4 citations · 13 across the 16 of their papers we have counts for
4 papers · 1 filter
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…
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…
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…
Oblique projection for scalable rank-adaptive reduced-order modeling of nonlinear stochastic PDEs with time-dependent bases
M. Donello, G. Palkar, M. H. Naderi +2
Time-dependent basis reduced order models (TDB ROMs) have successfully been used for approximating the solution to nonlinear stochastic partial differential equations (PDEs). For m…