3 papers
math.NA2026
Implicit Tensor-Train Cross Integration of High-Dimensional Nonlinear PDEs via Fiber-Dependency Elimination
Behzad Ghahremani, Hessam Babaee
Tensor-train (TT) representations have emerged as an effective framework for mitigating the curse of dimensionality in the numerical solution of high-dimensional tensor differentia…
math.NA2024
Cross Interpolation for Solving High-Dimensional Dynamical Systems on Low-Rank Tucker and Tensor Train Manifolds
Behzad Ghahremani, Hessam Babaee
We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifold…
math.NA2024
A DEIM Tucker Tensor Cross Algorithm and its Application to Dynamical Low-Rank Approximation
Behzad Ghahremani, Hessam Babaee
We introduce a Tucker tensor cross approximation method that constructs a low-rank representation of a -dimensional tensor by sparsely sampling its fibers. These fibers are sele…