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The Fokker-Planck (FP) equation is a linear partial differential equation which governs the temporal and spatial evolution of the probability density function (PDF) associated with the response of stochastic dynamical systems.
Nonlinear control systems with random inputs
Booton, R. C · 1954
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Study of the Random Vibration of Nonlinear Systems by the Gaussian Closure Technique
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Non-gaussian closure for random vibration of non-linear oscillators
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Stochastic jump and bifurcation of a duffing oscillator under narrow-band excitation
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Probabilistic structural dynamics
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High fidelity numerical solutions of the fokker-planck equation
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Introduction to multi-layer feed-forward neural networks
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Griewank, A. & Walther, A · 2008
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Some instances of the fokker-planck equation numerical analysis for systems with gaussian noises
Náprstek, J. & Král, R · 2008
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Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator
Finite element solution of fokker–planck equation of nonlinear oscillators subjected to colored non-gaussian noise
Kumar, P., Narayanan, S. & Gupta, S · 2014
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Sparse grid discontinuous galerkin methods for high-dimensional elliptic equations
Wang, Z., Tang, Q., Guo, W. & Cheng, Y · 2016
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Investigations on the bifurcation of a noisy duffing–van der pol oscillator
Kumar, P., Narayanan, S. & Gupta, S · 2016
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Impact of correlated noise in an energy depot model
Zeng, C., Zeng, J., Liu, F. & Wang, H · 2016
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Activation functions: Comparison of trends in practice and research for deep learning
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Zakharova, A., Vadivasova, T., Anishchenko, V., Koseska, A. & Kurths, J · 2010
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Understanding the difficulty of training deep feedforward neural networks
Glorot, X. & Bengio, Y · 2010
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Transfer learning
Torrey, L. & Shavlik, J · 2010
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A new method for the probabilistic solutions of large-scale nonlinear stochastic dynamic systems
Er, G. & Iu, V · 2011
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Miwadinou, C., Hinvi, L., Monwanou, A. & Orou, J · 2013
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Numerical solution of the fokker–planck equation by finite difference and finite element methods—a comparative study
Pichler, L., Masud, A. & Bergman, L. A · 2013
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Random vibration with inelastic impact: equivalent nonlinearization technique
Xu, M., Wang, Y., Jin, X. & Huang, Z · 2014
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Modeling nonlinear dissipative chemical dynamics by a forced modified van der pol-duffing oscillator with asymmetric potential: chaotic behaviors predictions
Miwadinou, C. et al · 2018
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Raissi, M., Perdikaris, P. & Karniadakis, G. E · 2019
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Solving fokker-planck equation using deep learning
Xu, Y. et al · 2019
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Solving inverse stochastic problems from discrete particle observations using the fokker–planck equation and physics-informed neural networks
Chen, X., Yang, L., Duan, J. & Karniadakis, G. E · 2021
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A deep learning method for solving fokker-planck equations
Zhai, J., Dobson, M. & Li, Y · 2022
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Monte carlo fpinns: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations
Guo, L., Wu, H., Yu, X. & Zhou, T · 2022
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Matlab version: 9.13.0 (r2022b) (2022)
Inc., T. M · 2022
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