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The probability density function of stochastic differential equations is governed by the Fokker-Planck (FP) equation.
G. Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of Control Signals & Systems 2 (1989) 303–314
1989
Earlier work this paper cites.
R. L. Honeycutt, Stochastic Runge-Kutta algorithms. i. white noise, Physical Review A 45 (1992) 600
1992
Earlier work this paper cites.
B. P. van Milligen, V. V. Tribaldos, J. A. Jiménez, Neural network differential equation and plasma equilibrium solver, Physical Review Letters 75 (1995) 3594
1995
Earlier work this paper cites.
J. Elgin, The Fokker-Planck equation: Methods of solution and applications, Optica Acta International Journal of Optics 31 (1996) 1206–1207
1996
Earlier work this paper cites.
C. Zhu, R. H. Byrd, P. Lu, J. Nocedal, Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, Acm Transactions on Mathematical Software 23 (1997) 550–560
1997
Earlier work this paper cites.
A. N. Drozdov, Accurate path integral representations of the Fokker-Planck equation with a linear reference system: Comparative study of current theories, Physical Review E 57 (1998) 146–158
1998
Earlier work this paper cites.
I. E. Lagaris, A. Likas, D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE Transactions on Neural Networks 9 (1998) 987–1000
1998
Earlier work this paper cites.
M. Escobedo, M. A. Herrero, J. J. L. Velazquez, Radiation dynamics in homogeneous plasma, Physica D 126 (1999) 236–260
1999
Earlier work this paper cites.
T. Leephakpreeda, Novel determination of differential-equation solutions: universal approximation method, Journal of Computational and Applied Mathematics 146 (2002) 443–457
2002
Earlier work this paper cites.
H. Karcher, S. Lee, M. Kaazempurmofrad, R. Kamm, A coarse-grained model for force-induced protein deformation and kinetics, Biophysical Journal 90 (2006) 2686–2697
2006
Earlier work this paper cites.
A. Malek, R. S. Beidokhti, Numerical solution for high order differential equations using a hybrid neural network-optimization method, Applied Mathematics & Computation 183 (2006) 260–271
2006
Earlier work this paper cites.
R. F. Galán, E. G Bard, N. N. Urban, Stochastic dynamics of uncoupled neural oscillators: Fokker-Planck studies with the finite element method, Physical Review E 76 (2007) 056110
2007
Earlier work this paper cites.
M. Chandrika, Y. N. Kaznessis, Path-integral method for predicting relative binding affinities of protein-ligand complexes, Journal of the American Chemical Society 131 (2009) 4521–8
2009
Earlier work this paper cites.
R. S. Beidokhti, A. Malek, Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques, Journal of the Franklin Institute 346 (2009) 898–913
2009
Cited alongside, same era.
J. Biazar, P. Gholamin, K. Hosseini, Variational iteration method for solving Fokker-Planck equation, Journal of the Franklin Institute 347 (2010) 1137–1147
2010
Cited alongside, same era.
Y. Zheng, C. Li, Z. Zhao, A fully discrete discontinuous Galerkin method for nonlinear fractional Fokker-Planck equation, Mathematical Problems in Engineering 2010 (2010) 279038
2010
Cited alongside, same era.
M. Torvattanabun, S. Duangpithak, Numerical simulations of Fokker-Planck equation by variational iteration method, International Journal of Mathematical Analysis 5 (2011) 2193–2201
2011
Cited alongside, same era.
I. S. M. Fokou, C. N. D. Buckjohn, M. S. Siewe, C. Tchawoua, Probabilistic behavior analysis of a sandwiched buckled beam under gaussian white noise with energy harvesting perspectives, Chaos Solitons & Fractals 92 (2016) 101–114
2016
Later among the works it cites.
G. Furioli, A. Pulvirenti, E. Terraneo, G. Toscani, Fokker-Planck equations in the modeling of socio-economic phenomena, Mathematical Models & Methods in Applied Sciences 27 (2016) 44
2016
Later among the works it cites.
Z. Sun, J. Carrillo, C. W. Shu, A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials, Journal of Computational Physics 352 (2017) 76–104
2017
Later among the works it cites.
M. Schirmer, M. Lehning, J. Schweizer, Statistical forecasting of regional avalanche danger using simulated snow-cover data, Journal of Glaciology 55 (2017) 761–768
2017
Later among the works it cites.
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Y. Xu, J. Feng, J. Li, H. Zhang, Lévy noise induced switch in the gene transcriptional regulatory system, Chaos 23 (2013) 013110
2013
Cited alongside, same era.
I. Norio, G. Kosuke, Thermal fluctuations and stability of a particle levitated by a repulsive casimir force in a liquid, Physical Review E 88 (2013) 052133
2013
Cited alongside, same era.
J. Náprstek, R. Král, Finite element method analysis of Fokker-Planck equation in stationary and evolutionary versions, Advances in Engineering Software 72 (2014) 28–38
2014
Cited alongside, same era.
B. M. Grafov, Fokker-Planck equations for stochastic diffusion associated with Markovian electrochemical noise, Russian Journal of Electrochemistry 51 (2015) 278–280
2015
Cited alongside, same era.
Y. Jiang, A new analysis of stability and convergence for finite difference schemes solving the time fractional Fokker-Planck equation, Applied Mathematical Modelling 39 (2015) 1163–1171
2015
Cited alongside, same era.
B. Sepehrian, M. K. Radpoor, Numerical solution of non-linear Fokker-Planck equation using finite differences method and the cubic spline functions, Applied Mathematics & Computation 262 (2015) 187–190
2015
Cited alongside, same era.
E. Hirvijoki, T. Kurki-Suonio, S. Äkäslompolo, J. Varje, T. Koskela, J. Miettunen, Monte Carlo method and high performance computing for solving Fokker-Planck equation of minority plasma particles, Journal of Plasma Physics 81 (2015) 435810301
2015
Cited alongside, same era.
Z. Wang, Y. Xu, H. Yang, Lévy noise induced stochastic resonance in an FHN model, Science china technological sciences 59 (2016) 371–375
2016
Cited alongside, same era.
A. Ceccato, D. Frezzato, Remarks on the chemical Fokker-Planck and Langevin equations: Nonphysical currents at equilibrium, Journal of Chemical Physics 148 (2018) 064114
2018
Later among the works it cites.
D. Barrow, N. Kourentzes, The impact of special days in call arrivals forecasting: A neural network approach to modelling special days, European Journal of Operational Research 264 (2018) 967–977
2018
Later among the works it cites.
J. Berg, K. Nyström, A unified deep artificial neural network approach to partial differential equations in complex geometries, Neurocomputing 317 (2018) 28–41
2018
Later among the works it cites.
J. Han, A. Jentzen, E. Weinan, Solving high-dimensional partial differential equations using deep learning, Proceedings of the National Academy of Sciences 115 (2018) 8505–8510
2018
Later among the works it cites.
J. Sirignano, K. Spiliopoulos, DGM: A deep learning algorithm for solving partial differential equations, Journal of Computational Physics 375 (2018) 1339–1364
2018
Later among the works it cites.
Y. Xu, W. Zan, W. Jia, J. Kurths, Path integral solutions of the governing equation of SDEs excited by Lévy white noise, Journal of Computational Physics 394 (2019) 41–45
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