Number Of Floating Point Operations Research Articles

Research on Coal Flow Visual Detection and the Energy-Saving Control Method Based on Deep Learning

In this paper, machine vision technology is used to recognize the coal flow on a conveyor belt and control the running speed of a motor according to the coal flow on the conveyor belt to achieve an energy-saving effect and provide technical support for the sustainable development of energy. In order to improve the accuracy of coal flow recognition, this paper proposes the color gain-enhanced multi-scale retina algorithm (AMSRCR) for image preprocessing. Based on the YOLOv8s-cls improved deep learning algorithm YOLO-CFS, the C2f-FasterNet module is designed to realize a lightweight network structure, and the three-dimensional weighted attention module, SimAm, is added to further improve the accuracy of the network without introducing additional parameters. The experimental results show that the recognition accuracy of the improved algorithm YOLO-CFS reaches 93.1%, which is 4.8% higher, and the detection frame rate reaches 32.68 frame/s, which is 5.9% higher. The number of parameters is reduced by 28.4%, and the number of floating-point operations is reduced by 33.3%. These data show that the YOLO-CFS algorithm has significantly improved the accuracy, lightness, and reasoning speed in the coal mine environment. Furthermore, it can satisfy the requirements of coal flow recognition, realize the energy-saving control of coal mine conveyor belts, and achieve the purpose of sustainable development of the coal mining industry.

Improved YOLOv8-Pose Algorithm for Albacore Tuna (Thunnus alalunga) Fork Length Extraction and Weight Estimation

Aiming at the problems of large statistical error and the poor real-time performance of catch weight in the ocean fishing tuna industry, an algorithm based on improved YOLOv8-Pose for albacore tuna (Thunnus alalunga) fork length extraction and weight estimation is proposed, with reference to the human body’s pose estimation algorithm. Firstly, a lightweight module constructed using a heavy parameterization technique is used to replace the backbone network, and secondly, a weighted bidirectional feature pyramid network BIFPN is utilized. Finally, the upper and lower jaw and tail feature points of the albacore tuna (Thunnus alalunga) were extracted using the key point detection algorithm, and the weight of the albacore tuna (Thunnus alalunga) was estimated based on the fitted relationship between fork length and weight. The experimental results show that the improved YOLOv8-Pose algorithm reduces the number of model parameters by 13.63% and the number of floating-point operations by 14.03% compared with the baseline model without decreasing the accuracy of the target detection and key point detection and improves the model inference speed by 374%. At the same time, it reduces the drift of the key point detection, and the error of the comparison with the actual albacore tuna (Thunnus alalunga) body weight is not more than 10%. The improved key point detection algorithm has high detection accuracy and inference speed, which provides accurate yield data for pelagic fishing and is expected to solve the existing statistical problems and improve the accuracy and real-time performance of data in the fishing industry.

RSU-Net: An Attention U-Net for Martian Rock Segmentation

Since rocks may collide with the rover or wear tires during the exploration mission of the Mars probe, and may contain rich geological information, identifying rocks in the scene is crucial for the navigation and obstacle avoidance of the Mars probe. Additionally, since the communication between the Mars rover and the earth is often intermittent and delayed during missions, it needs a certain degree of autonomy. Deep learning technologies such as semantic segmentation and target detection can meet this requirement to a certain extent, which facilitates the enhancement of safety and efficiency for the Mars rover. Rock segmentation is to divide the pixels of the rock from the image. However, the texture of the rock is often close to the texture of the surrounding sand, and some parts may be covered, so it is difficult to identify it correctly. To this end, this paper proposed RSU-Net (Rock Segmentation U-Net) and RSU-Net-L, which combine the SENet attention mechanism, and the latter achieves higher computational efficiency and inference speed by compressing the number of channels on the basis of the former. In addition, this paper established a dataset, MarsRock, for Mars rock segmentation to help the Mars rover for visual navigation. Its images come from “Tianwen-1”, which contains 1194 images, and each image has a corresponding rock label. And our experiments on the MarsRock dataset show that RSU-Net can achieve 99.07% accuracy and 67.71% F1-score. RSU-Net-L can achieve 98.99% accuracy and 66.67% F1-score while diminishing the number of parameter count by 43.7% and the number of FLOPs by 43.6%, while the FPS can reach 12.01 on a single RTX6000-24GB GPU.

Neural Architecture Search as Multiobjective Optimization Benchmarks: Problem Formulation and Performance Assessment

The ongoing advancements in network architecture design have led to remarkable achievements in deep learning across various challenging computer vision tasks. Meanwhile, the development of neural architecture search (NAS) has provided promising approaches to automating the design of network architectures for lower prediction error. Recently, the emerging application scenarios of deep learning (e.g., autonomous driving) have raised higher demands for network architectures considering multiple design criteria: number of parameters/weights, number of floating-point operations, inference latency, among others. From an optimization point of view, the NAS tasks involving multiple design criteria are intrinsically multiobjective optimization problems; hence, it is reasonable to adopt evolutionary multiobjective optimization (EMO) algorithms for tackling them. Nonetheless, there is still a clear gap confining the related research along this pathway: on the one hand, there is a lack of a general problem formulation of NAS tasks from an optimization point of view; on the other hand, there are challenges in conducting benchmark assessments of EMO algorithms on NAS tasks. To bridge the gap: (i) we formulate NAS tasks into general multi-objective optimization problems and analyze the complex characteristics from an optimization point of view; (ii) we present an end-to-end pipeline, dubbed EvoXBench, to generate benchmark test problems for EMO algorithms to run efficiently -without the requirement of GPUs or Pytorch/Tensorflow; (iii) we instantiate two test suites comprehensively covering two datasets, seven search spaces, and three hardware devices, involving up to eight objectives. Based on the above, we validate the proposed test suites using six representative EMO algorithms and provide some empirical analyses. The code of EvoXBench is available at https://github.com/EMI-Group/EvoXBench.

T-YOLO: a lightweight and efficient detection model for nutrient buds in complex tea-plantation environments.

Quick and accurate detection of nutrient buds is essential for yield prediction and field management in tea plantations. However, the complexity of tea plantation environments and the similarity in color between nutrient buds and older leaves make the location of tea nutrient buds challenging. This research presents a lightweight and efficient detection model, T-YOLO, for the accurate detection of tea nutrient buds in unstructured environments. First, a lightweight module, C2fG2, and an efficient feature extraction module, DBS, are introduced into the backbone and neck of the YOLOv5 baseline model. Second, the head network of the model is pruned to achieve further lightweighting. Finally, the dynamic detection head is integrated to mitigate the feature loss caused by lightweighting. The experimental data show that T-YOLO achieves a mean average precision (mAP) of 84.1%, the total number of parameters for model training (Params) is 11.26 million (M), and the number of floating-point operations (FLOPs) is 17.2 Giga (G). Compared with the baseline YOLOv5 model, T-YOLO reduces Params by 47% and lowers FLOPs by 65%. T-YOLO also outperforms the existing optimal detection YOLOv8 model by 7.5% in terms of mAP. The T-YOLO model proposed in this study performs well in detecting small tea nutrient buds. It provides a decision-making basis for tea farmers to manage smart tea gardens. The T-YOLO model outperforms mainstream detection models on the public dataset, Global Wheat Head Detection (GWHD), which offers a reference for the construction of lightweight and efficient detection models for other small target crops. © 2024 Society of Chemical Industry.

Optimization of YOLOv7 Based on PConv, SE Attention and Wise-IoU

With the rapid development of deep learning technology, object detection algorithms have made significant breakthroughs in the field of computer vision. However, due to the complexity and computational requirements of deep Convolutional Neural Network (CNN), these models face many challenges in practical applications, especially on resource-constrained edge devices. To address this problem, researchers have proposed many lightweight methods that aim to reduce the model size and computational complexity while maintaining high performance. The popularity of mobile devices and embedded systems has led to an increasing demand for lightweight models. However, existing lightweight methods often lead to accuracy loss, limiting their feasibility in practical applications. Therefore, how to realize the light weight of the model while maintaining high accuracy has become an urgent problem to be solved. To address this challenge, this paper proposes a lightweight YOLOv7 method based on PConv, Squeeze-and-Excitation (SE) attention mechanism and Wise-IoU (WIoU), which we refer to as YOLOv7-PSW. PConv can effectively reduce the number of parameters and computational complexity. The SE can help the model focus on important feature information, thereby improving performance. WIoU is introduced to measure the similarity between the detection box and the Ground Truth, so that the model can effectively reduce the False Positive rate. By applying these advanced techniques to the YOLOv7, we achieve a lightweight model while maintaining a high detection accuracy. Experimental results on PASCAL VOC dataset show that YOLOv7-PSW performs better than the original YOLOv7 on object detection tasks. The number of parameters is reduced by 12.3%, FLOPs is reduced by 18.86%, and the accuracy is improved by about 0.5%. While the detection accuracy is not decreased or even slightly improved, the number of FLOPs and parameters is greatly reduced, which realizes lightweight to a certain extent. The proposed method can provide new ideas and directions for the subsequent research on lightweight object detection, and is expected to promote its application on edge devices. Meanwhile, YOLOv7-PSW can also be applied to other computer vision tasks to improve its performance and efficiency. In summary, the proposed YOLOv7-PSW lightweight method realizes the light weight of the model while maintaining high accuracy. This is of great significance for promoting the application of object detection algorithms on edge devices.

Lightweight Algorithm for Apple Detection Based on an Improved YOLOv5 Model.

The detection algorithm of the apple-picking robot contains a complex network structure and huge parameter volume, which seriously limits the inference speed. To enable automatic apple picking in complex unstructured environments based on embedded platforms, we propose a lightweight YOLOv5-CS model for apple detection based on YOLOv5n. Firstly, we introduced the lightweight C3-light module to replace C3 to enhance the extraction of spatial features and boots the running speed. Then, we incorporated SimAM, a parameter-free attention module, into the neck layer to improve the model's accuracy. The results showed that the size and inference speed of YOLOv5-CS were 6.25 MB and 0.014 s, which were 45 and 1.2 times that of the YOLOv5n model, respectively. The number of floating-point operations (FLOPs) were reduced by 15.56%, and the average precision (AP) reached 99.1%. Finally, we conducted extensive experiments, and the results showed that the YOLOv5-CS outperformed mainstream networks in terms of AP, speed, and model size. Thus, our real-time YOLOv5-CS model detects apples in complex orchard environments efficiently and provides technical support for visual recognition systems for intelligent apple-picking devices.

BSN-ESC: A Big-Small Network-Based Environmental Sound Classification Method for AIoT Applications.

In recent years, environmental sound classification (ESC) has prevailed in many artificial intelligence Internet of Things (AIoT) applications, as environmental sound contains a wealth of information that can be used to detect particular events. However, existing ESC methods have high computational complexity and are not suitable for deployment on AIoT devices with constrained computing resources. Therefore, it is of great importance to propose a model with both high classification accuracy and low computational complexity. In this work, a new ESC method named BSN-ESC is proposed, including a big-small network-based ESC model that can assess the classification difficulty level and adaptively activate a big or small network for classification as well as a pre-classification processing technique with logmel spectrogram refining, which prevents distortion in the frequency-domain characteristics of the sound clip at the joint part of two adjacent sound clips. With the proposed methods, the computational complexity is significantly reduced, while the classification accuracy is still high. The proposed BSN-ESC model is implemented on both CPU and FPGA to evaluate its performance on both PC and embedded systems with the dataset ESC-50, which is the most commonly used dataset. The proposed BSN-ESC model achieves the lowest computational complexity with the number of floating-point operations (FLOPs) of only 0.123G, which represents a reduction of up to 2309 times in computational complexity compared with state-of-the-art methods while delivering a high classification accuracy of 89.25%. This work can achieve the realization of ESC being applied to AIoT devices with constrained computational resources.

An Improved Lightweight Real-Time Detection Algorithm Based on the Edge Computing Platform for UAV Images

Unmanned aerial vehicle (UAV) image detection algorithms are critical in performing military countermeasures and disaster search and rescue. The state-of-the-art object detection algorithm known as you only look once (YOLO) is widely used for detecting UAV images. However, it faces challenges such as high floating-point operations (FLOPs), redundant parameters, slow inference speed, and poor performance in detecting small objects. To address the above issues, an improved, lightweight, real-time detection algorithm was proposed based on the edge computing platform for UAV images. In the presented method, MobileNetV3 was used as the YOLOv5 backbone network to reduce the numbers of parameters and FLOPs. To enhance the feature extraction ability of MobileNetV3, the efficient channel attention (ECA) attention mechanism was introduced into MobileNetV3. Furthermore, in order to improve the detection ability for small objects, an extra prediction head was introduced into the neck structure, and two kinds of neck structures with different parameter scales were designed to meet the requirements of different embedded devices. Finally, the FocalEIoU loss function was introduced into YOLOv5 to accelerate bounding box regression and improve the localization accuracy of the algorithm. To validate the performance of the proposed improved algorithm, we compared our algorithm with other algorithms in the VisDrone-Det2021 dataset. The results showed that compared with YOLOv5s, MELF-YOLOv5-S achieved a 51.4% reduction in the number of parameters and a 38.6% decrease in the number of FLOPs. MELF-YOLOv5-L had 87.4% and 47.4% fewer parameters and FLOPs, respectively, and achieved higher detection accuracy than YOLOv5l.

SD-HRNet: Slimming and Distilling High-Resolution Network for Efficient Face Alignment.

Face alignment is widely used in high-level face analysis applications, such as human activity recognition and human-computer interaction. However, most existing models involve a large number of parameters and are computationally inefficient in practical applications. In this paper, we aim to build a lightweight facial landmark detector by proposing a network-level architecture-slimming method. Concretely, we introduce a selective feature fusion mechanism to quantify and prune redundant transformation and aggregation operations in a high-resolution supernetwork. Moreover, we develop a triple knowledge distillation scheme to further refine a slimmed network, where two peer student networks could learn the implicit landmark distributions from each other while absorbing the knowledge from a teacher network. Extensive experiments on challenging benchmarks, including 300W, COFW, and WFLW, demonstrate that our approach achieves competitive performance with a better trade-off between the number of parameters (0.98 M-1.32 M) and the number of floating-point operations (0.59 G-0.6 G) when compared to recent state-of-the-art methods.

Casting Defect Detection and Classification of Convolutional Neural Network Based on Recursive Attention Model

The method based on deep learning shows excellent performance in the recognition and classification of surface defects of some industrial products. The method based on deep learning has high efficiency in the identification and classification of surface defects of industrial products, and the false detection rate and missed detection rate are relatively low. However, the recognition accuracy of defect detection and classification of most industrial products needs to be improved, especially for those with similar contours and relatively large structural different casting. This paper takes casting defect detection as the goal and proposes a convolutional neural network casting defect detection and classification (RCNN-DC) algorithm based on the recursive attention model. Through this model, the casting can be better identified and detected, and casting defects can be avoided as much as possible, which is of great significance to the technological development of the industry. First, use a large amount of readily available defect-free sample data to detect anomalous defects. Next, we compare the accuracy and performance of the detection model and the general recognition model. The research results show that the test effect of the RCNN-DC casting defect detection network model is significantly better than the traditional detection model, with a classification accuracy of 96.67%. Then, we compare the RCNN-DC network with three classic popular networks, GooGleNet, ResNet-50, and AlexNet. Among them, AlexNet and ResNet-50 achieved 95.00% and 95.56% classification accuracy, respectively, while GooGleNet achieved slightly better results of 96.38%. In contrast, the accuracy of RCNN-DC is 1.67% higher than that of AlexNet, while the number of FLOPs is reduced by 17.2 times, and the accuracy is 1.09% higher than that of ResNet-50, while the number of FLOPs is reduced by 99.7 times, and the accuracy is higher than GooGleNet 0.29% while FLOPs whose number has been reduced by 36.5 times.

PF-ViT: Parallel and Fast Vision Transformer for Offline Handwritten Chinese Character Recognition.

Recently, Vision Transformer (ViT) has been widely used in the field of image recognition. Unfortunately, the ViT model repeatedly stacks 12-layer encoders, resulting in a large number of model computations, many parameters, and slow training speed, making it difficult to deploy on mobile devices. In order to reduce the computational complexity of the model and improve the training speed, a parallel and fast Vision Transformer method for offline handwritten Chinese character recognition is proposed. The method adds parallel branches of the encoder module to the structure of the Vision Transformer model. Parallel modes include two-way parallel, four-way parallel, and seven-way parallel. The original picture is fed to the encoder module after flattening and linear embedding processing operations. The core step in the encoder is the multihead attention mechanism. Multihead self-attention can learn the interdependence between image sequence blocks. In addition, the use of data expansion strategies increases the diversity of data. In the two-way parallel experiment, when the model is 98.1% accurate on the dataset, the number of parameters and the number of FLOPs are 43.11 million and 4.32 G, respectively. Compared with the ViT model, whose parameters and FLOPs are 86 million and 16.8 G, respectively, the two-way parallel model has a 50.1% decrease in parameters and a 34.6% decrease in FLOPs. This method has been demonstrated to effectively reduce the computational complexity of the model while indirectly improving image recognition speed.

Fusion sampling networks for skeleton-based human action recognition

After a few seconds of an action, the human eye only needs a few photos to judge, but the action recognition network needs hundreds of frames of input pictures for each action. This results in a large number of floating point operations (ranging from 16 to 100 G FLOPs) to process a single sample, which hampers the implementation of graph convolutional networks (GCN)-based action recognition methods when the computation capabilities are restricted. A common strategy is to retain only the portions of the frames, but this results in the loss of important information in the discarded frames. Furthermore, the selection progress of key frames is too independent and lacks connections with other frames. To solve these two problems, we propose a fusion sampling network to generate fused frames to extract key frames. Temporal aggregation is used to fuse adjacent similar frames, thereby reducing information loss and redundancy. The concept of self-attention is introduced to strengthen the long-term association of key frames. The experimental results on three benchmark datasets show that the proposed method achieves performance levels that are competitive with state-of-the-art methods while using only 16.7% of the number of frames (∼50 and 300 frames in total). On the NTU 60 dataset, the number of FLOPs and Params with a single-channel input are 3.776 G and 3.53 M, respectively. This would greatly reduce the excessive computational power cost in practical applications due to the large amount of data processed by action recognition.

Recurrent Neural Network-Based User Association and Power Control in Dynamic HetNets

This paper tackles the joint user association (UA) and power control (PC) problem for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dynamic</i> heterogeneous networks (HetNets), where the number of active users varies over time. Since the joint UA and PC problem is a mixed-integer problem, it is challenging to develop a joint UA and PC algorithm that closely achieves the optimal proportional fairness (PF) performance while satisfying the tight computation time budget of recent 3GPP standards. Although previous studies have reduced the computation time on the UA and PC by employing a fully-connected-neural network (FCN), the FCN architecture is not generally applicable to dynamic HetNets because of a varying number of users. In pursuit of scalable neural network design, we propose an unsupervised learning-based UA and PC algorithm using a recurrent neural network (RNN). Notably, in the RNN-based UA, we relax the combinatorial UA variable into a low-dimensional continuous variable, the length of which is invariant to the number of users. The optimality loss in the variable relaxation is upper-bounded by the negligibly small duality gap. Through extensive experiments, we show that the proposed scheme has a 10% higher PF performance than conventional optimization-based methods with the same number of flops and closely achieves the optimal PF performance for various numbers of users.

YOLOv5-R: lightweight real-time detection based on improved YOLOv5

In reality, deploying the traditional object detection algorithm on mobile and embedded devices is difficult due to the limited memory and computation resources. To solve this problem, we propose a lightweight, real-time detection algorithm, YOLOv5-R. First, inserting the efficient channel attention (ECA) module into the Ghost module achieves the information interaction between channels and suppresses the redundant features. And applying dense connections to it further improves feature reuse and network performance, forming a Ghost-ECA-Dense (GED) module. Utilizing the GED module to construct the F-GED, which is the backbone with fewer parameters and better performance, replace CSPDarknet53 in YOLOv5. Second, the redundant operations are replaced with Ghost modules and depthwise separable convolution in the neck and head of YOLOv5, and YOLOv5-R is constructed, which significantly reduces the network size and improves the inference speed. Finally, YOLOv5-R is deployed into the AI embedded device Jetson Nano for TensorRT acceleration. The experimental results indicated that the performance of YOLOv5-R outperformed the YOLOv5s. Specifically, the mean average precision was increased from 69.9% to 72.7%, the number of floating-point operations per second and parameters are reduced by 25% and 47.2%, respectively. The model weight was only 7.52 MB, and frames per second achieved 37, which can provide real-time detection.

Ultra-lightweight face activation for dynamic vision sensor with convolutional filter-level fusion using facial landmarks

As dynamic vision sensors can operate at low power while having a fast response, they can mitigate the disadvantages of gyro sensors when used for turning on mobile devices. Therefore, we propose an ultra-lightweight face activation neural network that combines handcrafted convolutional landmark filters extracted from facial features with randomly initialized trainable convolutional filters. Face activation is the task of identifying the presence or absence of a face intended to activate the mobile device. Our proposed model, F-LandmarkNet, has four steps. First, we construct customized landmark filters that can effectively identify numerous facial features. Second, F-LandmarkNet is constructed by using a convolutional layer that fuses handcrafted landmark filters and trainable convolution filters. Third, a compact version is constructed by selecting only the four most influential face filters according to their importance. Finally, performance is improved through knowledge distillation. The fusion of handcrafted landmark filters and trainable convolutional filters is quite effective in extremely lightweight models. It is observed that the classification accuracy of our proposed model is similar to that of existing lightweight convolutional neural network models, while the number of floating-point operations and parameters are markedly lower. Our model also runs faster under a central processing unit environment than comparison models. Thus, the proposed model shows high potential for use in actual mobile systems.

ULSED: An ultra-lightweight SED model for IoT devices

Sound event detection (SED) technology has been widely used in applications such as audio surveillance systems and smart home. Compared to the traditional machine learning methods, the neural networks (NN) based methods have been proposed in recent years to significantly improve the detection accuracy. However, a major issue of the NN-based SED models is that they often involve a large number of parameters and floating point operations (FLOPs), resulting in significant processing time, power consumption and memory storage. This poses a challenge to SED on IoT devices with constrained computational resources and power budget. To address this issue, in this work, an ultra-lightweight SED model (ULSED) with a selective separable convolution scheme and a coordinate attention scheme is proposed to significantly reduce the computational complexity while achieving high detection accuracy. The proposed ULSED model is evaluated on the ESC-10, ESC-50 and UrbanSound8K(US8K) datasets. Compared with several state-of-the-art models, the number of parameters and the number of FLOPs is significantly reduced by up to 388 times and 1140 times while achieving high detection accuracy of 97.0%, 88.3% and 83.5% on the ESC-10, ESC-50 and US8K respectively. The proposed ULSED model is suitable for power- and hardware-constrained IoT devices.

Compressing CNN Kernels for Videos Using Tucker Decompositions: Towards Lightweight CNN Applications

Convolutional Neural Networks (CNN) are the state-of-the-art in the field of visual computing. However, a major problem with CNNs is the large number of floating point operations (FLOPs) required to perform convolutions for large inputs. When considering the application of CNNs to video data, convolutional filters become even more complex due to the extra temporal dimension. This leads to problems when respective applications are to be deployed on mobile devices, such as smart phones, tablets, micro-controllers or similar, indicating less computational power. Kim et al. proposed using a Tucker-decomposition to compress the convolutional kernel of a pre-trained network for images in order to reduce the complexity of the network, i.e. the number of FLOPs. In this paper, we generalize the aforementioned method for application to videos (and other 3D signals) and evaluate the proposed method on a modified version of the THETIS data set, which contains videos of individuals performing tennis shots. We show that the compressed network reaches comparable accuracy, while indicating a memory compression by a factor of 51. However, the actual computational speed-up (factor 1.4) does not meet our theoretically derived expectation (factor 6).

Direct FE[formula omitted] for concurrent multilevel modeling of heterogeneous thin plate structures

The FE2 method systematically translates macro kinematic constraints to the underlying (micro) RVEs and extracts the effective RVE responses to macro continuum in an energetically consistent manner. In the literature, many researchers have demonstrated the predictive capability of FE2 across a wide range of problems. The conventional FE2 numerical framework adopts a staggered solution strategy between the macro and micro analyses. This limits the adoption of FE2 method by inexperienced researchers/ engineers to solve practical engineering problems using commercial FE software. To this end, a Direct FE2 method has been proposed in Tan et al. (2020) and implemented in the commercial software ABAQUS, where macro kinematic constraints are applied directly on the RVEs superimposed on the macro elements. This results in a monolithic numerical framework, without the need to write any subroutines. Compared to the conventional FE2 implementation using commercial software, the number of floating-point operations is also reduced because the nested FE calculations are condensed into one in Direct FE2 (Raju et al., 2021). In this contribution focusing on thin plate structures, the Direct FE2 method is extended based on Kirchhoff–Love thin plate kinematics and implemented in ABAQUS without the need for subroutines. The performance of the Direct FE2 method for this higher order formulation is demonstrated by comparing against reference solutions from direct numerical simulations. Sample files can be downloaded from https://github.com/leonghien/Direct-FE2-thin-plates.git.

Efficient Implementation of Equation-of-Motion Coupled-Cluster Singles and Doubles Method with the Density-Fitting Approximation: An Enhanced Algorithm for the Particle–Particle Ladder Term

An efficient implementation of the density-fitted equation-of-motion coupled-cluster singles and doubles (DF-EOM-CCSD) method is presented with an enhanced algorithm for the particle–particle ladder (PPL) term, which is the most expensive part of EOM-CCSD computations. To further improve the evaluation of the PPL term, a hybrid density-fitting/Cholesky decomposition (DF/CD) algorithm is also introduced. In the hybrid DF/CD approach, four virtual index integrals are constructed on-the-fly from the DF factors; then, their partial Cholesky decomposition is simultaneously performed. The computational cost of the DF-EOM-CCSD method for excitation energies is compared with that of the resolution of the identity EOM-CCSD (RI-EOM-CCSD) (from the Q-chem 5.3 package). Our results demonstrate that DF-EOM-CCSD excitation energies are significantly accelerated compared to RI-EOM-CCSD. There is more than a 2-fold reduction for the C8H18 molecule in the cc-pVTZ basis set with the restricted Hartree-Fock (RHF) reference. This cost savings results from the efficient evaluation of the PPL term. In the RHF based DF-EOM-CCSD method, the number of flops (NOF) is 1/4O2V4, while that of RI-EOM-CCSD was reported (Epifanovsky et al. J. Chem. Phys.2013, 139, 13410524116550) to be 5/8O2V4 for the PPL contraction term. Further, the NOF of VVVV-type integral transformation is 1/2V4Naux in our case, while it appears to be V4Naux for RI-EOM-CCSD. Hence, our implementation is 2.5 and 2.0 times more efficient compared to RI-EOM-CCSD for these expensive terms. For the unrestricted Hartree-Fock (UHF) reference, our implementation maintains its enhanced performance and provides a 1.8-fold reduction in the computational time compared to RI-EOM-CCSD for the C7H16 molecule. Our results indicate that our DF-EOM-CCSD implementation is 1.7 and 1.4 times more efficient compared with RI-EOM-CCSD for average computational cost per EOM-CCSD iteration. Moreover, our results show that the new hybrid DF/CD approach improves upon the DF algorithm, especially for large molecular systems. Overall, we conclude that the new hybrid DF/CD PPL algorithm is very promising for large-sized chemical systems.