34 citations · 269 across the 25 of their papers we have counts for
26 papers
Computing with traceable tensor networks
Sarah Ellwein, Daniele Venturi
We introduce a new SVD-based tensor decomposition method for tensor networks with arbitrary graph topologies, extending classical hierarchical SVD-based techniques to networks with…
Weighted Flow Matching and Physics-Informed Nonlinear Filtering for Parameter Estimation in Digital Twins
Yasar Yanik, Himadri Basu, Ricardo G. Sanfelice +1
Digital twins (DTs) rely on continuous synchronization between physical systems and their virtual counterparts through online parameter estimation under uncertainty. In many practi…
Tensor approximation of functional differential equations
Abram Rodgers, Daniele Venturi
Functional Differential Equations (FDEs) play a fundamental role in many areas of mathematical physics, including fluid dynamics (Hopf characteristic functional equation), quantum…
Coordinate-adaptive integration of PDEs on tensor manifolds
Alec Dektor, Daniele Venturi
We introduce a new tensor integration method for time-dependent PDEs that controls the tensor rank of the PDE solution via time-dependent diffeomorphic coordinate transformations.…
The Mori-Zwanzig formulation of deep learning
Daniele Venturi, Xiantao Li
We develop a new formulation of deep learning based on the Mori-Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duali…
Tensor rank reduction via coordinate flows
Alec Dektor, Daniele Venturi
Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutio…