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Tensor product approach for a black-box simulation of probabilistic models in computational physics, chemistry and biology
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Seminar
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- Time:
- 16:00
- Date:
- 27 June 2013
- Venue:
- Auditorium 2001 (LR1) Chemistry Building 27 Highfield Campus University of Southampton SO17 1BJ

For more information regarding this seminar, please email Dr Ilya Kuprov at I.Kuprov@soton.ac.uk .

## Event details

A Computational Chemistry Section Seminar

An essential part of modern scientific computing is mathematical models, which take into account various stochastic processes. Since the desired output is usually statistically averaged quantities, one of the most accurate ways is simulation of a function related to the joint probability distribution. Typical examples are the Schrödinger equation in quantum physics, Fokker-Planck and Master equations in fluid dynamics, cell biology and other applications. However, the principal difficulty of a straightforward probabilistic description of many body systems is the “curse of dimensionality”, since the storage cost of the probability function grows exponentially with the number of configuration coordinates (species, spins, etc.).

One way to reduce the number of degrees of freedom in a system is to employ a physical insight in a certain model to remove unnecessary components. As a “black-box” alternative, a purely mathematical approach based on the separation of variables may be suggested. We will consider the Matrix Product States (Tensor Train) decomposition as a low-parametric data representation, and discuss the computational methods in this format, such as the Density Matrix Renormalization Group (DMRG), as well as newer Alternating Minimal Energy (AMEn) techniques for linear system, eigenvalue and approximation problems. We will present several numerical examples to demonstrate the computational efficiency and potential of the methods proposed.

## Speaker information

Dr Sergey Dolgov , Max Planck Institute for Mathematics in the Sciences. .