• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제28권1호
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• pp.33-58
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• 2024

This paper reviews basic concepts for Physics-Informed Neural Networks (PINN) applied to the initial value problems for ordinary differential equations. In particular, using only basic calculus, we derive the error estimates where the error functions (the differences between the true solution and the approximations expressed by neural networks) are dominated by training loss functions. Numerical experiments are conducted to validate our error estimates, visualizing the relationship between the error and the training loss for various first-order differential equations and a second-order linear equation.

• Computers and Concrete
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• 제32권4호
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• pp.399-410
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• 2023

This study proposes a novel use of backpropagated Levenberg-Marquardt neural networks based on computational intelligence heuristics to comprehend the examination of hybrid nanoparticles on the flow of dusty liquid via stretched cylinder. A two-phase model is employed in the present work to describe the fluid flow. The use of desulphated nanoparticles of silver and molybdenum suspended in water as base fluid. The mathematical model represented in terms of partial differential equations, Implementing similarity transformationsis model is converted to ordinary differential equations for the analysis . By adjusting the particle mass concentration and curvature parameter, a unique technique is utilized to generate a dataset for the proposed Levenberg-Marquardt neural networks in various nanoparticle circumstances on the flow of dusty liquid via stretched cylinder. The intelligent solver Levenberg-Marquardt neural networks is trained, tested and verified to identify the nanoparticles on the flow of dusty liquid solution for various situations. The Levenberg-Marquardt neural networks approach is applied for the solution of the hybrid nanoparticles on the flow of dusty liquid via stretched cylinder model. It is validated by comparison with the standard solution, regression analysis, histograms, and absolute error analysis. Strong agreement between proposed results and reference solutions as well as accuracy provide an evidence of the framework's validity.

• Advances in Computational Design
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• 제7권1호
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• pp.1-17
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• 2022

In this study, a new strategy is presented to transmit the fundamental elastic beam problem into the modern optimization platform and solve it by using artificial intelligence (AI) tools. As a practical example, deflection of Euler-Bernoulli beam is mathematically formulated by 2nd-order ordinary differential equations (ODEs) in accordance to the classical beam theory. This fundamental engineer problem is then transmitted from classic formulation to its artificial-intelligence presentation where the behavior of the beam is simulated by using neural networks (NNs). The supervised training strategy is employed in the developed NNs implemented in the heuristic optimization algorithms as the fitness function. Different evolutionary optimization tools such as genetic algorithm (GA) and particle swarm optimization (PSO) are used to solve this non-linear optimization problem. The step-by-step procedure of the proposed method is presented in the form of a practical flowchart. The results indicate that the proposed method of using AI toolsin solving beam ODEs can efficiently lead to accurate solutions with low computational costs, and should prove useful to solve more complex practical applications.

• 한국컴퓨터정보학회:학술대회논문집
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• 한국컴퓨터정보학회 2023년도 제68차 하계학술대회논문집 31권2호
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• pp.5-6
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• 2023

본 연구에서는 언텍트 소비가 일반화됨에 따라 소상공인들을 지원하기 위해 캡티브-포털을 활용하여 주문하는 등의 시스템을 구축하고 있으며, 이에 상권 내 방문자들의 주문 정보를 기반으로 개인의 선호나 취향을 고려하고 기존 방문 순서를 고려하여 다음 방문지를 추천할 수 있는 모델을 개발하고자 한다. 모델 개발을 위한 데이터셋으로는 캡티브-포털을 통해 수집되는 변수 항목과 유사한 위치기반 SNS 데이터인 Foursquare 데이터를 활용했다. 본 논문에서는 데이터셋의 변수 중 상호명을 기반으로 22개의 행동 유형 카테고리로 묶어 현재 행동 유형 이후에 다음에 이어질 행동 유형을 예측하는 것을 제안한다. 개인 별 세션 기반의 데이터셋을 LightMove 알고리즘을 활용하여 행동유형 예측을 임베딩 차원의 변경하여 실험한 결과 500차원에서 Top-5가 82.72의 성능을 보임을 확인했다. 향후 국내 상권에 맞는 방문지 추천 시스템이 개발된다면 방문지 추천을 활용하여 다양한 마케팅 전략을 수립이 가능해질 수 있고, 이를 통해 지역 상권이 활성화될 것으로 기대된다.