiments and theoretical calculations. The size dependences of the ionization energy (Ei) for AlnPm NCs exhibit a local minimum of 5.37 eV at Al12P1, attributed to an endohedral P@Al12 superatom (SA). This SA originates from an excess electron toward the 2P shell closing (40e), coexisting with an exohedral isomer featuring a vertex P atom. The stability of the endohedral P@Al12 is further enhanced in its cationic state compared to the exohedral isomer, when complexed with a fluorine (F) atom, forming an SA salt denoted as P@Al12+F- with an elevated Ei ranging from 6.42 to 7.90 eV. In contrast, for the anionic Al12P1-, the exohedral form is found to be more stable than the endohedral one using anion photoelectron spectroscopy and calculations. The geometric and electronic robustness of neutral P@Al12 SAs against electron donation and acceptance is discussed in comparison to rare-gas-like Si@Al12 SAs.