Conventional Cellular Automata Research Articles

Simulation of container discharge dynamics using modified cellular automata

In the field of physical logistics, efficient and precise control of material flow during the emptying of containers such as silos and wagons is crucial. This study introduces a not conventional cellular automaton model to simulate spillage from containers. The model is implemented using Excel macros, providing a user-friendly and accessible platform for logistics professionals. By modifying the traditional cellular automaton framework, the simulation can accurately represents the dynamics of material flow during container emptying processes. The proposed method allows for fine-tuned control over the spillage by integrating specific constraints and parameters, enhancing operational efficiency and reducing material loss. The versatility of the model makes it applicable to a wide range of logistical scenarios, demonstrating its potential as a valuable tool in physical logistics management.

A new microscopic traffic-flow model based on the spatiotemporal continuous system concept considering nonlinear human response

A brand-new traffic model is introduced to precisely simulate the individual movement of vehicles, departing from the traditional macroscopic perspective (Eulerian scope or fluid dynamics concept) to adopt a microscopic approach (Lagrangian scope). This model is built on the first principle of Newton’s kinetic equation, explicitly incorporating nonlinear relations to represent human responses to a physical stimulus (observed information), such as the velocity gap between one’s own vehicle and a certain targeted one or the gap to a preceding vehicle, unlike the conventional car-following concept. The model posits that a driver’s recognition occurs intermittently rather than continuously, following specific probabilistic distributions of which the formulation is physically justified. Overall, the model can be described as a spatiotemporally continuous formulation unlike cellular automaton (CA) traffic models, crucial for capturing traffic dynamics at the micro and macro levels. The model is validated using a real traffic-flow dataset from a highway, and the results of the conventional CA traffic model are compared with those of the present one” along with a note for authorial verification. Animated simulations confirm that the present model can reproduce realistic flow dynamics characterized by smoother acceleration and deceleration compared to the conventional CA traffic model. The complete simulation source code for replicating the model is made publicly available.

DECA: Discrete Event inspired Cellular Automata for grain structure prediction in additive manufacturing

Microstructure largely dictates macroscopic material properties and is strongly affected by processing. Therefore, the simulation of microstructure evolution in response to thermal fields during processing is of significant interest within the computational materials science community. Additive manufacturing (AM) has emerged as a technique for producing complex geometries and unique microstructures. Yet, complex and rapid thermal cycles in AM pose computational challenges for existing microstructure models. This work proposes a discrete event inspired cellular automata (CA) approach, titled DECA, to accelerate simulation of grain structure evolution in AM. In contrast to conventional time-stepped CA models, this model directly solves the times capture events would take place allowing for stepping in events rather than time (a technique also found in the field of discrete-event simulation). In comparison to purely serial discrete-event models, DECA allows for temporary violation of the causality constraint, but detects and corrects these violations, leading to an emergent phenomenon dubbed causality rippling, in which previously calculated capture events are overwritten. The amount of repeated calculations, defined by the capture ratio, is taken as a measure of computational inefficiency, and the model parameters that affect this ratio are evaluated. The new DECA approach was found to be more computationally efficient than conventional time-stepped CA models while guaranteeing an accurate solution, which can only be achieved in the conventional models for vanishingly small time steps. Finally, opportunities for parallelization and scaling of the new approach are discussed.

A review of the application and implications of cellular automata-based urban growth model in Africa

ABSTRACT Africa’s urbanization rate has quadrupled from 14% in 1950 to about 44% in 2022. A variety of urban growth models have been used to measure and monitor urbanization, its drivers and implications for urban planning and sustainability. This paper reviews the performance of various Cellular Automata (CA)-based urban growth models and their implications for the urbanization processes in Africa. To this end, we employ a systematic review approach to identify the final 18 articles published in Web of Science-indexed journals until 2022. Our review found that the CA-based urban growth model has been successfully used in Africa to track the impacts of urban growth, assess different city growth scenarios and compare the performance of various CA-integrated models. Yet, most of the reviewed CA-based studies have focused on more urbanized regions of the continent. The result also reveals that integrating the CA model with other statistical methods improves its broader application and practicality than a conventional CA model. Our findings give planners, policymakers, and other urban stakeholders a more in-depth understanding of the challenges of unplanned urbanization and the need for meaningful participation from urban stakeholders in city growth and sustainable land use management that balances urban growth and the environment.

Land use and land cover change simulation enhanced by asynchronous communicating cellular automata

Land use and land cover change (LUCC) modeling is crucial to urban planning and policy making. A well-used and effective paradigm for LUCC is the ANN-CA model which employs an artificial neural network (ANN) to calculate a transition probability over each land cell from various driving factors, and then uses a cellular automaton (CA) to evolve all cells consecutively to update their land usage and coverage according to the estimated probability distribution. This paper focuses on the effect of delays or perturbations possibly taking place between land cells on the LUCC modeling. To this end, a new ANN-CA model is proposed which adopts an asynchronous communicating cellular automaton (ACCA), rather than the conventional synchronous CA. Especially, the ACCA allows every cell to communicate with its neighbors independently at random times via a specific protocol, which offers a natural way to include stochastic delays in exchanging the current land usages between cells. As a result, every change of a cell's land use in the ACCA may not affect its neighbors immediately, but is subject to delays that might play an important role in modeling the practical LUCC. Numerical analysis of the new model are carried out over three regions of Chongqing city, China with different scales: Yongchuan District, Sanjiao Town, and Huangguashan Village, and experimental results demonstrate that the proposed ANN-ACCA model can achieve a higher accuracy for LUCC simulation as compared to conventional ANN-CA models.

Neural cellular automata for solidification microstructure modelling

We propose Neural Cellular Automata (NCA) to simulate the microstructure development during the solidification process in metals. Based on convolutional neural networks, NCA can learn essential solidification features, such as preferred growth direction and competitive grain growth, and are up to six orders of magnitude faster than the conventional Cellular Automata (CA). Notably, NCA deliver reliable predictions also outside their training range, e.g. for larger domains, longer solidification duration, and different temperature fields and nucleation settings, which indicates that they learn the physics of the solidification process. While in this study we employ data produced by CA for training, NCA can be trained based on any microstructural simulation data, e.g. from phase-field models.

A cellular automaton traffic model by mechanical restriction and the slow-to-start rules in the framework of Kerner’s three-phase traffic theory

Most of the conventional cellular automaton (CA) traffic flow models have two shortcomings: unlimited deceleration capabilities and incapability of reproducing the synchronized flow in the three-phase traffic flow theory. Based on an original deceleration CA model that emphasizes limited mechanical capabilities and human overreaction as the origin of congested traffic states, this paper proposes a new deceleration CA model where the slow-to-start rules are incorporated. For periodic boundary conditions, one also finds that the present model can reproduce well the three different phases of traffic flow (free flow, synchronized traffic flow, wide moving jam) as well as two first-order phase transitions (the transitions from free flow to synchronized flow and from synchronized flow to wide moving jam) among them. Compared to the original deceleration CA model, one notes that the phase transition from the synchronized flow to wide moving jam becomes distinguishable. Furthermore, the present model can reliably reproduce most empirical findings including synchronized flow with different slopes, the so-called pinch effect, and the time-headway distribution of free flow and so on. Importantly, the synchronized flow with different slopes is supported by spatiotemporal diagrams and the statistical distribution of velocity and so on. For open boundary conditions, the present model can reproduce the spatiotemporal diagrams of well-known five patterns including moving synchronized flow pattern, localized synchronized flow pattern, widening synchronized flow pattern, dissolving general pattern and general pattern.

Cell-level coupling of a mechanistic model to cellular automata for improving land simulation

ABSTRACT The land use and land cover change (LUCC) process is crucial for climate and environmental change studies. Cellular automata (CA) models based on machine learning techniques have commonly been used to simulate LUCC. However, conventional CA models can only capture the historical relationship between driving forces and LUCC through statistics. Climate change significantly affects LUCC, especially natural vegetation. The statistical relationship between driving forces and LUCC may change with the climate. Furthermore, the existing coupled models of CA and mechanistic models are only loosely coupled in terms of the quantity of land demand provided by mechanistic models, which denotes that mechanistic models do not directly guide CA models in simulating spatial land dynamics. Thus, herein, a novel model that couples Lund Potsdam Jena (LPJ), a mechanistic model, and CA at the cell level is proposed to consider the mechanisms and statistics in LUCC simulations. The proposed coupled model (LPJ-FLUS) is validated by comparison with two historical LUCC simulations in China from 2001 to 2010 and 2015. The results show that the proposed coupled model affords higher simulation accuracy, especially on natural vegetation, compared to the two conventional CA models. The overall Figure of Merit value of the LPJ-FLUS model in the historical LUCC simulations is about 5% higher than that of the conventional CA model, reaching 23.37%, and is even 8% higher for some natural vegetation types. The proposed model is employed to predict the future LUCC under two SSP-RCP scenarios in China from 2015 to 2100. The simulation results show that the proposed model effectively combines the strengths of LPJ and CA, retaining the high spatial resolution of CA while representing the spatial possibilities of LUCC under different future climate scenarios assessed by LPJ. The quantitative validation results show that the simulation results of the LPJ-FLUS model are more spatially correlated with the LPJ model than those of conventional CA models. The proposed LPJ-FLUS model is a valuable attempt toward tightly coupling mechanistic and CA models at the cell level. Additionally, it has promising potential for high spatial resolution LUCC simulations and environmental impact analysis under future extreme climate scenarios.

Study of microstructure evolution of magnesium alloy cylindrical part with longitudinal inner ribs during hot flow forming by coupling ANN-modified CA and FEA

Hot flow forming (HFF) is a promising forming technology to manufacture thin-walled cylindrical part with longitudinal inner ribs (CPLIRs) made of magnesium (Mg) alloys, which has wide applications in the aerospace field. However, due to the thermo-mechanical coupling effect and the existence of stiffened structure, complex microstructure evolution and uneven microstructure occur easily at the cylindrical wall (CW) and inner rib (IR) of Mg alloy thin-walled CPLIRs during the HFF. In this paper, a modified cellular automaton (CA) model of Mg alloy considering the effects of deformation conditions on material parameters was developed using the artificial neural network (ANN) method. It is found that the ANN-modified CA model exhibits better predictability for the microstructure of hot deformation than the conventional CA model. Furthermore, the microstructure evolution of ZK61 alloy CPLIRs during the HFF was analyzed by coupling the modified CA model and finite element analysis (FEA). The results show that compared with the microstructure at the same layer of the IR, more refined grains and less sufficient DRX resulted from larger strain and strain rate occur at that of the CW; various differences of strain and strain rate in the wall-thickness exist between the CW and IR, which leads to the inhomogeneity of microstructure rising firstly and declining from the inside layer to outside layer; the obtained Hall-Petch relationship between the measured microhardness and predicted grain sizes at the CW and the IR indicates the reliability of the coupled FEA-CA simulation results.

Updating and backdating analyses for mitigating uncertainties in land change modeling: a case study of the Ci Kapundung upper water catchment area, Java Island, Indonesia

In developing countries, data gaps are common and lead to uncertainties in land cover change analysis. This study demonstrates how to mitigate uncertainties in modeling land change in the Ci Kapundung upper water catchment area by comparing the outcomes of two simulation phases. A conventional cellular automata (CA)–Markov model was complemented with a multilayer perceptron (MLP) to project future land cover maps in the study area. The CA–Markov–MLP model results in high uncertainties in forested sites where a data gap is apparent in the input data (land cover maps and driver variables) and parameters. The results show that the model accuracy is improved from 47.90% in the first phase to 81.36% in the second phase. Both first and second phases integrate six demographic–economic and environmental drivers in the modeling, but the second phase also incorporates an updating and backdating analysis to revise the base-maps. This study suggests that uncertainties can be mitigated by linking such base-map revision process with the updating and backdating analyses using remote sensing datasets retrieved at different times.

Asynchronous communicating cellular automata: Formalization, robustness and equivalence

This paper attempts at formalizing a novel type of cellular automata (CAs) in the framework of distributed systems under asynchronous communication. Called asynchronous communicating cellular automata (ACCAs), our models allow each cell to exchange states with its neighboring cells independently at random times, via a specific protocol for asynchronous communication. This can actually facilitate the separation of communication between cells from the cells’ state transitions in an ACCA. The effect of asynchronous communication on dynamical behavior will be analyzed on the well-studied elementary class of cellular automata, especially on their robustness. Despite the unpredictable randomness in both communication and state transitions, computational equivalence between ACCAs and conventional CAs can be achieved, based on effective methods for transforming every synchronous CA into an equivalent ACCA.

Tensor‐CA: A high‐performance cellular automata model for land use simulation based on vectorization and GPU

AbstractWith the ability to understand linkages and feedbacks between land use dynamics and human–land relationships, cellular automata (CA) are extensively applied in land use/cover change (LUCC) simulation. However, with complex transition rules and a growing volume of spatial data, conventional serial CA models cannot meet the demands of efficient computation. In this article, a Tensor‐CA model using vectorization and Graphics Processing Unit (GPU) technology based on a tensor computation framework for optimizing multiple LUCC simulations is presented. Complex transition rules of LUCC‐CA models are vectorized and formalized to tensor operations which are effectively solved by GPU. The proposed Tensor‐CA model was applied to LUCC simulations in the Pearl River Delta of China. The experimental results indicate that the proposed model effectively improved the performance compared to Serial‐CA, Parallel‐CA, and GPU‐CA.

Modeling and simulation of dynamic recrystallization in super austenitic stainless steel employing combined cellular automaton, artificial neural network and finite element method

A cellular automaton (CA) model for dynamic recrystallization (DRX) is established by employing Moore’s neighboring rule to predict flow stress, DRX grain size (DDRX) and DRX fraction (XDRX). The CA model has been optimized for super austenitic stainless steel at different strain rates (0.001–10 s−1) and temperatures (1173–1423 K) under isothermal deformation conditions. The output of the CA simulation has been used for establishing ANN-based constitutive models. The trained ANN-based constitutive models have been further implemented in FEM software (ABAQUS 6.14) to evaluate flow behavior and microstructure response of the alloy under various non-isothermal deformation conditions. The conventional CA (CAC) model has failed to provide a good depiction of the microstructure evolution, as it revealed a very low correlation coefficient (R) for XDRX (R ~ 0.75) and DDRX (R ~ 0.8). This inaccuracy of the model could be related to its inherent inability to consider the effect of solute drag on grain growth and DRX kinetics. Therefore, a modified cellular automata (CAM) model has been developed by introducing a new temperature-strain rate-dependent mobility parameter for numerically considering the solute drag effect. Employing non-isothermal simulations, the CAM model has revealed a higher correlation coefficient than the CAC model for predicting XDRX (R ~ 0.95) and DDRX (R ~ 0.98). Moreover, the developed CAM model has also predicted the flow behavior of the alloy in the entire domain investigated, revealing a higher correlation coefficient (R ~ 0.987) and a low average absolute relative error (8.6%).

Mixed-cell cellular automata: A new approach for simulating the spatio-temporal dynamics of mixed land use structures

When used for land use change modeling, Cellular Automata (CA) usually assume that each cell has only one land use type at each time step, ignoring the mixed land use structures that are often found in land units. Mixed cells, composed of cover proportions of multiple land use types, provide a new perspective for modeling the spatio-temporal dynamics of mixed land use structures. Simulating land use change with mixed cells is challenging because mixed-cell CAs are fundamentally different from conventional CAs. This study develops a mixed-cell CA (MCCA). The structure of the CA is re-designed based on the cover proportion of land uses, including the representations of cell state, lattice, and neighborhood. The transition rules are automatically constructed by random-forest regression using historical data and a competition mechanism among multiple land use types at the sub-cell scale is proposed. In addition, a mixed-cell figure of merit (mcFoM) accuracy measure is proposed to validate the MCCA. The MCCA was applied to the Wuhan metropolitan area in China, and the results show that the MCCA was able to simulate the subtle changes of land use proportions within land units. The MCCA represents a new breed of geospatial CA models for spatio-temporal dynamics of mixed land use structures, which enables mixed land use research to leap from static analysis to dynamic simulation. The software for MCCA has been made available at https://github.com/HPSCIL/Mixed_Cell_Cellullar_Automata.

A non-uniform cellular automata framework for topology and sizing optimization of truss structures subjected to stress and displacement constraints

The conventional Cellular Automata (CA) approach has the disadvantage of being particularly suited for design optimization of uniform truss ground structures with identical cells. Moreover, the conventional CA algorithms, which are intrinsically local, have to be modified in order to be able to tackle problems involving displacement constraints. This paper presents a new non-uniform Cellular Automata algorithm, which is based on non-identical cells and a modified FSD/FUD approach. The new algorithm can solve the minimum weight optimization problem of truss structures including both stress and displacement constraints. The efficiency and accuracy of the proposed methodology are proved on a number of benchmark truss design problems.

Incorporation of spatial heterogeneity-weighted neighborhood into cellular automata for dynamic urban growth simulation

Cellular automata (CA) are bottom-up models that have been widely applied to simulate urban growth and project future urban scenarios. Conventional CA models commonly use a homogeneous neighborhood to represent the interactions among nearby cells, failing to reflect the spatial heterogeneity in landscapes. We develop new CA models for urban growth simulation by incorporating spatial heterogeneity into the neighborhood and constructing transition rules using genetic algorithms (GA). We employ three methods to quantify the spatial heterogeneity: [1] the land-use hotspot obtained using Getis-Ord Gi*, [2] the hotspot gradient (HOTGDT), and [3] the land-use gradient (LANDGDT). We compare the three methods and a homogeneous GA-CA model to simulate the rapid urban growth in Shaoxing, a small city in China. Our results show that, as compared to the homogeneous GA-CA model, the hotspot-based model produces unrealistically smooth urban patches and a lower figure of merit (FOM; lower by ~2.8%) while the two gradient-based models yield more realistic urban patches and higher FOMs (higher by ~6.4% for HOTGDT and ~4% for LANDGDT). The gradient-based methods substantially improve model performance and produce more justifiable urban patterns. We recommend including spatial heterogeneity in the CA neighborhood to represent the spatially nonstationary urban growth dynamics. The proposed gradient-based GA-CA models also show strong predictive ability in projecting future scenarios, which should help assess the impacts of past and current land-use policies, and the planning regulations on future urban development.

Simulating urban growth in a megalopolitan area using a patch‐based cellular automata

AbstractAlthough traditional cellular automata (CA)‐based models can effectively simulate urban land‐use changes, they typically ignore the spatial evolution of urban patches, due to their use of cell‐based simulation strategies. This research proposes a new patch‐based CA model to incorporate a spatial constraint based on the growth patterns of urban patches into the conventional CA model for reducing the uncertainty of the distribution of simulated new urban patches. In this model, the growth pattern of urban patches is first estimated using a developed indicator that is based on the local variations in existing urban patches. The urban growth is then simulated by integrating the estimated growth pattern and land suitability using a pattern‐calibrated method. In this method, the pattern of new urban patches is gradually calibrated toward the dominant growth pattern through the steps of the CA model. The proposed model is applied to simulate urban growth in the Tehran megalopolitan area during 2000–2006–2012. The results from this model were compared with two common models: cell‐based CA and logistic‐patch CA. The proposed model yields a degree of patch‐level agreement that is 23.4 and 7.5% higher than those of these pre‐existing models, respectively. This reveals that the patch‐based CA model simulates actual development patterns much better than the two other models.

Integrating Cellular Automata with the Deep Belief Network for Simulating Urban Growth

Sustainable urban development is a focus of regional policy makers; therefore, how to measure and understand urban growth is an important research topic. This paper quantified the amount of urban growth on land use maps that were derived from multi-temporal Landsat images of Jiaxing City as a rapidly-growing city in Zhejiang Province from 2000–2015. Furthermore, a new approach coupled the heuristic bat algorithm (BA) and deep belief network (DBN) with the cellular automata (CA) model (DBN-CA), which was developed to simulate the urban expansion in 2015 and forecast the distribution of urban areas of Jiaxing City in 2024. The BA was proposed to obtain the best structure of the DBN, while the optimized DBN model considered the nonlinear spatial-temporal relationship of driving forces in urban expansion. Comparisons between the DBN-CA and the conventional artificial neural network-based CA (ANN-CA) model were also performed. This study demonstrates that the proposed model is more stable and accurate than the ANN-CA model, since the minimum and maximum values of the kappa coefficient of the DBN-CA were 77.109% and 78.366%, while the ANN-CA’s values were 63.460% and 76.151% over the 200 experiments, respectively. Therefore, the DBN-CA model is a potentially effective new approach to survey land use change and urban expansion and allows sustainability research to study the health of urban growth trends.

Improving urban cellular automata performance by integrating global and geographically weighted logistic regression models

AbstractIn many of the conventional cellular automata (CA) models, particularly Urban‐CA which are used for urban growth, the spatial heterogeneities and local differences of the land use conversion processes are ignored. Global logistic regression (LR) is a popular model employed to define the transition rules of Urban‐CA. By considering the local characteristics, Geographically Weighted Logistic Regression (GWLR) provides interesting capabilities for urban growth modelling. In this research, in addition to using GWLR in the definition of transition rules, the advantages of integrating GWLR and LR for urban growth simulation were evaluated; these have not been considered in previous studies. Local and global probabilities obtained from the calibration of GWLR and LR were combined to define the transition rules of an Urban‐CA. Urban growth was simulated in the Islamshahr sub‐region located southwest of Tehran, Iran for the two periods 1992‐1996 and 1996‐2002, and data from these periods were used for training and testing the prediction abilities, respectively. In the first period, GWLR showed good performance and a significant contribution to the enhancement of the simulation performance, but in the second period, the effectiveness of LR on the prediction accuracy increased. Due to their complementary roles, the integration of the GWLR and LR models resulted in improved simulation performance in both periods.

Integrating the multi-label land-use concept and cellular automata with the artificial neural network-based Land Transformation Model: an integrated ML-CA-LTM modeling framework

Cellular automata (CA) and artificial neural networks (ANNs) have been used by researchers over the last three decades to simulate land-use change (LUC). While conventional CA and ANN models assign a cell to only one land-use class, in reality, a cell may belong to several land-use classes simultaneously. The recently developed multi-label (ML) concept overcomes this limitation in land change science. Although the ML concept is a new paradigm with nonexclusive classes and has shown considerable merit in several applications, few studies in land change science have applied it. In addition, determining transition rules in conventional CA is difficult when the number of drivers is large. Since CA has been shown as a potential model to consider neighborhood effects and ANN has been shown effective in determining CA transition rules, we integrated both CA with an ANN model to overcome limitations of each tool. In this study, we specifically extended the ANN-based Land Transformation Model (LTM) with both a CA-based model and the ML concept to create an integrated ML-CA-LTM modeling framework. We also compared, using standard evaluation measures, differences between the proposed integrated model with a conventional CA-based LTM model (called the ml-CA-LTM). Parameterization was made using a learning and testing procedure common in machine learning. Results showed that the modified LUC model, ML-CA-LTM, produced consistently better goodness of fit calibration values compared to the ml-CA-LTM. The outcome of this modified model can be used by managers and decision makers for improved urban planning.