The Experts below are selected from a list of 255 Experts worldwide ranked by ideXlab platform
Yikai Su - One of the best experts on this subject based on the ideXlab platform.
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on chip tunable second order Differential Equation Solver based on a silicon photonic mode split microresonator
Journal of Lightwave Technology, 2015Co-Authors: Jiayang Wu, Jizong Peng, Xinhong Jiang, Christine Tremblay, Yikai SuAbstract:We propose and experimentally demonstrate an on-chip all-optical Differential-Equation Solver capable of solving second-order ordinary Differential Equations (ODEs) characterizing continuous-time linear time-invariant systems. The photonic device is implemented by a self-coupled microresonator on a silicon-on-insulator platform with mutual coupling between the cavity modes. Owing to the mutual mode coupling within the same resonant cavity, the resonance wavelengths induced by different cavity modes are self-aligned, thus avoiding precise wavelength alignment and unequal thermal wavelength drifts as in the case of cascaded resonators. By changing the mutual mode coupling strength, the proposed device can be used to solve second-order ODEs with tunable coefficients. System demonstration using the fabricated device is carried out for 10-Gb/s optical Gaussian and super-Gaussian input pulses. The experimental results are in good agreement with theoretical predictions of the solutions, which verify the feasibility of the fabricated device as a tunable second-order photonic ODE Solver.
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compact tunable silicon photonic Differential Equation Solver for general linear time invariant systems
Optics Express, 2014Co-Authors: Jiayang Wu, Yuxing Yang, Xiaofeng Hu, Xinhong Jiang, Christine Tremblay, Yikai SuAbstract:We propose and experimentally demonstrate an all-optical temporal Differential-Equation Solver that can be used to solve ordinary Differential Equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE Solver.
Jian Liang - One of the best experts on this subject based on the ideXlab platform.
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deep learning based least squares forward backward stochastic Differential Equation Solver for high dimensional derivative pricing
Quantitative Finance, 2021Co-Authors: Jian LiangAbstract:We propose a new forward-backward stochastic Differential Equation Solver for high-dimensional derivative pricing problems by combining a deep learning Solver with a least squares regression techni...
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deep learning based least square forward backward stochastic Differential Equation Solver for high dimensional derivative pricing
Social Science Research Network, 2020Co-Authors: Jian LiangAbstract:We propose a new forward-backward stochastic Differential Equation Solver for highdimensional derivative pricing problems by combining deep learning Solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonstrate the accuracy of our least square backward deep neural network Solver and its capability to produce accurate prices for complex early exercise derivatives, such as callable yield notes. Our method can serve as a generic numerical Solver for pricing derivatives across various asset groups, in particular, as an accurate means for pricing high-dimensional derivatives with early exercise features.
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deep learning based least square forward backward stochastic Differential Equation Solver for high dimensional derivative pricing
arXiv: Computational Finance, 2019Co-Authors: Jian Liang, Zhe Xu, Peter LiAbstract:We propose a new forward-backward stochastic Differential Equation Solver for high-dimensional derivatives pricing problems by combining deep learning Solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonstrate the efficiency and accuracy of our least square backward deep neural network Solver and its capability to provide accurate prices for complex early exercise derivatives such as callable yield notes. Our method can serve as a generic numerical Solver for pricing derivatives across various asset groups, in particular, as an efficient means for pricing high-dimensional derivatives with early exercises features.
Jiayang Wu - One of the best experts on this subject based on the ideXlab platform.
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on chip tunable second order Differential Equation Solver based on a silicon photonic mode split microresonator
Journal of Lightwave Technology, 2015Co-Authors: Jiayang Wu, Jizong Peng, Xinhong Jiang, Christine Tremblay, Yikai SuAbstract:We propose and experimentally demonstrate an on-chip all-optical Differential-Equation Solver capable of solving second-order ordinary Differential Equations (ODEs) characterizing continuous-time linear time-invariant systems. The photonic device is implemented by a self-coupled microresonator on a silicon-on-insulator platform with mutual coupling between the cavity modes. Owing to the mutual mode coupling within the same resonant cavity, the resonance wavelengths induced by different cavity modes are self-aligned, thus avoiding precise wavelength alignment and unequal thermal wavelength drifts as in the case of cascaded resonators. By changing the mutual mode coupling strength, the proposed device can be used to solve second-order ODEs with tunable coefficients. System demonstration using the fabricated device is carried out for 10-Gb/s optical Gaussian and super-Gaussian input pulses. The experimental results are in good agreement with theoretical predictions of the solutions, which verify the feasibility of the fabricated device as a tunable second-order photonic ODE Solver.
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compact tunable silicon photonic Differential Equation Solver for general linear time invariant systems
Optics Express, 2014Co-Authors: Jiayang Wu, Yuxing Yang, Xiaofeng Hu, Xinhong Jiang, Christine Tremblay, Yikai SuAbstract:We propose and experimentally demonstrate an all-optical temporal Differential-Equation Solver that can be used to solve ordinary Differential Equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE Solver.
Xinhong Jiang - One of the best experts on this subject based on the ideXlab platform.
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on chip tunable second order Differential Equation Solver based on a silicon photonic mode split microresonator
Journal of Lightwave Technology, 2015Co-Authors: Jiayang Wu, Jizong Peng, Xinhong Jiang, Christine Tremblay, Yikai SuAbstract:We propose and experimentally demonstrate an on-chip all-optical Differential-Equation Solver capable of solving second-order ordinary Differential Equations (ODEs) characterizing continuous-time linear time-invariant systems. The photonic device is implemented by a self-coupled microresonator on a silicon-on-insulator platform with mutual coupling between the cavity modes. Owing to the mutual mode coupling within the same resonant cavity, the resonance wavelengths induced by different cavity modes are self-aligned, thus avoiding precise wavelength alignment and unequal thermal wavelength drifts as in the case of cascaded resonators. By changing the mutual mode coupling strength, the proposed device can be used to solve second-order ODEs with tunable coefficients. System demonstration using the fabricated device is carried out for 10-Gb/s optical Gaussian and super-Gaussian input pulses. The experimental results are in good agreement with theoretical predictions of the solutions, which verify the feasibility of the fabricated device as a tunable second-order photonic ODE Solver.
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compact tunable silicon photonic Differential Equation Solver for general linear time invariant systems
Optics Express, 2014Co-Authors: Jiayang Wu, Yuxing Yang, Xiaofeng Hu, Xinhong Jiang, Christine Tremblay, Yikai SuAbstract:We propose and experimentally demonstrate an all-optical temporal Differential-Equation Solver that can be used to solve ordinary Differential Equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE Solver.
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compact high speed all optical Differential Equation Solver on a silicon on insulator platform
International Conference on Group IV Photonics, 2013Co-Authors: Liang Zhang, Xinhong Jiang, Pan Cao, Xiaowen Sun, Xi YinAbstract:We propose and experimentally demonstrate an all-optical temporal ordinary-Differential-Equation (ODE) Solver featuring compact footprint and high processing speed on a silicon-on-insulator platform. The device performance is theoretically studied and verified by 5-Gb/s ODE solving experiment.
Christine Tremblay - One of the best experts on this subject based on the ideXlab platform.
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on chip tunable second order Differential Equation Solver based on a silicon photonic mode split microresonator
Journal of Lightwave Technology, 2015Co-Authors: Jiayang Wu, Jizong Peng, Xinhong Jiang, Christine Tremblay, Yikai SuAbstract:We propose and experimentally demonstrate an on-chip all-optical Differential-Equation Solver capable of solving second-order ordinary Differential Equations (ODEs) characterizing continuous-time linear time-invariant systems. The photonic device is implemented by a self-coupled microresonator on a silicon-on-insulator platform with mutual coupling between the cavity modes. Owing to the mutual mode coupling within the same resonant cavity, the resonance wavelengths induced by different cavity modes are self-aligned, thus avoiding precise wavelength alignment and unequal thermal wavelength drifts as in the case of cascaded resonators. By changing the mutual mode coupling strength, the proposed device can be used to solve second-order ODEs with tunable coefficients. System demonstration using the fabricated device is carried out for 10-Gb/s optical Gaussian and super-Gaussian input pulses. The experimental results are in good agreement with theoretical predictions of the solutions, which verify the feasibility of the fabricated device as a tunable second-order photonic ODE Solver.
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compact tunable silicon photonic Differential Equation Solver for general linear time invariant systems
Optics Express, 2014Co-Authors: Jiayang Wu, Yuxing Yang, Xiaofeng Hu, Xinhong Jiang, Christine Tremblay, Yikai SuAbstract:We propose and experimentally demonstrate an all-optical temporal Differential-Equation Solver that can be used to solve ordinary Differential Equations (ODEs) characterizing general linear time-invariant (LTI) systems. The photonic device implemented by an add-drop microring resonator (MRR) with two tunable interferometric couplers is monolithically integrated on a silicon-on-insulator (SOI) wafer with a compact footprint of ~60 μm × 120 μm. By thermally tuning the phase shifts along the bus arms of the two interferometric couplers, the proposed device is capable of solving first-order ODEs with two variable coefficients. The operation principle is theoretically analyzed, and system testing of solving ODE with tunable coefficients is carried out for 10-Gb/s optical Gaussian-like pulses. The experimental results verify the effectiveness of the fabricated device as a tunable photonic ODE Solver.