Matrix Multiplication Research Articles

Tilt‐Engineered Molecular‐Scale Selector for Enhanced Learning in Artificial Neural Networks

AbstractMiniaturization of individual selectors in crossbar‐array‐based artificial neural networks is essential for the advancement of the underlying neuromorphic electronics, as it improves learning, recognition, and prediction accuracies. This study proposes a tilt‐engineered molecular‐scale selector comprising a heterostructure of biphenyl‐4‐thiol (OPT2) or 1‐octanethiol (C8) molecular layers and an n‐type two‐dimensional MoS2 monolayer (1L‐MoS2) at an approximate contact radius of 3 nm, which is evaluated via conductive atomic force microscopy under various tip‐loading forces. The molecular tilt configuration controlled by the tip‐loading force is used as a rectifying engineer for the OPT2/1L‐MoS2 and C8/1L‐MoS2 heterojunction accuracies. Rectification ratios and conductance levels are significantly influenced by the molecular backbones and tilt angle. The proposed tilt‐engineered selector can aid in controlling undesired neural signals affecting vector–matrix multiplications and adjusting the switching range compatibility of an integrated synaptic device cell, significantly influencing the pattern recognition accuracy. By controlling the tilt angle, the recognition accuracy on the MNIST dataset increases from 78.65% to 86.45% and from 7.74% to 86.09% when using the OPT2/1L‐MoS2 and C8/1L‐MoS2 selector, respectively. The proposed molecular tilt configuration can be used for developing customized molecular‐scale selectors for crossbar‐array‐based artificial neural networks to improve learning while suppressing undesired neural signals.

10.47435/jtmt.v4i02.1987 Error Analysis of Class XI Students of SMA in Solving Matrix Problems in terms of Mathematical Ability

This research aims to describe the types of errors made by students in solving matrix problems. The subjects in this research were three students of class XI MIPA SMA 5 Palu who were divided into three categories based on their level of mathematical ability, namely students with high, medium, and low mathematics ability. The selection of these three students was based on students report cards which were categorized into three types, namely high, medium and low, which were then selected through considerations, namely students who were able to take part in the entire of data collection activities carried out by researchers as well as considerations from mathematics subject at the school. This type of research is descriptive research with a qualitative approach. Data collection was carried out by administering written tests and interviews. The results of this research show that students of class XI MIPA SMA Negeri 5 Palu made mistakes in solving questions (1) high mathematics ability students made conceptual mistakes, namely students were wrong in writing the concept of matrix multiplication that had different orders. (2) students with moderate mathematics ability made procedural errors, namely students were wrong in carrying out the steps of solving the problem and students in solving the problem did not reach that students do not write the sign of mathematical operations that should be used. (3) students with low mathematics ability made conceptual errors, namely students did not solve the problems given, only rewrote the matrix members. Procedural errors, namely students are not careful in understanding the question instruction so that the steps for solving the problem are not appropriate and students do not solve the problem until the final stage. Technical errors, namely students are wrong in doing calculations so that the students answers do not match the alternative answers. This research is highly recommended for other researchers to explore further because the coverage of the matrix material is quite broad so researchers cannot discuss everything in this research and there are many more reviews that need to be analyzed through this material.

Kalman Filter for Linear Discrete-Time Rectangular Singular Systems Considering Causality

This paper proposes a Kalman filter for linear rectangular singular discrete-time systems, where the singular matrix in the system is a rectangular matrix without full column rank. By using two different restricted equivalent transformation methods and adding the measurement equation to the state equation, the system is transformed into a square singular system satisfying regularity and observability. During this process, the causality of the system is taken into account, and multiple matrix transformations are applied accordingly. Based on these modifications, state estimation results are obtained using the Kalman filter. Finally, a numerical example is employed to demonstrate the effectiveness of our approach.

Stock Price Prediction Based on Markov Chains

Short-term trend prediction in the stock market is of significant importance for effective market regulation by the government and optimizing resource allocation for investors. It has become a research hotspot in both academia and the industry in recent years. In addressing the long-term stock price prediction problem, a Markov Chain-based stock price prediction method is proposed. This method is based on the concept of state transitions in Markov Chains, where stock indicator data is transformed into state data. A transition probability matrix is generated, and predictions are made using matrix multiplication. Testing and verification are conducted using two datasets, BJ#430510 (Feng Guang Precision) and SZ#000009 (China Baoan). The results indicate that the stock price prediction model proposed in this paper exhibits high accuracy and stability.

Analysis of Student Errors in Solving Matrix Problems in Class XI of SMK Muhammadiyah Delanggu

This study sought to describe mistakes made by SMK Muhammadiyah Delanggu's grade XI students with high, medium, and low abilities when solving matrix problems. It also sought to describe mistakes made by SMK Muhammadiyah Delanggu's grade XI students with concepts, principles, and procedures. This exploration is an engaging subjective examination. The instrument utilized a composed test that included two things, four framework material test questions and meetings were utilized as extra instruments. 14 XI students who had studied matrix material served as the study's subjects. By gathering information from giving composed test questions, understudy mistakes can be distinguished. According to the findings of this study, students of high ability understood the concepts and principles, but performed mathematical operations incorrectly; students of medium ability made procedural errors due to a lack of accuracy in matrix multiplication calculations; and students of low ability made numerous concept, principle, and procedure errors.

An information-analytical system for assessing the level of automated news content according to the population structure – A platform for media literacy system development

An increasingly complicated communications environment, including artificially manufactured information, requires new skills. No research has designed a mechanism to assess public views and attitudes toward automated news material in this changing environment. This study used a fuzzy information–analytical system to assess public perceptions and attitudes toward automated news content as a tool for building a national and international media literacy system. Our two-stage innovative information approach uses three social indicators and eight criteria to assess public views toward artificially manufactured content. We defined the input–data processing system first. In the second stage, we used a multiple-criteria fuzzy model to assess public opinion on artificially manufactured information. We modified a generalized logical conclusion to varied query answers. For multiple criteria evaluation, we employed matrix multiplication and multidimensional membership functions to determine public opinion toward artificially manufactured content for different social indicator groups. Aggregated ratings and public attitude toward artificially manufactured content were the output. Experimental data from 1041 Czech respondents supported the information–analytical system's efficacy. With this knowledge, national and institutional decision-makers and other stakeholders can analyze citizens of different social and economic backgrounds' public attitudes toward artificially created content and create information security-related decision-making support scenarios.

A fast matrix-based method for two-phase and three-phase daylight simulations

This study introduced a sequential contribution coefficient calculation method with an ambient cache to expedite the computation of daylight coefficient (DC) matrices and view matrices for the two-phase method (2-PM) and three-phase method (3-PM) in daylight simulations. This innovation resulted in the development of swifter two-phase and three-phase methods. Additionally, a novel tool for high-speed matrix multiplication was developed to enhance climate-based daylight modeling. The results demonstrate the effectiveness of the proposed sequence contribution coefficient calculation, showing a reduction in computation time for the DC matrix by 53.1% and 55.8% for 145 sky patches and 1297 sky patches, respectively. Furthermore, the view matrix computation time shows an impressive reduction of 86.4%. The tool for rapid matrix multiplication further contributes to a reduction in computation time exceeding 80%. Overall, the fast two-phase method and three-phase method achieve a reduction in computation time exceeding 60% and 80%, respectively, compared to the original two-phase and three-phase methods. Notably, the simulation results affirm that the accelerated matrix-based method does not compromise the accuracy of glare metric calculations.

Application of Fuzzy-ISM-MICMAC in the Risk Analysis Affecting Swivel Bridge Construction Spanning Existing Railway Lines: A Case Study

Swivel bridge construction (SBC) technology has significant advantages in building bridges that span existing railway lines (ERLs), but it also entails complex risks from ‘skylight’ windows and railway boundaries. A notable challenge is the relationships and interdependencies among these risks, which collectively increase safety hazards through mutual influence. Prior research has typically focused on mitigating the risks inherent in particular tasks or operations, with less emphasis on the risks from interdependencies. A novel framework was developed to explore this research gap by integrating fuzzy logic, interpretive structural modeling (ISM) and the cross-impact matrix multiplication applied to classification (MICMAC) approach (Fuzzy-ISM-MICMAC) to investigate the relationships and interdependencies among the risks of SBC spanning ERLs and the critical points of risk control. Furthermore, the data collected from a literature review, a case analysis and expert interviews resulted in 28 risk factors. Then, the application of ISM distilled complex risk relationships into a clear, multilevel hierarchy, accurately illustrating the complex interrelationships among risk factors. Combined with MICMAC analysis, the research findings indicate that preliminary works such as the selection of construction technology, scheme design, construction rehearsal and the provision of safety facilities are essential for preventing risks in SBC spanning ERLs. We applied these findings to the double T-structure swivel construction of the Xiaojizhuang Bridge, where its practicality and efficiency were thoroughly tested and validated. This research’s critical contribution is identifying, clarifying and visualizing the interrelationships of the complex risk factors of SBC spanning ERLs and providing specific solutions for safety management in similar bridge construction projects. The research results and risk control recommendations offer valuable insights for managing other swivel bridge construction risks.

AN ORDER-P TENSOR MULTIPLICATION WITH CIRCULANT STRUCTURE

Research on mathematical operations involving multidimensional arrays or tensors has increased along with the growing applications involving multidimensional data analysis. The -product of order- tensor is one of tensor multiplications. The -product is defined using two operations that transform the multiplication of two tensors into the multiplication of two block matrices, then the result is a block matrix which is further transformed back into a tensor. The composition of both operations used in the definition of -product can transform a tensor into a block circulant matrix. This research discusses the -product of tensors based on their circulant structure. First, we present a theorem of the -product of tensors involving circulant matrices. Second, we use the definition of identity, transpose, and inverse tensors under -product operation and investigate their relationship with circulant matrices. Third, we manifest the computation of the -product involving circulant matrices. The results of the discussion show that the -product of tensors fundamentally involves circulant matrix multiplication, which means that the operation at its core relies on multiplying circulant matrices. This implies the -product operation of tensors having properties analogous to standard matrix multiplication. Furthermore, since the -product of tensors fundamentally involves circulant matrix multiplication, its computation can be simplified by diagonalizing the circulant matrix first using the discrete Fourier transform matrix. Finally, based on the obtained results, an algorithm is constructed in MATLAB to calculate the -product.

Polarization-artifact reduction and accuracy improvement of Jones-matrix polarization-sensitive optical coherence tomography by multi-focus-averaging based multiple scattering reduction.

Polarization-sensitive optical coherence tomography (PS-OCT) is a promising biomedical imaging tool for the differentiation of various tissue properties. However, the presence of multiple-scattering (MS) signals can degrade the quantitative polarization measurement accuracy. We demonstrate a method to reduce MS signals and increase the measurement accuracy of Jones matrix PS-OCT. This method suppresses MS signals by averaging multiple Jones matrix volumes measured using different focal positions. The MS signals are decorrelated among the volumes by focus position modulation and are thus reduced by averaging. However, the single scattering signals are kept consistent among the focus-modulated volumes by computational refocusing. We validated the proposed method using a scattering phantom and a postmortem medaka fish. The results showed reduced artifacts in birefringence and degree-of-polarization uniformity measurements, particularly in deeper regions in the samples. This method offers a practical solution to mitigate MS-induced artifacts in PS-OCT imaging and improves quantitative polarization measurement accuracy.

Mathematical Framework for Optimizing Crossbar Allocation for ReRAM-based CNN Accelerators

The resistive random-access memory (ReRAM) has widely been used to accelerate convolutional neural networks (CNNs) thanks to its analog in-memory computing capability. ReRAM crossbars not only store layers’ weights, but also perform in-situ matrix-vector multiplications which are core operations of CNNs. To boost the performance of ReRAM-based CNN accelerators, crossbars can be duplicated to explore more intra-layer parallelism. The crossbar allocation scheme can significantly influence both the computing throughput and bandwidth requirements of ReRAM-based CNN accelerators. Under the resource constraints (i.e., crossbars and memory bandwidths), how to find the optimal number of crossbars for each layer to maximize the inference performance for an entire CNN is an unsolved problem. In this work, we find the optimal crossbar allocation scheme by mathematically modeling the problem as a constrained optimization problem and solving it with a dynamic programming based solver. Experiments demonstrate that our model for CNN inference time is almost precise, and the proposed framework can obtain solutions with near-optimal inference time. We also emphasize that communication (i.e., data access) is an important factor and must also be considered when determining the optimal crossbar allocation scheme.

Integrated WDM-compatible optical mode division multiplexing neural network accelerator

On-chip photonic neural networks (PNN) are emerging as an attractive solution for artificial neural networks due to their high computing density, low energy consumption, and compact size. Matrix-vector multiplication (MVM) plays a key role in on-chip PNN, and can achieve high-speed multiply-accumulate operation. Most current schemes implement MVM by adopting wavelength division multiplexing technology to accumulate the power of different wavelengths together. This requires multiple laser sources. Additionally, both positive and negative domain MVM are inevitable for realizing precise PNNs, but because of the innate limitations of light, effective solutions to perform negative value computing are still inadequate. Here, we propose and demonstrate a PNN accelerator based on mode division multiplexing technology to reduce the use of multi-wavelength lasers. We show that it can satisfactorily tackle real-number-field computing (including positive and negative domains) based on a novel, to our knowledge, transformation mapping approach. As a proof-of-concept, we demonstrate a fabricated accelerator for image convolution and letter pattern detection, achieving a computing density of 1.37TOPS/mm2 under the 22.38 Gbaud modulation rate.

Novel neuromorphic architectures based on crossbar arrays of (Co-Fe-B)<sub>x</sub>(LiNbO<sub>3</sub>)<sub>100−x</sub> nanocomposite memristors

Memristor-based neuromorphic computing systems (NСSs) provide a fast, high computational and energy efficient approach to neural network (NN) training and solving cognitive problems (pattern recognition, big data processing, prediction, etc.) [1]. Memristors could be organized in large crossbar arrays to perform vector-matrix multiplication (VMM) in a natural one-step way by the weighted electrical current summation (according to the Ohm’s and Kirchhoff’s laws) [1]. In contrast, being the most massively parallel operation in NN learning and inference, VMM is extremely time- and energy-expensive in traditional von Neumann architectures. Owing to this difference, memristor-based NCSs are of high interest. Memristors have already been successfully implemented for diverse NCS realizations, and such schemes as multi-layer perceptron (MLP) [2], long short-term memory and others have been demonstrated. Most of these NCSs are usually trained by various types of gradient descent learning algorithm, the hardware realization of which is challenging due to unreliable cycle-to-cycle (c2c) and device-to-device (d2d) variations of memristive devices. Several approaches have been proposed to partially mitigate these problems, including reservoir computing [3] and fine feature engineering [4]. The general idea of such approaches is to reduce the number of required weights (i.e. memristors) compared with fully connected NNs. In this respect, such novel architectures as convolutional NN (CNN) and MLP-mixer are of high interest as they provide significant weight reduction without classification efficiency drop. Although CNN based on memristors was already demonstrated, different aspects of its realization (such as hybrid hardware-software co-design) have yet to be studied. MLP-mixer was realized only in software. Therefore, in this work we have studied the possibility of hardware realization of CNN and MLP-mixer networks based on crossbar arrays of memristors. For this purpose, we studied (Co-Fe-B)x(LiNbO3)100−x nanocomposite (CFB-LNO NC) memristors, which operate through a multifilamentary resistive switching (RS) mechanism, demonstrate high endurance, long retention and possess multilevel RS [5]. Crossbar array of memristors was fabricated using laser photolithography for patterning electrode buses and ion-beam sputtering on the original facility for active layer deposition (~10 nm thick LiNbO3 and ~290 nm thick CFB-LNO NC with x ≈10–25 at.%). Details of the fabrication process could be found elsewhere [5]. I-V curves of the fabricated memristors showed small c2c and d2d variations, plasticity with 16 different resistive states and endurance of more than 105 cycles. Using the nanocomposite based crossbar arrays, we implemented a hybrid CNN, consisting of a hardware feature extractor with one/two kernels and a software classifier. Additionally, we have demonstrated in simulation that the usage of the memristors under study in the accurately adapted MLP-Mixer architecture results in high classification accuracy that is resilient to memristive variations and stuck devices.

Improved privacy-preserving PCA using optimized homomorphic matrix multiplication

Principal Component Analysis (PCA) is a pivotal technique widely utilized in the realms of machine learning and data analysis. It aims to reduce the dimensionality of a dataset while minimizing the loss of information. In recent years, there have been endeavors to utilize homomorphic encryption in privacy-preserving PCA algorithms for secure cloud computing. These approaches commonly employ a PCA routine known as PowerMethod, which takes the covariance matrix as input and generates an approximate eigenvector corresponding to the primary component of the dataset. However, their performance is constrained by the absence of an efficient homomorphic covariance matrix computation circuit and an accurate homomorphic vector normalization strategy in the PowerMethod algorithm. In this study, we propose a novel approach to privacy-preserving PCA that addresses these limitations, resulting in superior efficiency, accuracy, and scalability compared to previous approaches.We attain such efficiency and precision through the following contributions: (i) We implement space and speed optimization techniques for a homomorphic matrix multiplication method, specifically tailored for parallel computing scenarios. (ii) Leveraging the benefits of this optimized matrix multiplication, we devise an efficient homomorphic circuit for computing the covariance matrix homomorphically. (iii) Utilizing the covariance matrix, we develop a novel and efficient homomorphic circuit for the PowerMethod that incorporates a universal homomorphic vector normalization strategy to enhance both its accuracy and practicality.Our privacy-preserving PCA scheme, implemented using our innovative homomorphic PowerMethod circuit, surpasses the state-of-the-art approach with an average speedup of 1.9 times on datasets with size 200×256. Notably, our scheme demonstrates an even more remarkable estimated speedup of 25 times when applied to larger datasets of size 60000×256, along with an R2 accuracy improvement of up to 0.285, showcasing efficiency and accuracy that has not been reported by previous approaches.

Identifying design spaces as linear combinations of parameter ranges for biopharmaceutical control strategies

According to ICH Q8 guidelines, a biopharmaceutical manufacturer may submit a design space (DS) definition as part of the regulatory approval application, in which case process parameter (PP) deviations within this space are not considered changes and do not trigger a regulatory post approval procedure. A DS can be described by non-linear PP ranges, i.e., the range of one PP conditioned on specific values of another. However, independent PP ranges (linear combinations) are often preferred in biopharmaceutical manufacturing due to their operational simplicity, as mentioned in the guideline. While statistical software such as Modde supports the calculation of a DS comprised of linear combinations, their algorithms are generally based on discretizing the parameter space - an approach that suffers from the curse of dimensionality as the number of PPs increases. Here, we introduce a novel method for finding linear PP combinations using a numeric optimizer to calculate the largest design space within the parameter space that results in critical quality attribute boundaries within acceptance criteria, predicted by a regression model. A precomputed approximation of tolerance intervals is used in inequality constraints to facilitate fast evaluations of this boundary using a single matrix multiplication. The correctness of the method was validated by comparing results to that of a grid-based approach and, in a simple case, to an analytically defined ground truth. In the examples investigated, the volume of the resulting DS was significantly larger than that of the grid method, with the improvement being proportional to the granularity of the grid and the number of parameters involved. Furthermore, computational time for the optimization-based approach is several orders of magnitude faster in higher dimensions. In addition, a proposed weighting scheme can be used to favor certain PPs over others and therefore enabling a more dynamic approach to DS definition and exploration. The increased PP ranges of the larger DS provide greater operational flexibility for biopharmaceutical manufacturers.

The implementation of the method of reduced matrix D-trees in the Udf MAOPCs environment

The article explores the content of the MatrixDtrees function, which extends the functionality of the UDF MAOPCs and is designed to generate symbolic transfer functions of linear parametric circuits. This function represents a software implementation of the Transformed Matrix D-trees method. This method is an extension of the symbolic d-trees method, developed for constant parameters circuits, to parametric circuits. The extension involves the transition from algebraic operations with numbers and symbols in the d-trees method to matrix algebraic operations, taking into account the non-commutativity of matrix multiplication. The Transformed Matrix D-trees method significantly reduces computational time for modeling parametric circuits by factoring out similarities in complex symbolic expressions generated during the analysis process. The MatrixDtrees function allows for the steady-state analysis in highly complex parametric circuits. By such circuits, we mean circuits that contain dozens or hundreds of nodes and elements (including parametric ones). The article includes the results of analyzing a parametric long line model, which is represented by a combination of lumped parameters and consists of many cascaded elementary sections. Each of these sections is a combination of parametric inductance and constant capacitance. The paper presents the results of an experiment to determine the output voltage of a long line model containing 1025 nodes, 1024 constant capacitances, and 1024 parametric inductances. The results are comparable to calculations of the same long line model using the MicroCap program. The relative deviation between the calculation results for both programs was less than 1%. The calculation time for the Transformed Matrix D-trees method using the MatrixDtrees function was 18 minutes, whereas for the MicroCap program, it was 36 hours.

Addressing data scarcity in optical matrix multiplier modeling using transfer learning

We present and experimentally evaluate the use of transfer learning to address experimental data scarcity when training neural network (NN) models for Mach–Zehnder interferometer mesh-based optical matrix multipliers. Our approach involves pretraining the model using synthetic data generated from a less accurate analytical model and fine-tuning it with experimental data. Our investigation demonstrates that this method yields significant reductions in modeling errors compared to using an analytical model or a standalone NN model when training data is limited. Utilizing regularization techniques and ensemble averaging, we achieve <1 dB root-mean-square error on the 3×3 matrix weights implemented by a photonic chip while using only 25% of the available data.

Real block-circulant matrices and DCT-DST algorithm for transformer neural network

In the encoding and decoding process of transformer neural networks, a weight matrix-vector multiplication occurs in each multihead attention and feed forward sublayer. Assigning the appropriate weight matrix and algorithm can improve transformer performance, especially for machine translation tasks. In this study, we investigate the use of the real block-circulant matrices and an alternative to the commonly used fast Fourier transform (FFT) algorithm, namely, the discrete cosine transform–discrete sine transform (DCT-DST) algorithm, to be implemented in a transformer. We explore three transformer models that combine the use of real block-circulant matrices with different algorithms. We start from generating two orthogonal matrices, U and Q. The matrix U is spanned by the combination of the reals and imaginary parts of eigenvectors of the real block-circulant matrix, whereas Q is defined such that the matrix multiplication QU can be represented in the shape of a DCT-DST matrix. The final step is defining the Schur form of the real block-circulant matrix. We find that the matrix-vector multiplication using the DCT-DST algorithm can be defined by assigning the Kronecker product between the DCT-DST matrix and an orthogonal matrix in the same order as the dimension of the circulant matrix that spanned the real block circulant. According to the experiment's findings, the dense-real block circulant DCT-DST model with largest matrix dimension was able to reduce the number of model parameters up to 41%. The same model of 128 matrix dimension gained 26.47 of BLEU score, higher compared to the other two models on the same matrix dimensions.

Barriers to TQM implementation in SMEs in Bangladesh: an interpretive structural modeling approach

PurposeThis study aims to recognize the significant barriers of small and medium-sized enterprises (SMEs) in Bangladesh, hindering the adoption of total quality management (TQM). Additionally, this research intends to explore the interrelations among these barriers to develop essential managerial insights for promoting TQM implementation in SMEs.Design/methodology/approachThe interpretive structural modeling (ISM) approach and Matrice d'impacts croisés multiplication appliquée á un classment (MICMAC) a cross-impact matrix multiplication applied to classification show the relationship among the barriers and classification of the barriers to TQM implementation respectively, and partial least squares structural equation modeling (PLS-SEM) is applied for ISM model validation.FindingsThis study examined previous literature and conducted interviews with professionals to identify 17 barriers. The study then develops and investigates a model that outlines the relationships and priorities among these barriers and categorizes them based on their impact and interdependence. This analysis can assist SMEs in implementing TQM during their operations successfully.Practical implicationsThis research emphasizes the crucial obstacles that greatly affect other barriers and require immediate attention. Furthermore, this study provides valuable information for SMEs to effectively prioritize their resources and efforts to overcome these obstacles.Originality/valueThis study delves into the primary obstacles impeding the integration of TQM in SMEs through a novel approach. Additionally, this study constructs a verified contextual framework that depicts the hierarchies and interconnections among these barriers.

Research on Carbon Footprint Accounting in the Materialization Stage of Prefabricated Housing Based on DEMATEL-ISM-MICMAC

This work employs the carbon emission factor method to offer real-world instances for carbon footprint accounting, allowing for a thorough analysis of the carbon footprint and important influencing elements throughout the materialization stage of prefabricated housing. To identify the 18 important influencing factors that need to be examined from the five stages of building material production, conveyance of building materials, component manufacturing, component transportation, and building, this paper applies the DEMATEL-ISM-MICMAC (Decision-Making Trial and Evaluation Laboratory–Interpretive Structure Modeling–Cross-Influence Matrix Multiplication) model based on data quantification. Following the findings, the case project’s physical phase generated a carbon footprint of approximately 4.68 × 106 kg CO2. The building materials’ production and processing phase contributed the highest carbon footprint of the entire physical phase, totaling 4,005,935.99 kg CO2, or 88.24% of the total carbon footprint. To determine the centrality and causality of the influencing factors, four major influencing factors—energy consumption of raw materials (S4), construction planning and organization (S15), transportation energy type (S6), and waste disposal (S2)—were identified using the DEMATEL approach. The influencing factor system hierarchy was divided into six levels using the ISM technique. Level L6, which comprises one influencing factor for organizing and planning, is construction planning and organization (S15). Utilizing the MICMAC technique, it was possible to identify the energy consumption of raw materials (S4) as the primary cause of the materialization phase of built dwellings’ carbon footprint. The building material production phases have the largest influence on carbon footprints, according to both case accounting and modeling research. The study’s findings can offer some conceptual guidance for the creation of low-carbon emission reduction schemes.