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09/19/2023
Γ-convergence of Nonlocal Dirichlet Energies With Penalty Formulations of Dirichlet Boundary Data
We study nonlocal Dirichlet energies associated with a class of nonlocal...
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04/28/2023
Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array
We present discontinuous Galerkin (DG) methods for solving a first-order...
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02/13/2023
Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing
We analyze the convergence of a nonlocal gradient descent method for min...
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01/02/2023
Asymptotically compatibility of a class of numerical schemes for a nonlocal traffic flow model
This paper considers numerical discretization of a nonlocal conservation...
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03/28/2022
A nonlocal Stokes system with volume constraints
In this paper, we introduce a nonlocal model for linear steady Stokes sy...
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03/01/2022
Nonlocal diffusion models with consistent local and fractional limits
For some spatially nonlocal diffusion models with a finite range of nonl...
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01/20/2022
Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions
We study the propagation of singularities in solutions of linear convect...
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09/26/2021
On some nonlocal models with radially symmetric interaction domains and the effect of domain truncation
Many nonlocal models have adopted a finite and radially symmetric nonloc...
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06/06/2021
A Physics-Informed Deep Learning Paradigm for Traffic State Estimation and Fundamental Diagram Discovery
Traffic state estimation (TSE) bifurcates into two main categories, mode...
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03/21/2021
The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation
Identifying hidden dynamics from observed data is a significant and chal...
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01/21/2021
A fast two-stage algorithm for non-negative matrix factorization in streaming data
In this article, we study algorithms for nonnegative matrix factorizatio...
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01/17/2021
Physics-Informed Deep Learning for Traffic State Estimation
Traffic state estimation (TSE), which reconstructs the traffic variables...
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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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04/13/2020
A non-cooperative meta-modeling game for automated third-party calibrating, validating, and falsifying constitutive laws with parallelized adversarial attacks
The evaluation of constitutive models, especially for high-risk and high...
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03/07/2020
Nonlocal-in-time dynamics and crossover of diffusive regimes
We study a simple nonlocal-in-time dynamic system proposed for the effec...
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03/06/2020
The Graph Limit of The Minimizer of The Onsager-Machlup Functional and Its Computation
The Onsager-Machlup (OM) functional is well-known for characterizing the...
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02/04/2020
Numerical methods for nonlocal and fractional models
Partial differential equations (PDEs) are used, with huge success, to mo...
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12/29/2019
Discovery of Dynamics Using Linear Multistep Methods
Linear multistep methods (LMMs) are popular time discretization techniqu...
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10/13/2019
Variational Phase Field Formulations of Polarization and Phase Transition in Ferroelectric Thin Films
Electric field plays an important role in ferroelectric phase transition...
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09/02/2019
Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues
In this work, we review the connection between the subjects of homogeniz...
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06/15/2019
Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods
In this work, we consider a time-fractional Allen-Cahn equation, where t...
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03/08/2019
A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation
We introduce a multi-agent meta-modeling game to generate data, knowledg...
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12/01/2018
Stochastic Training of Residual Networks: a Differential Equation Viewpoint
During the last few years, significant attention has been paid to the st...
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06/02/2018
Hierarchical Attention-Based Recurrent Highway Networks for Time Series Prediction
Time series prediction has been studied in a variety of domains. However...
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06/02/2018
Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling
Nonlocal neural networks have been proposed and shown to be effective in...
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05/09/2018