A Dynamical Low-Rank Approach to the Chemical Master Equation

By Tobias Jahnke, Wilhelm Huisinga. 2008

89 citations recorded by the source corpus.

Subfields: Biophysics, Molecular Biology

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “…PDEs [30,113]; • the solution of the Boltzmann equation [129, 149], and the chemical master / Fokker-Planck equations [4,6,61,64,86,122,133,135,196] • the solution of high-dimensional Schr¨odinger equations [46,160,172,184,192,193]; • computational tasks in micromagnetics [80,81]; •…”
Tensor-product approach to global time-space-parametric discretization of chemical master equation (2012, methodology): “As such reduced grid-based methods, we would like to mention the sparse grids technique [13], as well as the initial tensor-structured approaches: the greedy algorithm in the canonical tensor format [14, 15, 16, 17, 18], and the solver in the Tucker format, based on the manifold dynamics via the pro”
Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains (2014, background): “Another approach [33], related to the present work, attempts to avoid the problem of approximation in the CP format entirely by projecting the dynamics onto a manifold composed of all tensors with a CP decomposition of some predetermined maximal tensor Author Summary”
Dynamical low-rank approximation: applications and numerical experiments (2008, methodology): “An interesting application of the DLRA approach to the chemical master equation is given by Jahnke & Huisinga [ 10 ].”
On the numerical solution of the chemical master equation with sums of rank one tensors (2011, methodology): “A related approach to the one discussed here was suggested by Jahnke and Huisinga [5].”
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, methodology): “Existing techniques include the Monte-Carlo-type methods (so-called SSA [11] and its descendants), as well as more tensor-related ones: Sparse Grids [13], greedy approximations in the canonical tensor format [1] and tensor manifold dynamics [15].”
ALTERNATING MINIMAL ENERGY METHODS FOR LINEAR SYSTEMS IN HIGHER DIMENSIONS∗ (2014, methodology): “Existing techniques either leave the CME aside (the SSA method [16] and its descendants) or employ high-dimensional techniques like Smolyak’s sparse grids [22], greedy approximations [1], or dynamics on tensor manifolds [26].”
The geometry of algorithms using hierarchical tensors (2013, unknown): “In addition to theoretical bounds on the approximation quality, the authors show in the numerical experiments that this continuous-time updating compares favorably to point-wise approximations like ALS; see also [39,40] for applications.”