Search Results - "Communications in computational physics"

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations by Ameya D. Jagtap, Ameya D. Jagtap, George Em Karniadakis, George Em Karniadakis

“…Here we propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential…”
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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs by Yeonjong Shin, Yeonjong Shin, Jérôme Darbon, Jérôme Darbon, George Em Karniadakis, George Em Karniadakis

“…Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encountered in computational…”
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Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks by Zhi-Qin John Xu, Zhi-Qin John Xu, Yaoyu Zhang, Yaoyu Zhang, Tao Luo, Tao Luo, Yanyang Xiao, Yanyang Xiao, Zheng Ma, Zheng Ma

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Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations by Jiang, Shidong, Zhang, Jiwei, Zhang, Qian, Zhang, Zhimin

“…The computational work and storage of numerically solving the time fractional PDEs are generally huge for the traditional direct methods since they require…”
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Deep Network Approximation Characterized by Number of Neurons by Zuowei Shen, Zuowei Shen, Haizhao Yang, Haizhao Yang, Shijun Zhang, Shijun Zhang

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Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains by Ziqi Liu, Ziqi Liu, Wei Cai, Wei Cai, Zhi-Qin John Xu, Zhi-Qin John Xu

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Dying ReLU and Initialization: Theory and Numerical Examples by Lu Lu, Lu Lu, Yeonjong Shin, Yeonjong Shin, Yanhui Su, Yanhui Su, George Em Karniadakis, George Em Karniadakis

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Deep Potential: A General Representation of a Many-Body Potential Energy Surface by Han, Jiequn, Zhang, Linfeng, Car, Roberto, E, Weinan

“…Not provided…”
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Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems

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A second-order energy stable BDF numerical scheme for the Cahn-Hilliard equation

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Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions by Yulei Liao, Yulei Liao, Pingbing Ming, Pingbing Ming

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Solving Allen-Cahn and Cahn-Hilliard Equations Using the Adaptive Physics Informed Neural Networks by Colby L. Wight, Colby L. Wight, Jia Zhao, Jia Zhao

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Natural Convection Heat Transfer in a Porous Cavity with Sinusoidal Temperature Distribution Using Cu/Water Nanofluid: Double MRT Lattice Boltzmann Method by Hasan Sajjadi, Hasan Sajjadi, Amin Amiri Delouei, Amin Amiri Delouei, Rasul Mohebbi, Rasul Mohebbi, Mohsen Izadi, Mohsen Izadi, Sauro Succi, Sauro Succi

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Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme by Yan, Yonggui, Sun, Zhi-Zhong, Zhang, Jiwei

“…The fractional derivatives include nonlocal information and thus their calculation requires huge storage and computational cost for long time simulations. We…”
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Numerical Methods for Fluid-Structure Interaction — A Review by Hou, Gene, Wang, Jin, Layton, Anita

“…The interactions between incompressible fluid flows and immersed structures are nonlinear multi-physics phenomena that have applications to a wide range of…”
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A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem by Hong-Lin Liao, Hong-Lin Liao, William McLean, William McLean, Jiwei Zhang, Jiwei Zhang

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Phase-Field Models for Multi-Component Fluid Flows by Kim, Junseok

“…In this paper, we review the recent development of phase-field models and their numerical methods for multi-component fluid flows with interfacial phenomena…”
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A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure by Carrillo, José A., Chertock, Alina, Huang, Yanghong

“…We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties…”
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An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation by Kelong Cheng, Kelong Cheng, Cheng Wang, Cheng Wang, Steven M. Wise, Steven M. Wise

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Particle based gPC methods for mean-field models of swarming with uncertainty

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