9,549 research outputs found
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
Optimizing large parameter sets in variational quantum Monte Carlo
We present a technique for optimizing hundreds of thousands of variational
parameters in variational quantum Monte Carlo. By introducing iterative Krylov
subspace solvers and by multiplying by the Hamiltonian and overlap matrices as
they are sampled, we remove the need to construct and store these matrices and
thus bypass the most expensive steps of the stochastic reconfiguration and
linear method optimization techniques. We demonstrate the effectiveness of this
approach by using stochastic reconfiguration to optimize a correlator product
state wavefunction with a pfaffian reference for four example systems. In two
examples on the two dimensional Hubbard model, we study 16 and 64 site
lattices, recovering energies accurate to 1% in the smaller lattice and
predicting particle-hole phase separation in the larger. In two examples
involving an ab initio Hamiltonian, we investigate the potential energy curve
of a symmetrically dissociated 4x4 hydrogen lattice as well as the
singlet-triplet gap in free base porphin. In the hydrogen system we recover 98%
or more of the correlation energy at all geometries, while for porphin we
compute the gap in a 24 orbital active space to within 0.02eV of the exact
result. The numbers of variational parameters in these examples range from
4x10^3 to 5x10^5, demonstrating an ability to go far beyond the reach of
previous formulations of stochastic reconfiguration.Comment: 5 pages, 4 figures, suggested PACS numbers 02.70.Ss, 71.10.Fd,
31.15.-
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
Further developments in correlator product states: deterministic optimization and energy evaluation
Correlator product states (CPS) are a class of tensor network wavefunctions
applicable to strongly correlated problems in arbitrary dimensions. Here, we
present a method for optimizing and evaluating the energy of the CPS
wavefunction that is non-variational but entirely deterministic. The
fundamental assumption underlying our technique is that the CPS wavefunction is
an exact eigenstate of the Hamiltonian, allowing the energy to be obtained
approximately through a projection of the Schr\"odinger equation. The validity
of this approximation is tested on two dimensional lattices for the spin-1/2
antiferromagnetic Heisenberg model, the spinless Hubbard model, and the full
Hubbard model. In each of these models, the projected method reproduces the
variational CPS energy to within 1%. For fermionic systems, we also demonstrate
the incorporation of a Slater determinant reference into the ansatz, which
allows CPS to act as a generalization of the Jastrow-Slater wavefunction.Comment: 8 pages, 2 tables, 3 figure
Tensor Computation: A New Framework for High-Dimensional Problems in EDA
Many critical EDA problems suffer from the curse of dimensionality, i.e. the
very fast-scaling computational burden produced by large number of parameters
and/or unknown variables. This phenomenon may be caused by multiple spatial or
temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit
simulation), nonlinearity of devices and circuits, large number of design or
optimization parameters (e.g. full-chip routing/placement and circuit sizing),
or extensive process variations (e.g. variability/reliability analysis and
design for manufacturability). The computational challenges generated by such
high dimensional problems are generally hard to handle efficiently with
traditional EDA core algorithms that are based on matrix and vector
computation. This paper presents "tensor computation" as an alternative general
framework for the development of efficient EDA algorithms and tools. A tensor
is a high-dimensional generalization of a matrix and a vector, and is a natural
choice for both storing and solving efficiently high-dimensional EDA problems.
This paper gives a basic tutorial on tensors, demonstrates some recent examples
of EDA applications (e.g., nonlinear circuit modeling and high-dimensional
uncertainty quantification), and suggests further open EDA problems where the
use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and
System
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