22 citations · 32 across the 7 of their papers we have counts for
8 papers
An End-to-End Deep Learning Method for Solving Nonlocal Allen-Cahn and Cahn-Hilliard Phase-Field Models
Yuwei Geng, Olena Burkovska, Lili Ju +2
We propose an efficient end-to-end deep learning method for solving nonlocal Allen-Cahn (AC) and Cahn-Hilliard (CH) phase-field models. One motivation for this effort emanates from…
An efficient proximal-based approach for solving nonlocal Allen-Cahn equations
Olena Burkovska, Ilyas Mustapha
In this work, we present an efficient approach for the spatial and temporal discretization of the nonlocal Allen-Cahn equation, which incorporates various double-well potentials an…
Multifidelity Methods for Uncertainty Quantification of a Nonlocal Model for Phase Changes in Materials
Parisa Khodabakhshi, Olena Burkovska, Karen Willcox +1
This study is devoted to the construction of a multifidelity Monte Carlo (MFMC) method for the uncertainty quantification of a nonlocal, non-mass-conserving Cahn-Hilliard model for…
Non-isothermal nonlocal phase-field models with a double-obstacle potential
Olena Burkovska
Phase-field models are a popular choice in computational physics to describe complex dynamics of substances with multiple phases and are widely used in various applications. We pre…
An optimization-based approach to parameter learning for fractional type nonlocal models
Olena Burkovska, Christian Glusa, Marta D'Elia
Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal si…
On a nonlocal Cahn-Hilliard model permitting sharp interfaces
Olena Burkovska, Max Gunzburger
A nonlocal Cahn-Hilliard model with a nonsmooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactio…
Affine approximation of parametrized kernels and model order reduction for nonlocal and fractional Laplace models
Olena Burkovska, Max Gunzburger
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius…
Regularity and approximation analyses of nonlocal variational equality and inequality problems
Olena Burkovska, Max Gunzburger
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators…