메뉴 건너뛰기




Volumn 9, Issue 1, 2009, Pages 20-29

Multilayer perceptron neural networks with novel unsupervised training method for numerical solution of the partial differential equations

Author keywords

Hydrogen atom; Multilayer perceptron; Nonlinear Schrodinger equation; Ordinary differential equation; Partial differential equation; Radial basis function; Triangle shaped quantum well

Indexed keywords

ARTIFICIAL INTELLIGENCE; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; COMPUTATIONAL FLUID DYNAMICS; CONTROL NONLINEARITIES; CONTROL THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); ELECTRIC LOADS; FEEDFORWARD NEURAL NETWORKS; FINITE ELEMENT METHOD; HYDROGEN; IMAGE SEGMENTATION; MULTILAYER NEURAL NETWORKS; MULTILAYERS; NETWORK PROTOCOLS; NONLINEAR EQUATIONS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RADIAL BASIS FUNCTION NETWORKS; RUNGE KUTTA METHODS; SCHRODINGER EQUATION; SENSOR NETWORKS;

EID: 53749088345     PISSN: 15684946     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.asoc.2008.02.003     Document Type: Article
Times cited : (114)

References (36)
  • 2
    • 0032002859 scopus 로고    scopus 로고
    • Characterizing the dynamics of constrained physical systems with unsupervised neural network
    • Monterola C., and Saloma C. Characterizing the dynamics of constrained physical systems with unsupervised neural network. Phys. Rev. E (1998) 1247R-1250R
    • (1998) Phys. Rev. E
    • Monterola, C.1    Saloma, C.2
  • 4
    • 0001742775 scopus 로고
    • Computational complexity and observation of physical signals
    • Saloma C. Computational complexity and observation of physical signals. J. Appl. Phys. 74 (1993) 53149
    • (1993) J. Appl. Phys. , vol.74 , pp. 53149
    • Saloma, C.1
  • 6
    • 0028543366 scopus 로고
    • Training feedforward neural network with the Marquardt algorithm
    • Hagan M.T., and Menhaj M.B. Training feedforward neural network with the Marquardt algorithm. IEEE Trans. Neural Netw. 5 6 (1994)
    • (1994) IEEE Trans. Neural Netw. , vol.5 , Issue.6
    • Hagan, M.T.1    Menhaj, M.B.2
  • 10
    • 0036679717 scopus 로고    scopus 로고
    • Quantum mechanical analysis of the equilateral triangle billiard: periodic orbit theory and wave packet revivals
    • Doncheski M.A., and Robinett R.W. Quantum mechanical analysis of the equilateral triangle billiard: periodic orbit theory and wave packet revivals. Ann. Phys. 299 (2002) 208-227
    • (2002) Ann. Phys. , vol.299 , pp. 208-227
    • Doncheski, M.A.1    Robinett, R.W.2
  • 11
    • 4243777814 scopus 로고    scopus 로고
    • Quantum wave packet revivals in circular billiards
    • Robinett R.W., and Heppelmann S. Quantum wave packet revivals in circular billiards. Phys. Rev. A 65 (2002) 062103-1-062103-10
    • (2002) Phys. Rev. A , vol.65
    • Robinett, R.W.1    Heppelmann, S.2
  • 17
    • 0032165970 scopus 로고    scopus 로고
    • Artificial neural networks for solving ordinary and partial differential equations
    • Lagaris L.E., Likas A., and Fotiadis D.I. Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Netw. 9 5 (1998)
    • (1998) IEEE Trans. Neural Netw. , vol.9 , Issue.5
    • Lagaris, L.E.1    Likas, A.2    Fotiadis, D.I.3
  • 20
    • 33846586018 scopus 로고    scopus 로고
    • Quantum scattering via the discretisation of Schrdingers equation
    • Alexopoulos A. Quantum scattering via the discretisation of Schrdingers equation. Phys. Lett. A 363 (2007) 66-70
    • (2007) Phys. Lett. A , vol.363 , pp. 66-70
    • Alexopoulos, A.1
  • 21
    • 33845451254 scopus 로고    scopus 로고
    • Symplectic methods for the numerical integration of the Schrodinger equation
    • Monovasilis Th., and Simos T.E. Symplectic methods for the numerical integration of the Schrodinger equation. Computat. Mater. Sci. 38 (2007) 526-532
    • (2007) Computat. Mater. Sci. , vol.38 , pp. 526-532
    • Monovasilis, Th.1    Simos, T.E.2
  • 22
    • 33846136410 scopus 로고    scopus 로고
    • Solution of time-independent Schrodinger equation by the imaginary time propagation method
    • Lehtovaara L., Toivanen J., and Eloranta J. Solution of time-independent Schrodinger equation by the imaginary time propagation method. J. Comput. Phys. 221 (2007) 148-157
    • (2007) J. Comput. Phys. , vol.221 , pp. 148-157
    • Lehtovaara, L.1    Toivanen, J.2    Eloranta, J.3
  • 23
    • 33750460951 scopus 로고    scopus 로고
    • Solution of the time-dependent, multi-particle Schrodinger equation using Monte Carlo and numerical integration
    • Mazzone A.M., and Morandi V. Solution of the time-dependent, multi-particle Schrodinger equation using Monte Carlo and numerical integration. Comput. Mater. Sci. 38 (2006) 231-239
    • (2006) Comput. Mater. Sci. , vol.38 , pp. 231-239
    • Mazzone, A.M.1    Morandi, V.2
  • 24
    • 0022695120 scopus 로고
    • Stable explicit schemes for equations of the Schrodinger type
    • Chan T.F., Lee D., and Shen L. Stable explicit schemes for equations of the Schrodinger type. SIAM J. Numer. Anal. 23 (1986) 274-281
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 274-281
    • Chan, T.F.1    Lee, D.2    Shen, L.3
  • 25
    • 0005727359 scopus 로고    scopus 로고
    • Multi-symplectic Fourier pseuospectral method for the nonlinear Schrodinger equation
    • Chen J.B., and Qin M.Z. Multi-symplectic Fourier pseuospectral method for the nonlinear Schrodinger equation. Electron. Trans. Numer. Anal. 12 (2001) 193-204
    • (2001) Electron. Trans. Numer. Anal. , vol.12 , pp. 193-204
    • Chen, J.B.1    Qin, M.Z.2
  • 26
    • 0000902090 scopus 로고
    • A numerical study of the nonlinear Schrodinger equation involving quintic terms
    • Cloot A., Herbst B.M., and Weideman J.A.C. A numerical study of the nonlinear Schrodinger equation involving quintic terms. J. Comput. Phys. 86 (1990) 127-146
    • (1990) J. Comput. Phys. , vol.86 , pp. 127-146
    • Cloot, A.1    Herbst, B.M.2    Weideman, J.A.C.3
  • 27
    • 0026818262 scopus 로고
    • An unconditionally stable three-level explicit difference scheme for the Schrodinger equation with a variable coefficient
    • Dai W. An unconditionally stable three-level explicit difference scheme for the Schrodinger equation with a variable coefficient. SIAM J. Numer. Anal. 29 (1992) 174-181
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 174-181
    • Dai, W.1
  • 28
    • 27844570513 scopus 로고    scopus 로고
    • On the stability of the FDTD method for solving a time-dependent Schrodinger equation
    • Dai W., Li G., Nassar R., and Su S. On the stability of the FDTD method for solving a time-dependent Schrodinger equation. Numer. Methods Partial Differ. Eq. 21 (2005) 1140-1154
    • (2005) Numer. Methods Partial Differ. Eq. , vol.21 , pp. 1140-1154
    • Dai, W.1    Li, G.2    Nassar, R.3    Su, S.4
  • 29
    • 49149137309 scopus 로고
    • Finite-difference solutions of a non-linear Schrodinger equation
    • Delfour M., Fortin M., and Payre G. Finite-difference solutions of a non-linear Schrodinger equation. J. Comput. Phys. 44 (1981) 277-288
    • (1981) J. Comput. Phys. , vol.44 , pp. 277-288
    • Delfour, M.1    Fortin, M.2    Payre, G.3
  • 30
    • 0001257175 scopus 로고
    • Numerical experience with the nonlinear Schrodinger equation
    • Herbst B.M., Morris J.L., and Michell A.R. Numerical experience with the nonlinear Schrodinger equation. J. Comput. Phys. 60 (1985) 282-305
    • (1985) J. Comput. Phys. , vol.60 , pp. 282-305
    • Herbst, B.M.1    Morris, J.L.2    Michell, A.R.3
  • 31
    • 0041730125 scopus 로고    scopus 로고
    • On convergence and stabili of the explicit difference method for solution of nonlinear Schrodinger equation
    • Ivanauskas F., and Radziunas M. On convergence and stabili of the explicit difference method for solution of nonlinear Schrodinger equation. SIAM J. Numer. Anal. 36 (1999) 1466-1481
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1466-1481
    • Ivanauskas, F.1    Radziunas, M.2
  • 32
    • 0031568191 scopus 로고    scopus 로고
    • Efficient difference solutions to the time-dependent Schrodinger equation
    • Nash P.L., and Chen L.Y. Efficient difference solutions to the time-dependent Schrodinger equation. J. Comput. Phys. 130 (1997) 266-268
    • (1997) J. Comput. Phys. , vol.130 , pp. 266-268
    • Nash, P.L.1    Chen, L.Y.2
  • 33
    • 84961470712 scopus 로고
    • Methods for the numerical solution of the Schrodinger equation
    • Sanz-Serna J.M. Methods for the numerical solution of the Schrodinger equation. Math. Comput. 43 (1984) 21-27
    • (1984) Math. Comput. , vol.43 , pp. 21-27
    • Sanz-Serna, J.M.1
  • 34
    • 0001028014 scopus 로고
    • A method for the integration in time of certain partial differential equations
    • Sanz-Serna J.M., and Manoranjan V.S. A method for the integration in time of certain partial differential equations. J. Comput. Phys. 52 (1983) 273-289
    • (1983) J. Comput. Phys. , vol.52 , pp. 273-289
    • Sanz-Serna, J.M.1    Manoranjan, V.S.2
  • 35
    • 48549114390 scopus 로고
    • Analytic and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrodinger equation
    • Taha T.R., and Ablowitz M.J. Analytic and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrodinger equation. J. Comput. Phys. 55 (1984) 203-230
    • (1984) J. Comput. Phys. , vol.55 , pp. 203-230
    • Taha, T.R.1    Ablowitz, M.J.2
  • 36
    • 0011495032 scopus 로고    scopus 로고
    • DufortFrankel-type methods for linear and nonlinear Schrodinger equation
    • Wu L. DufortFrankel-type methods for linear and nonlinear Schrodinger equation. SIAM J. Numer. Anal. 33 (1996) 1526-1533
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1526-1533
    • Wu, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.