The Experts below are selected from a list of 197766 Experts worldwide ranked by ideXlab platform
Tomoaki Ohtsuki - One of the best experts on this subject based on the ideXlab platform.
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polynomial networks representation of Nonlinear mixtures with application in underdetermined blind source separation
International Conference on Acoustics Speech and Signal Processing, 2019Co-Authors: Lu Wang, Tomoaki OhtsukiAbstract:Similar to the deep architectures, a novel multi-layer architecture is used to extend the linear blind source separation (BSS) method to the Nonlinear Case in this paper. The approach approximates the Nonlinearities based on a polynomial network, where the layer of our network begins with the polynomial of degree 1, up to build an output layer that can represent data with a small bias by a good approximate basis. Relying on several transformations of the input data, with higher-level representation from lower-level ones, the networks are to fulfill a mapping implicitly to the high-dimensional space. Once the polynomial networks are built, the coefficient matrix can be estimated by solving an l 1 -regularization on the coding coefficient vector. The experiment shows that the proposed approach exhibits a higher separation accuracy than the comparison algorithms.
Sergei K Turitsyn - One of the best experts on this subject based on the ideXlab platform.
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conditional probability calculations for the Nonlinear schrodinger equation with additive noise
Physical Review Letters, 2014Co-Authors: I S Terekhov, S S Vergeles, Sergei K TuritsynAbstract:The method for the computation of the conditional probability density function for the Nonlinear Schrodinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly Nonlinear Case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.
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conditional probability calculations for the Nonlinear schr odinger equation with additive noise
arXiv: Information Theory, 2014Co-Authors: I S Terekhov, S S Vergeles, Sergei K TuritsynAbstract:The method for computation of conditional probability density function for the Nonlinear Schr\"odinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of a small noise and analytically derive it in a weakly Nonlinear Case. The general theory results are illustrated using fibre-optic communications as a particular, albeit practically very important, example.
Lu Wang - One of the best experts on this subject based on the ideXlab platform.
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polynomial networks representation of Nonlinear mixtures with application in underdetermined blind source separation
International Conference on Acoustics Speech and Signal Processing, 2019Co-Authors: Lu Wang, Tomoaki OhtsukiAbstract:Similar to the deep architectures, a novel multi-layer architecture is used to extend the linear blind source separation (BSS) method to the Nonlinear Case in this paper. The approach approximates the Nonlinearities based on a polynomial network, where the layer of our network begins with the polynomial of degree 1, up to build an output layer that can represent data with a small bias by a good approximate basis. Relying on several transformations of the input data, with higher-level representation from lower-level ones, the networks are to fulfill a mapping implicitly to the high-dimensional space. Once the polynomial networks are built, the coefficient matrix can be estimated by solving an l 1 -regularization on the coding coefficient vector. The experiment shows that the proposed approach exhibits a higher separation accuracy than the comparison algorithms.
Jianfeng Lu - One of the best experts on this subject based on the ideXlab platform.
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a numerical method for coupling the bgk model and euler equations through the linearized knudsen layer
Journal of Computational Physics, 2019Co-Authors: Hongxu Chen, Qin Li, Jianfeng LuAbstract:Abstract The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is small. In practice, however, Knudsen layers emerge at the physical boundary, or at the interfaces between the two regimes. We model the Knudsen layer using a half-space kinetic equation, and apply a half-space numerical solver [19] , [20] to quantify the transition between the kinetic to the fluid regime. A full domain numerical solver is developed with a domain-decomposition approach, where we apply the Euler solver and kinetic solver on the appropriate subdomains and connect them via the half-space solver. In the Nonlinear Case, linearization is performed upon local Maxwellian. Despite the lack of analytical support, the numerical evidence nevertheless demonstrate that the linearization approach is promising.
Germain Maximilien - One of the best experts on this subject based on the ideXlab platform.
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Neural networks-based backward scheme for fully Nonlinear PDEs
'Springer Science and Business Media LLC', 2021Co-Authors: Pham Huyen, Warin Xavier, Germain MaximilienAbstract:International audienceWe propose a numerical method for solving high dimensional fully Nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, while the Hessian is approximated by automatic differentiation of the gradient at previous step. This methodology extends to the fully Nonlinear Case the approach recently proposed in \cite{HPW19} for semi-linear PDEs. Numerical tests illustrate the performance and accuracy of our method on several examples in high dimension with Nonlinearity on the Hessian term including a linear quadratic control problem with control on the diffusion coefficient, Monge-Ampère equation and Hamilton-Jacobi-Bellman equation in portfolio optimization
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Neural networks-based backward scheme for fully Nonlinear PDEs
2021Co-Authors: Pham Huyen, Warin Xavier, Germain MaximilienAbstract:We propose a numerical method for solving high dimensional fully Nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, while the Hessian is approximated by automatic differentiation of the gradient at previous step. This methodology extends to the fully Nonlinear Case the approach recently proposed in \cite{HPW19} for semi-linear PDEs. Numerical tests illustrate the performance and accuracy of our method on several examples in high dimension with Nonlinearity on the Hessian term including a linear quadratic control problem with control on the diffusion coefficient, Monge-Amp{\`e}re equation and Hamilton-Jacobi-Bellman equation in portfolio optimization.Comment: to appear in SN Partial Differential Equations and Application
