• 제목/요약/키워드: Diffusion models

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REVIEW OF DIFFUSION MODELS: THEORY AND APPLICATIONS

  • HYUNGJIN CHUNG;HYELIN NAM;JONG CHUL YE
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제28권1호
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    • pp.1-21
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    • 2024
  • This review comprehensively explores the evolution, theoretical underpinnings, variations, and applications of diffusion models. Originating as a generative framework, diffusion models have rapidly ascended to the forefront of machine learning research, owing to their exceptional capability, stability, and versatility. We dissect the core principles driving diffusion processes, elucidating their mathematical foundations and the mechanisms by which they iteratively refine noise into structured data. We highlight pivotal advancements and the integration of auxiliary techniques that have significantly enhanced their efficiency and stability. Variants such as bridges that broaden the applicability of diffusion models to wider domains are introduced. We put special emphasis on the ability of diffusion models as a crucial foundation model, with modalities ranging from image, 3D assets, and video. The role of diffusion models as a general foundation model leads to its versatility in many of the downstream tasks such as solving inverse problems and image editing. Through this review, we aim to provide a thorough and accessible compendium for both newcomers and seasoned researchers in the field.

신제품 수용$\cdot$확산모형에 관한 연구 (A Study on Adoption/Diffusion Models for New Product)

  • 김용준;박영근
    • 산업경영시스템학회지
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    • 제10권16호
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    • pp.149-158
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    • 1987
  • The Adoption/Diffusion of Innovations(New Product), a topic of study and research that has frown rapidly in the past few decades, deals with how a new product is adopted in a society. It is of high importance to marketing organizations because New Products must be brought out continuously in order to service. The purpose of this paper is to examine the Adoption/Diffusion Models for New product which will help to analyze the Adoption/Diffusion process of Adopters. There are a number of models that, with varying degrees of success, have been used to predict market acceptance of new product. In this paper, following types of new product Adoption/Diffusion Models was suggested. (1) Adoption Models : The Alternative Models of Adoption. The Rogers Model of the Innovation Decision Process. (2) Diffusion Models : First Purchase Models(Basic Models, Extension of the Basic Models), Repeat Purchase Models

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세계 유선인터넷 서비스에 대한 확산모형의 예측력 비교 (Comparative Evaluation of Diffusion Models using Global Wireline Subscribers)

  • 민의정;임광선
    • Journal of Information Technology Applications and Management
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    • 제21권4_spc호
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    • pp.403-414
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    • 2014
  • Forecasting technology in economic activity is a quite intricate procedure so researchers should grasp the point of the data to use. Diffusion models have been widely used for forecasting market demand and measuring the degree of technology diffusion. However, there is a question that a model, explaining a certain market with goodness of fit, always shows good performance with markets of different conditions. The primary aim of this paper is to explore diffusion models which are frequently used by researchers, and to help readers better understanding on those models. In this study, Logistic, Gompertz and Bass models are used for forecasting Global Wireline Subscribers and the performance of models is measured by Mean Absolute Percentage Error. Logistic model shows better MAPE than the other two. A possible extension of this study may verify which model reflects characteristics of industry better.

확산이론 관점에서 로지스틱 모형과 Bass 모형의 비교 (Comparison of the Bass Model and the Logistic Model from the Point of the Diffusion Theory)

  • 홍정식;구훈영
    • 한국경영과학회지
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    • 제37권2호
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    • pp.113-125
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    • 2012
  • The logistic model and the Bass model have diverse names and formulae in diffusion theory. This diversity makes users or readers confused while it also contributes to the flexibility of modeling. The method of handling the integration constant, which is generated in process of deriving the closed form solution of the differential equation for a diffusion model, results in two different 'actual' models. We rename the actual four models and propose the usage of the models with respect to the purpose of model applications. The application purpose would be the explanation of historical diffusion pattern or the forecasting of future demand. Empirical validation with 86 historical diffusion data shows that misuse of the models can draw improper conclusions for the explanation of historical diffusion pattern.

생물 종의 개체 수 변화를 기술하는 수학적 모델의 확산현상 표현에 대한 역사적 고찰 (A Historical Study on the Representations of Diffusion Phenomena in Mathematical Models for Population Changes of Biological Species)

  • 심성아
    • 한국수학사학회지
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    • 제29권6호
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    • pp.353-363
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    • 2016
  • In mathematical population ecology which is an academic field that studies how populations of biological species change as times flows at specific locations in their habitats, PDE models have been studied in many aspects and found to have different properties from the classical ODE models. And different approaches to PDE type models in mathematical biology are still being tried currently. This article investigate various forms to express diffusion effects and review the history of PDE models involving diffusion terms in mathematical ecology. Semi-linear systems representing the spatial movements of each individual as random simple diffusion and quasi-linear systems describing more complex diffusions reflecting interspecific interactions are studied. Also it introduce a few of important problems to be solved in this field.

확산모형에 대한 누율생성함수의 근사와 가우도 추정법 (An Approximation of the Cumulant Generating Functions of Diffusion Models and the Pseudo-likelihood Estimation Method)

  • 이윤동;이은경
    • 한국경영과학회지
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    • 제38권1호
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    • pp.201-216
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    • 2013
  • Diffusion is a basic mathematical tool for modern financial engineering. The theory of the estimation methods for diffusion models is an important topic of the financial engineering. Many researches have been tried to apply the likelihood estimation method for estimating diffusion models. However, the likelihood estimation method for diffusion is complicated and needs much amount of computing. In this paper we develop the estimation methods which are simple enough to be compared to the Euler approximation method, and efficient enough statistically to be compared to the likelihood estimation method. We devise pseudo-likelihood and propose the maximum pseudo-likelihood estimation methods. The pseudo-likelihoods are obtained by approximating the transition density with normal distributions. The means and the variances of the distributions are obtained from the delta expansion suggested by Lee, Song and Lee (2012). We compare the newly suggested estimators with other existing estimators by simulation study. From the simulation study we find the maximum pseudo-likelihood estimator has very similar properties with the maximum likelihood estimator. Also the maximum pseudo-likelihood estimator is easy to apply to general diffusion models, and can be obtained by simple numerical steps.

브라운다리 근사를 통한 확산모형의 우도 근사법 (Likelihood Approximation of Diffusion Models through Approximating Brownian Bridge)

  • 이은경;심송용;이윤동
    • 응용통계연구
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    • 제28권5호
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    • pp.895-906
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    • 2015
  • 확산모형은 입자의 운동현상과 금융자산의 미시적 가격변동을 설명하기 위하여 사용되는 수리적 모형이다. 확산모형의 추정방법에 관한 논의는 다양한 분야에서 이루어져 왔다. 통계학적 관점에서 우도적 방법에 기반한 확산모형의 추정방법을 개발하려는 시도가 계속되어 왔다. 이산시간 간격으로 관측된 자료를 이용하여 확산모형을 추정할 때 최대우도 추정법을 적용하기 위해서는 확산모형에 대한 전이확률 밀도함수를 구해야 한다. 본 연구에서는 확산모형의 전이확률밀도를 근사하기 위하여, 정규분포를 따르는 확률변수를 이용하여 브라운다리 확률과정에 대한 경로적분을 대체하는 방법을 제안하고, 그 수치적 성질을 다른 방법들과 비교한다.

Generalized Replacement Demand Forecasting to Complement Diffusion Models

  • Chung, Kyu-Suk;Park, Sung-Joo
    • 대한산업공학회지
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    • 제14권1호
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    • pp.103-117
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    • 1988
  • Replacement demand plays an important role to forecast the total demand of durable goods, while most of the diffusion models deal with only adoption data, namely initial purchase demand. This paper presents replacement demand forecasting models incorporating repurchase rate, multi-ownership, and dynamic product life to complement the existing diffusion models. The performance of replacement demand forecasting models are analyzed and practical guidelines for the application of the models are suggested when life distribution data or adoption data are not available.

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메탄-수소 층류확산화염에서 $H_2$와 H의 선호확산이 NO 거동에 미치는 영향에 관한 연구 (A Study on NO Emission Behavior through Preferential Diffusion of $H_2$ and H in $CH_4-H_2$ Laminar Diffusion Flames)

  • 박정;권오붕;윤진한;길상인
    • 한국수소및신에너지학회논문집
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    • 제18권3호
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    • pp.265-274
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    • 2007
  • A study has been conducted to clarify NO emission behavior through preferential diffusion effects of $H_2$ and H in methane-hydrogen diffusion flames. A comparison is made by employing three species diffusion models. Special concerns are focused on what is the deterministic role of the preferential diffusion effects in flame structure and NO emission. The behavior of maximum flame temperatures with three species diffusion models is not explained by scalar dissipation rate but the nature of chemical kinetics. The preferential diffusion of H into reaction zone suppresses the populations of the chain carrier radicals and then flame temperature while that of $H_2$ produces the increase of flame temperature. These preferential diffusion effects of $H_2$ and H are also discussed about NO emissions through the three species diffusion models.

메탄-수소 대향류확산화염에서 H2와 H의 선호확산을 통한 화학적 효과에 관한 연구 (A Study on Chemical Effecta Through Preferential Diffusion of H2 and H in CH4-H2 Counterflow Diffusion Flames)

  • 박정;권오붕;이의주;윤진한;길상인
    • 대한기계학회논문집B
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    • 제31권12호
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    • pp.1009-1016
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    • 2007
  • Numerical study on preferential diffusion effects in flame structure in $CH_4-H_2$ diffusion flames is conducted with detailed chemistry. Comparison of flame structures with mixture-averaged species diffusion and suppression of the diffusivities of $H_2$ and H was made. Discernible differences in flame structures are displayed with three species diffusion models. The behaviors of maximum flame temperatures with those species diffusion models are not explained by scalar dissipation rate but by the nature of chemical kinetics. It is seen that the modifcation of flame structure is mainly due to the preferential diffusion of H2 and thereby the nature of chemical kinetics. It is also found that the behaviors of major species with the three species diffusion models are addressed to the nature of chemical kinetics, and this is evident by examining importantly contributing reaction steps to the production and destruction of those chemical species.