2,502 research outputs found
Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations
In this paper we propose a new class of coupling methods for the sensitivity
analysis of high dimensional stochastic systems and in particular for lattice
Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically
based on approximating continuous derivatives with respect to model parameters
by the mean value of samples from a finite difference scheme. Instead of using
independent samples the proposed algorithm reduces the variance of the
estimator by developing a strongly correlated-"coupled"- stochastic process for
both the perturbed and unperturbed stochastic processes, defined in a common
state space. The novelty of our construction is that the new coupled process
depends on the targeted observables, e.g. coverage, Hamiltonian, spatial
correlations, surface roughness, etc., hence we refer to the proposed method as
em goal-oriented sensitivity analysis. In particular, the rates of the coupled
Continuous Time Markov Chain are obtained as solutions to a goal-oriented
optimization problem, depending on the observable of interest, by considering
the minimization functional of the corresponding variance. We show that this
functional can be used as a diagnostic tool for the design and evaluation of
different classes of couplings. Furthermore the resulting KMC sensitivity
algorithm has an easy implementation that is based on the Bortz-Kalos-Lebowitz
algorithm's philosophy, where here events are divided in classes depending on
level sets of the observable of interest. Finally, we demonstrate in several
examples including adsorption, desorption and diffusion Kinetic Monte Carlo
that for the same confidence interval and observable, the proposed
goal-oriented algorithm can be two orders of magnitude faster than existing
coupling algorithms for spatial KMC such as the Common Random Number approach
Variance Reduction with Array-RQMC for Tau-Leaping Simulation of Stochastic Biological and Chemical Reaction Networks
We explore the use of Array-RQMC, a randomized quasi-Monte Carlo method designed for the simulation of Markov chains, to reduce the variance when simulating stochastic biological or chemical reaction networks with -leaping. The task is to estimate the expectation of a function of molecule copy numbers at a given future time by the sample average over sample paths, and the goal is to reduce the variance of this sample-average estimator. We find that when the method is properly applied, variance reductions by factors in the thousands can be obtained. These factors are much larger than those observed previously by other authors who tried RQMC methods for the same examples. Array-RQMC simulates an array of realizations of the Markov chain and requires a sorting function to reorder these chains according to their states, after each step. The choice of sorting function is a key ingredient for the efficiency of the method, although in our experiments, Array-RQMC was never worse than ordinary Monte Carlo, regardless of the sorting method. The expected number of reactions of each type per step also has an impact on the efficiency gain.ERDF, ESF, EXP. 2019/00432, Canada Research Chair, IVADO Research Grant, NSERC Discovery Grant RGPIN-110050
Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
Stochasticity is a key characteristic of intracellular processes such as gene
regulation and chemical signalling. Therefore, characterising stochastic
effects in biochemical systems is essential to understand the complex dynamics
of living things. Mathematical idealisations of biochemically reacting systems
must be able to capture stochastic phenomena. While robust theory exists to
describe such stochastic models, the computational challenges in exploring
these models can be a significant burden in practice since realistic models are
analytically intractable. Determining the expected behaviour and variability of
a stochastic biochemical reaction network requires many probabilistic
simulations of its evolution. Using a biochemical reaction network model to
assist in the interpretation of time course data from a biological experiment
is an even greater challenge due to the intractability of the likelihood
function for determining observation probabilities. These computational
challenges have been subjects of active research for over four decades. In this
review, we present an accessible discussion of the major historical
developments and state-of-the-art computational techniques relevant to
simulation and inference problems for stochastic biochemical reaction network
models. Detailed algorithms for particularly important methods are described
and complemented with MATLAB implementations. As a result, this review provides
a practical and accessible introduction to computational methods for stochastic
models within the life sciences community
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
- …