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01/27/2023
TransNet: Transferable Neural Networks for Partial Differential Equations
Transfer learning for partial differential equations (PDEs) is to develo...
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11/08/2022
Low regularity integrators for semilinear parabolic equations with maximum bound principles
This paper is concerned with conditionally structure-preserving, low reg...
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11/02/2022
A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with general mobility
In this paper, we propose and analyze a linear second-order numerical me...
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10/14/2022
Stabilized exponential time differencing schemes for the convective Allen-Cahn equation
The convective Allen-Cahn equation has been widely used to simulate mult...
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09/24/2022
Efficient Exponential Integrator Finite Element Method for Semilinear Parabolic Equations
In this paper, we propose an efficient exponential integrator finite ele...
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06/15/2022
A Multifidelity Monte Carlo Method for Realistic Computational Budgets
A method for the multifidelity Monte Carlo (MFMC) estimation of statisti...
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04/17/2022
Energetically Consistent Model Reduction for Metriplectic Systems
The metriplectic formalism is useful for describing complete dynamical s...
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03/14/2022
Stabilized exponential-SAV schemes preserving energy dissipation law and maximum bound principle for the Allen-Cahn type equations
It is well-known that the Allen-Cahn equation not only satisfies the ene...
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03/09/2022
Generalized SAV-exponential integrator schemes for Allen-Cahn type gradient flows
The energy dissipation law and the maximum bound principle (MBP) are two...
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12/09/2021
Style Mixing and Patchwise Prototypical Matching for One-Shot Unsupervised Domain Adaptive Semantic Segmentation
In this paper, we tackle the problem of one-shot unsupervised domain ada...
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12/02/2021
Level set learning with pseudo-reversible neural networks for nonlinear dimension reduction in function approximation
Due to the curse of dimensionality and the limitation on training data, ...
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10/05/2021
A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling
The popularity of deep convolutional autoencoders (CAEs) has engendered ...
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07/10/2021
Unconditionally stable exponential time differencing schemes for the mass-conserving Allen-Cahn equation with nonlocal and local effects
It is well known that the classic Allen-Cahn equation satisfies the maxi...
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05/27/2021
High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations
In order to treat the multiple time scales of ocean dynamics in an effic...
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05/23/2021
Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver
Partial differential equations are often used to model various physical ...
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04/29/2021
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations
A dimension reduction method based on the "Nonlinear Level set Learning"...
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04/22/2021
DANNet: A One-Stage Domain Adaptation Network for Unsupervised Nighttime Semantic Segmentation
Semantic segmentation of nighttime images plays an equally important rol...
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04/20/2021
Stabilized integrating factor Runge-Kutta method and unconditional preservation of maximum bound principle
Maximum bound principle (MBP) is an important property for a large class...
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10/23/2020
Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations
A large class of semilinear parabolic equations satisfy the maximum boun...
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05/23/2020
Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes
The ubiquity of semilinear parabolic equations has been illustrated in t...
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03/05/2020
A diagonal sweeping domain decomposition method with trace transfer for the Helmholtz equation
In this paper, the diagonal sweeping domain decomposition method (DDM) f...
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02/13/2020
A diagonal sweeping domain decomposition method with source transfer for the Helmholtz equation
In this paper, we propose a novel diagonal sweeping domain decomposition...
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02/06/2020
Conservative numerical schemes with optimal dispersive wave relations – Part II. Numerical evaluations
A new energy and enstrophy conserving scheme is evaluated using a suite ...
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09/10/2018