• Title/Summary/Keyword: method of fundamental solution

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Solving partial differential equation for atmospheric dispersion of radioactive material using physics-informed neural network

  • Gibeom Kim;Gyunyoung Heo
    • Nuclear Engineering and Technology
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    • v.55 no.6
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    • pp.2305-2314
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    • 2023
  • The governing equations of atmospheric dispersion most often taking the form of a second-order partial differential equation (PDE). Currently, typical computational codes for predicting atmospheric dispersion use the Gaussian plume model that is an analytic solution. A Gaussian model is simple and enables rapid simulations, but it can be difficult to apply to situations with complex model parameters. Recently, a method of solving PDEs using artificial neural networks called physics-informed neural network (PINN) has been proposed. The PINN assumes the latent (hidden) solution of a PDE as an arbitrary neural network model and approximates the solution by optimizing the model. Unlike a Gaussian model, the PINN is intuitive in that it does not require special assumptions and uses the original equation without modifications. In this paper, we describe an approach to atmospheric dispersion modeling using the PINN and show its applicability through simple case studies. The results are compared with analytic and fundamental numerical methods to assess the accuracy and other features. The proposed PINN approximates the solution with reasonable accuracy. Considering that its procedure is divided into training and prediction steps, the PINN also offers the advantage of rapid simulations once the training is over.

Numerical solution of beam equation using neural networks and evolutionary optimization tools

  • Babaei, Mehdi;Atasoy, Arman;Hajirasouliha, Iman;Mollaei, Somayeh;Jalilkhani, Maysam
    • Advances in Computational Design
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    • v.7 no.1
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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.

Optimal Design of Fluid Mount Using Artificial Life Algorithm (인공생명 알고리듬을 이용한 유체마운트의 최적설계)

  • 안영공;송진대;양보석;김동조
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.12 no.8
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    • pp.598-608
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    • 2002
  • This paper shows the optimal design methodology for the fluid engine mount by the artificial life algorithm. The design has been commonly modified by trial and error because there is many design parameters that can be varied in order to minimize transmissibility at the desired fundamental resonant and notch frequencies. The application of trial and error method to optimization of the fluid mount is a great work. Many combinations of parameters are possible to give us the desired resonant and notch frequencies, but the question is which combination Provides the lowest resonant peak and notch depth. In this study the enhanced artificial life algorithm is applied to get the desired fundamental resonant and notch frequencies of a fluid mount and to minimize transmissibility at these frequencies. The present hybrid algorithm is the synthesis of and artificial life algorithm with the random tabu (R-tabu) search method. The hybrid algorithm has some advantages, which is not only faster than the conventional artificial life algorithm, but also gives a more accurate solution. In addition, this algorithm can find all globa1 optimum solutions. The results show that the performance of the optimized mount compared with the original mount is improved significantly.

The Fundamental Study on the Properties of Foam for Foamed Concrete (기포 콘크리트용 기포의 특성에 관한 기초 연구)

  • Kawg, Eun-Gu;Kang, Gie-Hyun;Kang, Cheol;Kwon, Ki-Joo;Kim, Jin-Man
    • Proceedings of the Korea Concrete Institute Conference
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    • 2004.05a
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    • pp.680-683
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    • 2004
  • This study is to obtain basic data concerned with properties of foam for foamed concrete and foaming method. Main factors of this study are types of foaming agents, temperature of solution with foaming agents, and types of foam generator. Testing items are size distribution of foam, foaming ratio to solution, and stability of foam. The results of this study were shown as follow. It is optimum condition of foam generator that length/diameter of foaming tube is 2.0, bead size within foaming tube is $4\~6mm$, and nozzle size of foaming tube is 10mm. AES and AOS are good results to produce high quality foam, and stability of foam is good in foaming temperature of $20^{\circ}C$.

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Thermodynamic Study of Liquid Pb-Bi, Pb-Na, Bi-Na Binaries and Pb-Bi-Na Ternary Solutions (熔融 Pb-Bi, Pb-Na, Bi-Na 및 Pb-Bi-Na 系의 物理化學的硏究)

  • Koh, Chang-Shik
    • Journal of the Korean Chemical Society
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    • v.6 no.2
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    • pp.133-142
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    • 1962
  • This study was carried out to investigate the lead-bismuth-sodium ternary system which a basis of the Dittmer method as a part of "the fundamental study of pyrometallurgical debismuthizing of lead". Thermodynamic properties of each liquid Pb-Bi, Pb-Na binaries as well as liquid Pb-Bi-Na ternary solution were measured by e.m.f. of these concentration cells, and those of each component were also determined. Furthermore, iso-activity lines including Pb rich side composition of Pb-Bi-Na ternary solution were determined. The relationship between those thermodynamic characteristics and tendency of intermetallic compound formation was discussed through the above experiments.

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Fundamental Study on the CO2 fixation method using the Cement-saturated solution (시멘트 수용액을 이용한 CO2 고정화 방안에 관한 기초적 연구)

  • Kwack, Jae-Seok;Kang, Chang-Soo;Ahn, Hee-Sung;Lee, Han-Seung
    • Proceedings of the Korean Institute of Building Construction Conference
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    • 2011.11a
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    • pp.41-42
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    • 2011
  • The purpose of this study is not only fixation of carbon dioxide using the cement-saturated solution by wet carbonating reaction but also evaluate the possibility of storage technology of Carbon dioxide. wet carbonation is reaction of CO2 injection by CO2 reactor. As a result of experiment, the carbon dioxide is fixed, and high-purity Calcium Carbonate is eluted.

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Fundamental Study on the CO2 gas Fixation Method using the Cement-Paste Solution's Calcium ion (시멘트 페이스트 수용액의 칼슘 이온을 이용한 CO2 가스 고정화에 관한 기초적 연구)

  • Kwack, Jae-Seok;Kang, Chang-Soo;Lee, Han-Seung
    • Proceedings of the Korean Institute of Building Construction Conference
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    • 2012.05a
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    • pp.71-72
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    • 2012
  • The purpose of this study is not only fixation of carbon dioxide using the cement-Paste solution's calcium ion by wet carbonating reaction but also quantitatively evaluate the possibility of storage technology of Carbon dioxide. wet carbonation is reaction of CO2 injection by CO2 reactor. As a result of experiment, the carbon dioxide is fixed, and high-purity Calcium Carbonate is eluted.

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In-Plane Inextensional and Extensional Vibration Analysis of Curved Beams Using DQM (미분구적법(DQM)을 이용한 곡선보의 내평면 비신장 및 신장 진동해석)

  • Kang, Ki-jun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.16 no.11
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    • pp.8064-8073
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    • 2015
  • One of the efficient procedures for the solution of partial differential equations is the method of differential quadrature. This method has been applied to a large number of cases to circumvent the difficulties of the complex algorithms of programming for the computer, as well as excessive use of storage due to conditions of complex geometry and loading. In-plane vibrations of curved beams with inextensibility and extensibility of the arch axis are analyzed by the differential quadrature method (DQM). Fundamental frequencies are calculated for the member with various end conditions and opening angles. The results are compared with exact experimental and numerical results by other methods for cases in which they are available. The DQM gives good accuracy even when only a limited number of grid points is used, and new results according to diverse variation are also suggested.

Desorption Characteristics of $H^{14}CO_3$ ion from Spent Ion Exchanged Resin by Solution Stripping Technology

  • Park Geun-IL;Kim In-Tae;Kim Kwang-Wook;Lee Jung-Won;Won Jang-Sik;Yang Ho-Yeon
    • Proceedings of the Korean Radioactive Waste Society Conference
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    • 2005.11b
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    • pp.214-221
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    • 2005
  • Spent ion-exchanged resin generated from various purification systems in CANDU reactor is causing concern due to a limited storage capacity and safe disposal. As a suggestion for a proper treatment technology for the spent ion-exchanged resin containing a high activity of C­14 radionuclide which would be classified as Class A and C wastes, a fundamental study for the development of C-14 removal technology from a spent resin was performed. The adsorption characteristics of the inactive $HCO_3^-$ ion and other ions in a stripping solution on IRN-150 mixed resin was evaluated and the removal technology of the $HCO_3^-$ ion adsorbed on IRN-150 by an alkaline stripping method was proposed.

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A Study of 2-D Eddy Current Problem Using Boundary Element Method (경계요소법을 이용한 2차원 와전류 문제에 대한 연구)

  • Lim, Eui-Soo;Lee, Hyang-Beom
    • Proceedings of the KIEE Conference
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    • 1999.07a
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    • pp.217-219
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    • 1999
  • This paper presents a study of 2-dimensional(2-D) eddy current problem using boundary element method(BEM). When compared with finite element method(FEM), there are only a few unknown variables in BEM because it implements numerical analysis only for the surface or boundary of a model. As a result, a lot of computational memory and time can be saved. In order to analyze 2-D eddy current problem, potentials and its derivatives(flux) in a boundary are used as variables. The Mantel function of the second kind of the zero order is used here as a fundamental solution. In order to remove singularity and to solve the integral equations in a boundary, Subtracting Singularity Method and Gauss Quadrature Formula are adopted in this paper.

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