Huandong Wang

Yuan Yuan, Huandong Wang, Jingtao Ding et al.

Daily activity data that records individuals' various types of activities in daily life are widely used in many applications such as activity scheduling, activity recommendation, and policymaking. Though with high value, its accessibility is limited due to high collection costs and potential privacy issues. Therefore, simulating human activities to produce massive high-quality data is of great importance to benefit practical applications. However, existing solutions, including rule-based methods with simplified assumptions of human behavior and data-driven methods directly fitting real-world data, both cannot fully qualify for matching reality. In this paper, motivated by the classic psychological theory, Maslow's need theory describing human motivation, we propose a knowledge-driven simulation framework based on generative adversarial imitation learning. To enhance the fidelity and utility of the generated activity data, our core idea is to model the evolution of human needs as the underlying mechanism that drives activity generation in the simulation model. Specifically, this is achieved by a hierarchical model structure that disentangles different need levels, and the use of neural stochastic differential equations that successfully captures piecewise-continuous characteristics of need dynamics. Extensive experiments demonstrate that our framework outperforms the state-of-the-art baselines in terms of data fidelity and utility. Besides, we present the insightful interpretability of the need modeling. The code is available at https://github.com/tsinghua-fib-lab/SAND.

Wenjie Fu, Huandong Wang, Chen Gao et al.

Membership Inference Attacks (MIA) aim to infer whether a target data record has been utilized for model training or not. Existing MIAs designed for large language models (LLMs) can be bifurcated into two types: reference-free and reference-based attacks. Although reference-based attacks appear promising performance by calibrating the probability measured on the target model with reference models, this illusion of privacy risk heavily depends on a reference dataset that closely resembles the training set. Both two types of attacks are predicated on the hypothesis that training records consistently maintain a higher probability of being sampled. However, this hypothesis heavily relies on the overfitting of target models, which will be mitigated by multiple regularization methods and the generalization of LLMs. Thus, these reasons lead to high false-positive rates of MIAs in practical scenarios. We propose a Membership Inference Attack based on Self-calibrated Probabilistic Variation (SPV-MIA). Specifically, we introduce a self-prompt approach, which constructs the dataset to fine-tune the reference model by prompting the target LLM itself. In this manner, the adversary can collect a dataset with a similar distribution from public APIs. Furthermore, we introduce probabilistic variation, a more reliable membership signal based on LLM memorization rather than overfitting, from which we rediscover the neighbour attack with theoretical grounding. Comprehensive evaluation conducted on three datasets and four exemplary LLMs shows that SPV-MIA raises the AUC of MIAs from 0.7 to a significantly high level of 0.9. Our code and dataset are available at: https://github.com/tsinghua-fib-lab/NeurIPS2024_SPV-MIA

Huiming Chen, Huandong Wang, Qingyue Long et al.

Federated learning (FL) is a promising technique for addressing the rising privacy and security issues. Its main ingredient is to cooperatively learn the model among the distributed clients without uploading any sensitive data. In this paper, we conducted a thorough review of the related works, following the development context and deeply mining the key technologies behind FL from both theoretical and practical perspectives. Specifically, we first classify the existing works in FL architecture based on the network topology of FL systems with detailed analysis and summarization. Next, we abstract the current application problems, summarize the general techniques and frame the application problems into the general paradigm of FL base models. Moreover, we provide our proposed solutions for model training via FL. We have summarized and analyzed the existing FedOpt algorithms, and deeply revealed the algorithmic development principles of many first-order algorithms in depth, proposing a more generalized algorithm design framework. Based on these frameworks, we have instantiated FedOpt algorithms. As privacy and security is the fundamental requirement in FL, we provide the existing attack scenarios and the defense methods. To the best of our knowledge, we are among the first tier to review the theoretical methodology and propose our strategies since there are very few works surveying the theoretical approaches. Our survey targets motivating the development of high-performance, privacy-preserving, and secure methods to integrate FL into real-world applications.

Huandong Wang, Huan Yan, Can Rong et al.

Complex system simulation has been playing an irreplaceable role in understanding, predicting, and controlling diverse complex systems. In the past few decades, the multi-scale simulation technique has drawn increasing attention for its remarkable ability to overcome the challenges of complex system simulation with unknown mechanisms and expensive computational costs. In this survey, we will systematically review the literature on multi-scale simulation of complex systems from the perspective of knowledge and data. Firstly, we will present background knowledge about simulating complex system simulation and the scales in complex systems. Then, we divide the main objectives of multi-scale modeling and simulation into five categories by considering scenarios with clear scale and scenarios with unclear scale, respectively. After summarizing the general methods for multi-scale simulation based on the clues of knowledge and data, we introduce the adopted methods to achieve different objectives. Finally, we introduce the applications of multi-scale simulation in typical matter systems and social systems.

Jinzhu Mao, Liu Cao, Chen Gao et al.

Understanding and characterizing the vulnerability of urban infrastructures, which refers to the engineering facilities essential for the regular running of cities and that exist naturally in the form of networks, is of great value to us. Potential applications include protecting fragile facilities and designing robust topologies, etc. Due to the strong correlation between different topological characteristics and infrastructure vulnerability and their complicated evolution mechanisms, some heuristic and machine-assisted analysis fall short in addressing such a scenario. In this paper, we model the interdependent network as a heterogeneous graph and propose a system based on graph neural network with reinforcement learning, which can be trained on real-world data, to characterize the vulnerability of the city system accurately. The presented system leverages deep learning techniques to understand and analyze the heterogeneous graph, which enables us to capture the risk of cascade failure and discover vulnerable infrastructures of cities. Extensive experiments with various requests demonstrate not only the expressive power of our system but also transferring ability and necessity of the specific components.

Nan Zhou, Huandong Wang, Jiahao Li et al.

Fine-grained wildfire spread prediction is crucial for enhancing emergency response efficacy and decision-making precision. However, existing research predominantly focuses on coarse spatiotemporal scales and relies on low-resolution satellite data, capturing only macroscopic fire states while fundamentally constraining high-precision localized fire dynamics modeling capabilities. To bridge this gap, we present FireSentry, a provincial-scale multi-modal wildfire dataset characterized by sub-meter spatial and sub-second temporal resolution. Collected using synchronized UAV platforms, FireSentry provides visible and infrared video streams, in-situ environmental measurements, and manually validated fire masks. Building on FireSentry, we establish a comprehensive benchmark encompassing physics-based, data-driven, and generative models, revealing the limitations of existing mask-only approaches. Our analysis proposes FiReDiff, a novel dual-modality paradigm that first predicts future video sequences in the infrared modality, and then precisely segments fire masks in the mask modality based on the generated dynamics. FiReDiff achieves state-of-the-art performance, with video quality gains of 39.2% in PSNR, 36.1% in SSIM, 50.0% in LPIPS, 29.4% in FVD, and mask accuracy gains of 3.3% in AUPRC, 59.1% in F1 score, 42.9% in IoU, and 62.5% in MSE when applied to generative models. The FireSentry benchmark dataset and FiReDiff paradigm collectively advance fine-grained wildfire forecasting and dynamic disaster simulation. The processed benchmark dataset is publicly available at: https://github.com/Munan222/FireSentry-Benchmark-Dataset.

Wenjie Fu, Huandong Wang, Liyuan Zhang et al.

Membership Inference Attack (MIA) identifies whether a record exists in a machine learning model's training set by querying the model. MIAs on the classic classification models have been well-studied, and recent works have started to explore how to transplant MIA onto generative models. Our investigation indicates that existing MIAs designed for generative models mainly depend on the overfitting in target models. However, overfitting can be avoided by employing various regularization techniques, whereas existing MIAs demonstrate poor performance in practice. Unlike overfitting, memorization is essential for deep learning models to attain optimal performance, making it a more prevalent phenomenon. Memorization in generative models leads to an increasing trend in the probability distribution of generating records around the member record. Therefore, we propose a Probabilistic Fluctuation Assessing Membership Inference Attack (PFAMI), a black-box MIA that infers memberships by detecting these trends via analyzing the overall probabilistic fluctuations around given records. We conduct extensive experiments across multiple generative models and datasets, which demonstrate PFAMI can improve the attack success rate (ASR) by about 27.9% when compared with the best baseline.

Ruikun Li, Huandong Wang, Jingtao Ding et al.

Data-driven dynamics prediction often fails under environmental shifts, while traditional fine-tuning remains computationally prohibitive for hardware-constrained or data-scarce applications. We propose DynaDiff, a generative meta-learning framework that transitions the paradigm from gradient-based tuning or modulation to direct weight-space generation. Specifically, we first abstract expert weights as novel weight graphs, utilizing multi-head attention to explicitly capture topological coupling within weights. Subsequently, we design a functional loss to ensure that the generated models achieve consistency with expert models in physical behavior. Finally, we develop a dynamics-informed prompter that extracts cross-domain physical and spectral features from observation sequences to condition the diffusion model. Experiments demonstrate that DynaDiff boosts average prediction accuracy by 10.78% over competitive baselines. Furthermore, by pre-constructing a model zoo of expert predictors, we amortize the fine-tuning overhead into a one-time offline cost, significantly boosting deployment efficiency in new environments.

Wenjie Fu, Huandong Wang, Chen Gao et al.

The increasing parameters and expansive dataset of large language models (LLMs) highlight the urgent demand for a technical solution to audit the underlying privacy risks and copyright issues associated with LLMs. Existing studies have partially addressed this need through an exploration of the pre-training data detection problem, which is an instance of a membership inference attack (MIA). This problem involves determining whether a given piece of text has been used during the pre-training phase of the target LLM. Although existing methods have designed various sophisticated MIA score functions to achieve considerable detection performance in pre-trained LLMs, how to achieve high-confidence detection and how to perform MIA on aligned LLMs remain challenging. In this paper, we propose MIA-Tuner, a novel instruction-based MIA method, which instructs LLMs themselves to serve as a more precise pre-training data detector internally, rather than design an external MIA score function. Furthermore, we design two instruction-based safeguards to respectively mitigate the privacy risks brought by the existing methods and MIA-Tuner. To comprehensively evaluate the most recent state-of-the-art LLMs, we collect a more up-to-date MIA benchmark dataset, named WIKIMIA-24, to replace the widely adopted benchmark WIKIMIA. We conduct extensive experiments across various aligned and unaligned LLMs over the two benchmark datasets. The results demonstrate that MIA-Tuner increases the AUC of MIAs from 0.7 to a significantly high level of 0.9.

Can Rong, Huandong Wang, Yong Li

Origin-destination (OD) flow, which contains valuable population mobility information including direction and volume, is critical in many urban applications, such as urban planning, transportation management, etc. However, OD data is not always easy to access due to high costs or privacy concerns. Therefore, we must consider generating OD through mathematical models. Existing works utilize physics laws or machine learning (ML) models to build the association between urban structures and OD flows while these two kinds of methods suffer from the limitation of over-simplicity and poor generalization ability, respectively. In this paper, we propose to adopt physics-informed ML paradigm, which couple the physics scientific knowledge and data-driven ML methods, to construct a model named Origin-Destination Generation Networks (ODGN) for better population mobility modeling by leveraging the complementary strengths of combining physics and ML methods. Specifically, we first build a Multi-view Graph Attention Networks (MGAT) to capture the urban features of every region and then use a gravity-guided predictor to obtain OD flow between every two regions. Furthermore, we use a conditional GAN training strategy and design a sequence-based discriminator to consider the overall topological features of OD as a network. Extensive experiments on real-world datasets have been done to demonstrate the superiority of our proposed method compared with baselines.

Nan Zhou, Weijie Hong, Huandong Wang et al.

Fine-grained air pollution forecasting is crucial for urban management and the development of healthy buildings. Deploying portable sensors on mobile platforms such as cars and buses offers a low-cost, easy-to-maintain, and wide-coverage data collection solution. However, due to the random and uncontrollable movement patterns of these non-dedicated mobile platforms, the resulting sensor data are often incomplete and temporally inconsistent. By exploring potential training patterns in the reverse process of diffusion models, we propose Spatio-Temporal Physics-Informed Diffusion Models (STeP-Diff). STeP-Diff leverages DeepONet to model the spatial sequence of measurements along with a PDE-informed diffusion model to forecast the spatio-temporal field from incomplete and time-varying data. Through a PDE-constrained regularization framework, the denoising process asymptotically converges to the convection-diffusion dynamics, ensuring that predictions are both grounded in real-world measurements and aligned with the fundamental physics governing pollution dispersion. To assess the performance of the system, we deployed 59 self-designed portable sensing devices in two cities, operating for 14 days to collect air pollution data. Compared to the second-best performing algorithm, our model achieved improvements of up to 89.12% in MAE, 82.30% in RMSE, and 25.00% in MAPE, with extensive evaluations demonstrating that STeP-Diff effectively captures the spatio-temporal dependencies in air pollution fields.

Ruikun Li, Huandong Wang, Qingmin Liao et al.

Energy landscapes play a crucial role in shaping dynamics of many real-world complex systems. System evolution is often modeled as particles moving on a landscape under the combined effect of energy-driven drift and noise-induced diffusion, where the energy governs the long-term motion of the particles. Estimating the energy landscape of a system has been a longstanding interdisciplinary challenge, hindered by the high operational costs or the difficulty of obtaining supervisory signals. Therefore, the question of how to infer the energy landscape in the absence of true energy values is critical. In this paper, we propose a physics-informed self-supervised learning method to learn the energy landscape from the evolution trajectories of the system. It first maps the system state from the observation space to a discrete landscape space by an adaptive codebook, and then explicitly integrates energy into the graph neural Fokker-Planck equation, enabling the joint learning of energy estimation and evolution prediction. Experimental results across interdisciplinary systems demonstrate that our estimated energy has a correlation coefficient above 0.9 with the ground truth, and evolution prediction accuracy exceeds the baseline by an average of 17.65\%. The code is available at github.com/tsinghua-fib-lab/PESLA.

Yinzhou Tang, Jinghua Piao, Huandong Wang et al.

Cascading failures (CF) entail component breakdowns spreading through infrastructure networks, causing system-wide collapse. Predicting CFs is of great importance for infrastructure stability and urban function. Despite extensive research on CFs in single networks such as electricity and road networks, interdependencies among diverse infrastructures remain overlooked, and capturing intra-infrastructure CF dynamics amid complex evolutions poses challenges. To address these gaps, we introduce the \textbf{I}ntegrated \textbf{I}nterdependent \textbf{I}nfrastructure CF model ($I^3$), designed to capture CF dynamics both within and across infrastructures. $I^3$ employs a dual GAE with global pooling for intra-infrastructure dynamics and a heterogeneous graph for inter-infrastructure interactions. An initial node enhancement pre-training strategy mitigates GCN-induced over-smoothing. Experiments demonstrate $I^3$ achieves a 31.94\% in terms of AUC, 18.03\% in terms of Precision, 29.17\% in terms of Recall, 22.73\% in terms of F1-score boost in predicting infrastructure failures, and a 28.52\% reduction in terms of RMSE for cascade volume forecasts compared to leading models. It accurately pinpoints phase transitions in interconnected and singular networks, rectifying biases in models tailored for singular networks. Access the code at https://github.com/tsinghua-fib-lab/Icube.

Wenjie Fu, Huandong Wang, Junyao Gao et al.

As Large Language Models (LLMs) achieve remarkable success across a wide range of applications, such as chatbots and code copilots, concerns surrounding the generation of harmful content have come increasingly into focus. Despite significant advances in aligning LLMs with safety and ethical standards, adversarial prompts can still be crafted to elicit undesirable responses. Existing mitigation strategies are predominantly based on post-hoc filtering, which introduces substantial latency or computational overhead, and is incompatible with token-level streaming generation. In this work, we introduce Self-Sanitize, a novel LLM-driven mitigation framework inspired by cognitive psychology, which emulates human self-monitor and self-repair behaviors during conversations. Self-Sanitize comprises a lightweight Self-Monitor module that continuously inspects high-level intentions within the LLM at the token level via representation engineering, and a Self-Repair module that performs in-place correction of harmful content without initiating separate review dialogues. This design allows for real-time streaming monitoring and seamless repair, with negligible impact on latency and resource utilization. Given that privacy-invasive content has often been insufficiently focused in previous studies, we perform extensive experiments on four LLMs across three privacy leakage scenarios. The results demonstrate that Self-Sanitize achieves superior mitigation performance with minimal overhead and without degrading the utility of LLMs, offering a practical and robust solution for safer LLM deployments. Our code is available at the following link: https://github.com/wjfu99/LLM_Self_Sanitize

Huandong Wang, Wenjie Fu, Yingzhou Tang et al.

While large language models (LLMs) present significant potential for supporting numerous real-world applications and delivering positive social impacts, they still face significant challenges in terms of the inherent risk of privacy leakage, hallucinated outputs, and value misalignment, and can be maliciously used for generating toxic content and unethical purposes after been jailbroken. Therefore, in this survey, we present a comprehensive review of recent advancements aimed at mitigating these issues, organized across the four phases of LLM development and usage: data collecting and pre-training, fine-tuning and alignment, prompting and reasoning, and post-processing and auditing. We elaborate on the recent advances for enhancing the performance of LLMs in terms of privacy protection, hallucination reduction, value alignment, toxicity elimination, and jailbreak defenses. In contrast to previous surveys that focus on a single dimension of responsible LLMs, this survey presents a unified framework that encompasses these diverse dimensions, providing a comprehensive view of enhancing LLMs to better serve real-world applications.

Qingyue Long, Can Rong, Huandong Wang et al.

Trajectory data play a crucial role in many applications, ranging from network optimization to urban planning. Existing studies on trajectory data are task-specific, and their applicability is limited to the specific tasks on which they have been trained, such as generation, recovery, or prediction. However, the potential of a unified model has not yet been fully explored in trajectory modeling. Although various trajectory tasks differ in inputs, outputs, objectives, and conditions, they share common mobility patterns. Based on these common patterns, we can construct a general framework that enables a single model to address different tasks. However, building a trajectory task-general framework faces two critical challenges: 1) the diversity in the formats of different tasks and 2) the complexity of the conditions imposed on different tasks. In this work, we propose a general trajectory modeling framework via masked conditional diffusion (named GenMove). Specifically, we utilize mask conditions to unify diverse formats. To adapt to complex conditions associated with different tasks, we utilize historical trajectory data to obtain contextual trajectory embeddings, which include rich contexts such as spatiotemporal characteristics and user preferences. Integrating the contextual trajectory embedding into diffusion models through a classifier-free guidance approach allows the model to flexibly adjust its outputs based on different conditions. Extensive experiments on mainstream tasks demonstrate that our model significantly outperforms state-of-the-art baselines, with the highest performance improvement exceeding 13% in generation tasks.

En Xu, Huandong Wang, Yunke Zhang et al.

Urban systems are typical examples of complex systems, where the integration of physics-based modeling with artificial intelligence (AI) presents a promising paradigm for enhancing predictive accuracy, interpretability, and decision-making. In this context, AI excels at capturing complex, nonlinear relationships, while physics-based models ensure consistency with real-world laws and provide interpretable insights. We provide a comprehensive review of physics-informed AI methods in urban applications. The proposed taxonomy categorizes existing approaches into three paradigms - Physics-Integrated AI, Physics-AI Hybrid Ensemble, and AI-Integrated Physics - and further details seven representative methods. This classification clarifies the varying degrees and directions of physics-AI integration, guiding the selection and development of appropriate methods based on application needs and data availability. We systematically examine their applications across eight key urban domains: energy, environment, economy, transportation, information, public services, emergency management, and the urban system as a whole. Our analysis highlights how these methodologies leverage physical laws and data-driven models to address urban challenges, enhancing system reliability, efficiency, and adaptability. By synthesizing existing methodologies and their urban applications, we identify critical gaps and outline future research directions, paving the way toward next-generation intelligent urban system modeling.

Fanhang Man, Huandong Wang, Jianjie Fang et al.

User sentiment on social media reveals the underlying social trends, crises, and needs. Researchers have analyzed users' past messages to trace the evolution of sentiments and reconstruct sentiment dynamics. However, predicting the imminent sentiment of an ongoing event is rarely studied. In this paper, we address the problem of \textbf{sentiment forecasting} on social media to predict the user's future sentiment in response to the development of the event. We extract sentiment-related features to enhance the modeling skill and propose a multi-perspective role-playing framework to simulate the process of human response. Our preliminary results show significant improvement in sentiment forecasting on both microscopic and macroscopic levels.

Chang Liu, Bohao Zhao, Jingtao Ding et al.

Long-term forecasting of chaotic systems remains a fundamental challenge due to the intrinsic sensitivity to initial conditions and the complex geometry of strange attractors. Conventional approaches, such as reservoir computing, typically require training data that incorporates long-term continuous dynamical behavior to comprehensively capture system dynamics. While advanced deep sequence models can capture transient dynamics within the training data, they often struggle to maintain predictive stability and dynamical coherence over extended horizons. Here, we propose PhyxMamba, a framework that integrates a Mamba-based state-space model with physics-informed principles to forecast long-term behavior of chaotic systems given short-term historical observations on their state evolution. We first reconstruct the attractor manifold with time-delay embeddings to extract global dynamical features. After that, we introduce a generative training scheme that enables Mamba to replicate the physical process. It is further augmented by multi-patch prediction and attractor geometry regularization for physical constraints, enhancing predictive accuracy and preserving key statistical properties of systems. Extensive experiments on simulated and real-world chaotic systems demonstrate that PhyxMamba delivers superior forecasting accuracy and faithfully captures essential statistics from short-term historical observations.

Zefang Zong, Xiaochen Wei, Guozhen Zhang et al.

Combinatorial Optimization (CO) encompasses a wide range of problems that arise in many real-world scenarios. While significant progress has been made in developing learning-based methods for specialized CO problems, a unified model with a single architecture and parameter set for diverse CO problems remains elusive. Such a model would offer substantial advantages in terms of efficiency and convenience. In this paper, we introduce UniCO, a unified model for solving various CO problems. Inspired by the success of next-token prediction, we frame each problem-solving process as a Markov Decision Process (MDP), tokenize the corresponding sequential trajectory data, and train the model using a transformer backbone. To reduce token length in the trajectory data, we propose a CO-prefix design that aggregates static problem features. To address the heterogeneity of state and action tokens within the MDP, we employ a two-stage self-supervised learning approach. In this approach, a dynamic prediction model is first trained and then serves as a pre-trained model for subsequent policy generation. Experiments across 10 CO problems showcase the versatility of UniCO, emphasizing its ability to generalize to new, unseen problems with minimal fine-tuning, achieving even few-shot or zero-shot performance. Our framework offers a valuable complement to existing neural CO methods that focus on optimizing performance for individual problems.

Huiming Chen, Huandong Wang, Quanming Yao et al.

Federated optimization (FedOpt), which targets at collaboratively training a learning model across a large number of distributed clients, is vital for federated learning. The primary concerns in FedOpt can be attributed to the model divergence and communication efficiency, which significantly affect the performance. In this paper, we propose a new method, i.e., LoSAC, to learn from heterogeneous distributed data more efficiently. Its key algorithmic insight is to locally update the estimate for the global full gradient after {each} regular local model update. Thus, LoSAC can keep clients' information refreshed in a more compact way. In particular, we have studied the convergence result for LoSAC. Besides, the bonus of LoSAC is the ability to defend the information leakage from the recent technique Deep Leakage Gradients (DLG). Finally, experiments have verified the superiority of LoSAC comparing with state-of-the-art FedOpt algorithms. Specifically, LoSAC significantly improves communication efficiency by more than $100\%$ on average, mitigates the model divergence problem and equips with the defense ability against DLG.

Huandong Wang, Qiaohong Yu, Yu Liu et al.

With the rapid development of the mobile communication technology, mobile trajectories of humans are massively collected by Internet service providers (ISPs) and application service providers (ASPs). On the other hand, the rising paradigm of knowledge graph (KG) provides us a promising solution to extract structured "knowledge" from massive trajectory data. In this paper, we focus on modeling users' spatio-temporal mobility patterns based on knowledge graph techniques, and predicting users' future movement based on the "knowledge'' extracted from multiple sources in a cohesive manner. Specifically, we propose a new type of knowledge graph, i.e., spatio-temporal urban knowledge graph (STKG), where mobility trajectories, category information of venues, and temporal information are jointly modeled by the facts with different relation types in STKG. The mobility prediction problem is converted to the knowledge graph completion problem in STKG. Further, a complex embedding model with elaborately designed scoring functions is proposed to measure the plausibility of facts in STKG to solve the knowledge graph completion problem, which considers temporal dynamics of the mobility patterns and utilizes PoI categories as the auxiliary information and background knowledge. Extensive evaluations confirm the high accuracy of our model in predicting users' mobility, i.e., improving the accuracy by 5.04% compared with the state-of-the-art algorithms. In addition, PoI categories as the background knowledge and auxiliary information are confirmed to be helpful by improving the performance by 3.85% in terms of accuracy. Additionally, experiments show that our proposed method is time-efficient by reducing the computational time by over 43.12% compared with existing methods.