第70回統計的機械学習セミナー / The 70th Statistical Machine Learning Seminar (Hyblid)
- 【Date & Time】
- September 12nd (Friday), 2025 11:00 - 12:00
Admission Free
- 【Place】
- Seminar Room 5, The Institute of Statistical Mathematics
Online :
Please register from the URL below to get a Zoom link:
https://us06web.zoom.us/meeting/register/TxSuPM70QpuAxeq7Jyexog
- 【Speaker】
- André Uschmajew (Augsburg)
- 【Title】
- Low-rank approximability and Krylov methods for nearest neighbor interaction systems
- 【Abstract】
-
Low-rank tensor methods are an important tool in the numerical treatment
of equations with a high-dimensional state space. Nearest neighbor
interaction systems like the Ising model or certain chemical master
equations are examples for such problems. While low-rank tensor
train/MPS models have shown to be highly efficient for their simulation,
providing theoretical justification for this is a challenging task. For
ground states of 1D quantum spin systems such arguments have been found
in theoretical physics, and some of the ideas can be generalized. One
approach is to study rank-increasing properties of Krylov subspace
methods based on the partial commutativity of local operators in nearest
neighbor Hamiltonians. In this talk, we will explain this idea and
present numerical examples.
