The Experts below are selected from a list of 170850 Experts worldwide ranked by ideXlab platform
Nanzhe Wang - One of the best experts on this subject based on the ideXlab platform.
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weak form theory guided neural network tgnn wf for deep learning of subsurface single and two phase flow
Journal of Computational Physics, 2021Co-Authors: Dongxiao Zhang, Miao Rong, Nanzhe WangAbstract:Abstract Deep neural networks (DNNs) are widely used as surrogate models, and incorporating theoretical guidance into DNNs has improved generalizability. However, most such approaches define the loss function based on the strong form of conservation laws (via partial differential equations, PDEs), which is subject to diminished accuracy when the PDE has high-order derivatives or the solution has strong discontinuities. Herein, we propose a weak form Theory-guided Neural Network (TgNN-wf), which incorporates the weak form residual of the PDE into the loss function, combined with Data Constraint and initial and boundary condition regularizations, to overcome the aforementioned difficulties. The original loss minimization problem is reformulated into a Lagrangian duality problem, so that the weights of the terms in the loss function are optimized automatically. We use domain decomposition with locally-defined test functions, which captures local discontinuity effectively. Two numerical cases demonstrate the superiority of the proposed TgNN-wf over the strong form TgNN, including hydraulic head prediction for unsteady-state 2D single-phase flow problems and saturation profile prediction for 1D two-phase flow problems. Results show that TgNN-wf consistently achieves higher accuracy than TgNN, especially when strong discontinuity in the parameter or solution space is present. TgNN-wf also trains faster than TgNN when the number of integration subdomains is not too large (
Dongxiao Zhang - One of the best experts on this subject based on the ideXlab platform.
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weak form theory guided neural network tgnn wf for deep learning of subsurface single and two phase flow
Journal of Computational Physics, 2021Co-Authors: Dongxiao Zhang, Miao Rong, Nanzhe WangAbstract:Abstract Deep neural networks (DNNs) are widely used as surrogate models, and incorporating theoretical guidance into DNNs has improved generalizability. However, most such approaches define the loss function based on the strong form of conservation laws (via partial differential equations, PDEs), which is subject to diminished accuracy when the PDE has high-order derivatives or the solution has strong discontinuities. Herein, we propose a weak form Theory-guided Neural Network (TgNN-wf), which incorporates the weak form residual of the PDE into the loss function, combined with Data Constraint and initial and boundary condition regularizations, to overcome the aforementioned difficulties. The original loss minimization problem is reformulated into a Lagrangian duality problem, so that the weights of the terms in the loss function are optimized automatically. We use domain decomposition with locally-defined test functions, which captures local discontinuity effectively. Two numerical cases demonstrate the superiority of the proposed TgNN-wf over the strong form TgNN, including hydraulic head prediction for unsteady-state 2D single-phase flow problems and saturation profile prediction for 1D two-phase flow problems. Results show that TgNN-wf consistently achieves higher accuracy than TgNN, especially when strong discontinuity in the parameter or solution space is present. TgNN-wf also trains faster than TgNN when the number of integration subdomains is not too large (
Miao Rong - One of the best experts on this subject based on the ideXlab platform.
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weak form theory guided neural network tgnn wf for deep learning of subsurface single and two phase flow
Journal of Computational Physics, 2021Co-Authors: Dongxiao Zhang, Miao Rong, Nanzhe WangAbstract:Abstract Deep neural networks (DNNs) are widely used as surrogate models, and incorporating theoretical guidance into DNNs has improved generalizability. However, most such approaches define the loss function based on the strong form of conservation laws (via partial differential equations, PDEs), which is subject to diminished accuracy when the PDE has high-order derivatives or the solution has strong discontinuities. Herein, we propose a weak form Theory-guided Neural Network (TgNN-wf), which incorporates the weak form residual of the PDE into the loss function, combined with Data Constraint and initial and boundary condition regularizations, to overcome the aforementioned difficulties. The original loss minimization problem is reformulated into a Lagrangian duality problem, so that the weights of the terms in the loss function are optimized automatically. We use domain decomposition with locally-defined test functions, which captures local discontinuity effectively. Two numerical cases demonstrate the superiority of the proposed TgNN-wf over the strong form TgNN, including hydraulic head prediction for unsteady-state 2D single-phase flow problems and saturation profile prediction for 1D two-phase flow problems. Results show that TgNN-wf consistently achieves higher accuracy than TgNN, especially when strong discontinuity in the parameter or solution space is present. TgNN-wf also trains faster than TgNN when the number of integration subdomains is not too large (
Harald P. Pfeiffer - One of the best experts on this subject based on the ideXlab platform.
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Comparison of binary black hole initial Data sets
Physical Review D, 2018Co-Authors: Vijay Varma, Mark A. Scheel, Harald P. PfeifferAbstract:We present improvements to the construction of binary black hole initial Data used in the Spectral Einstein Code (SpEC). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision surfaces to be slightly inside rather than on the apparent horizons, thus avoiding extrapolation into the black holes at the last stage of initial Data construction. We find that this improves initial Data Constraint violations near and inside the apparent horizons by about 3 orders of magnitude. We construct several initial Data sets that are intended to be astrophysically equivalent but use different free Data, boundary conditions, and initial gauge conditions. These include free Data chosen as a superposition of two black holes in time-independent horizon-penetrating harmonic and damped harmonic coordinates. We also implement initial Data for which the initial gauge satisfies the harmonic and damped harmonic gauge conditions; this can be done independently of the free Data, since this amounts to a choice of the time derivatives of the lapse and shift. We compare these initial Data sets by evolving them. We show that the gravitational waveforms extracted during the evolution of these different initial Data sets agree very well after excluding initial transients. However, we do find small differences between these waveforms, which we attribute to small differences in initial orbital eccentricity, and in initial BH masses and spins, resulting from the different choices of free Data. Among the cases considered, we find that superposed harmonic initial Data lead to significantly smaller transients, smaller variation in BH spins and masses during these transients, smaller Constraint violations, and more computationally efficient evolutions. Finally, we study the impact of initial Data choices on the construction of zero-eccentricity initial Data.
Vijay Varma - One of the best experts on this subject based on the ideXlab platform.
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Comparison of binary black hole initial Data sets
Physical Review D, 2018Co-Authors: Vijay Varma, Mark A. Scheel, Harald P. PfeifferAbstract:We present improvements to the construction of binary black hole initial Data used in the Spectral Einstein Code (SpEC). We introduce new boundary conditions for the extended conformal thin sandwich elliptic equations that enforce the excision surfaces to be slightly inside rather than on the apparent horizons, thus avoiding extrapolation into the black holes at the last stage of initial Data construction. We find that this improves initial Data Constraint violations near and inside the apparent horizons by about 3 orders of magnitude. We construct several initial Data sets that are intended to be astrophysically equivalent but use different free Data, boundary conditions, and initial gauge conditions. These include free Data chosen as a superposition of two black holes in time-independent horizon-penetrating harmonic and damped harmonic coordinates. We also implement initial Data for which the initial gauge satisfies the harmonic and damped harmonic gauge conditions; this can be done independently of the free Data, since this amounts to a choice of the time derivatives of the lapse and shift. We compare these initial Data sets by evolving them. We show that the gravitational waveforms extracted during the evolution of these different initial Data sets agree very well after excluding initial transients. However, we do find small differences between these waveforms, which we attribute to small differences in initial orbital eccentricity, and in initial BH masses and spins, resulting from the different choices of free Data. Among the cases considered, we find that superposed harmonic initial Data lead to significantly smaller transients, smaller variation in BH spins and masses during these transients, smaller Constraint violations, and more computationally efficient evolutions. Finally, we study the impact of initial Data choices on the construction of zero-eccentricity initial Data.
