5 papers
Quantitative uniqueness for bi-Laplace equations with potentials
Long Teng, Zhiwei Wang, Jiuyi Zhu
We study quantitative unique continuation for bi-Laplace equations \[Δ^{2}u+V(x)u=0 \] by introducing some new weighted frequency functions. We establish quantitative three-ball in…
Quantitative unique continuation for elliptic equations with Hölder continuous potentials
Long Teng, Zhiwei Wang, Jiuyi Zhu
We study quantitative unique continuation for second order elliptic equations with lower-order terms of Hölder regularity via a weighted frequency function method. We establish qua…
A forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations
Lorenc Kapllani, Long Teng
In this work, we present a novel forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs). Motiv…
A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations
Lorenc Kapllani, Long Teng
In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), wher…
Uncertainty quantification for deep learning-based schemes for solving high-dimensional backward stochastic differential equations
Lorenc Kapllani, Long Teng, Matthias Rottmann
Deep learning-based numerical schemes for solving high-dimensional backward stochastic differential equations (BSDEs) have recently raised plenty of scientific interest. While they…