DeepAI AI Chat
Log In Sign Up

Tensor-train approximation of the chemical master equation and its application for parameter inference

by   Ion Gabriel Ion, et al.

In this work, we perform Bayesian inference tasks for the chemical master equation in the tensor-train format. The tensor-train approximation has been proven to be very efficient in representing high dimensional data arising from the explicit representation of the chemical master equation solution. An additional advantage of representing the probability mass function in the tensor train format is that parametric dependency can be easily incorporated by introducing a tensor product basis expansion in the parameter space. Time is treated as an additional dimension of the tensor and a linear system is derived to solve the chemical master equation in time. We exemplify the tensor-train method by performing inference tasks such as smoothing and parameter inference using the tensor-train framework. A very high compression ratio is observed for storing the probability mass function of the solution. Since all linear algebra operations are performed in the tensor-train format, a significant reduction of the computational time is observed as well.


page 1

page 2

page 3

page 4


Analysis of tensor methods for stochastic models of gene regulatory networks

The tensor-structured parametric analysis (TPA) has been recently develo...

Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries

This work develops a numerical solver based on the combination of isogeo...

Tensor product approach to modelling epidemics on networks

To improve mathematical models of epidemics it is essential to move beyo...

Approximation and inference methods for stochastic biochemical kinetics - a tutorial review

Stochastic fluctuations of molecule numbers are ubiquitous in biological...

Post-Processing of High-Dimensional Data

Scientific computations or measurements may result in huge volumes of da...

Black box approximation in the tensor train format initialized by ANOVA decomposition

Surrogate models can reduce computational costs for multivariable functi...