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22
Implicit particle methods and their connection with variational data assimilation
 Monthly Weather Review
"... The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the highprobability regions via a sequence of steps that includes minimizations. We present a new and more general derivation of this approach and extend the method to particle smoothi ..."
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The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the highprobability regions via a sequence of steps that includes minimizations. We present a new and more general derivation of this approach and extend the method to particle smoothing as well as to data assimilation for perfect models. We show that the minimizations required by implicit particle methods are similar to the ones one encounters in variational data assimilation and explore the connection of implicit particle methods with variational data assimilation. In particular, we argue that existing variational codes can be converted into implicit particle methods at a low cost, often yielding better estimates, that are also equipped with quantitative measures of the uncertainty. A detailed example is presented. 1
Conditions for successful data assimilation
"... We show that numerical data assimilation is feasible in principle for an idealized model only if an effective dimension of the noise is bounded; this effective dimension is bounded when the noises in model and data satisfy a certain natural balance condition. If this balance condition is satisfied, ..."
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We show that numerical data assimilation is feasible in principle for an idealized model only if an effective dimension of the noise is bounded; this effective dimension is bounded when the noises in model and data satisfy a certain natural balance condition. If this balance condition is satisfied, data assimilation is feasible even if the number of variables in the problem is huge. We then analyze several data assimilation algorithms, including particle filters and variational data assimilation. We show that a particle filter can successfully solve most of the data assimilation problems which are feasible in principle, provided the particle filter is well designed. We also compare the conditions under which variational data assimilation can be successful with the conditions for successful particle filtering. We draw conclusions from our analysis and discuss its limitations. 1
Improved diffusion Monte Carlo
 Commun. Pure Appl. Math
"... We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm. The new algorithm has a lower variance per workload, regard ..."
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We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm. The new algorithm has a lower variance per workload, regardless of the regime considered. In particular, it makes it feasible to use DMC in situations where the “naı̈ve ” generalisation of the standard algorithm would be impractical, due to an exponential explosion of its variance. We numerically demonstrate the effectiveness of the new algorithm on a standard rare event simulation problem (probability of an unlikely transition in a
A hybrid particleensemble Kalman filter for high dimensional Lagrangian data assimilation
"... Abstract. We apply the recently proposed hybrid particleensemble Kalman filter to assimilate Lagrangian data into a nonlinear, highdimensional quasigeostrophic ocean model. Effectively the hybrid filter applies a particle filter to the highly nonlinear, lowdimensional Lagrangian instrument va ..."
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Abstract. We apply the recently proposed hybrid particleensemble Kalman filter to assimilate Lagrangian data into a nonlinear, highdimensional quasigeostrophic ocean model. Effectively the hybrid filter applies a particle filter to the highly nonlinear, lowdimensional Lagrangian instrument variables while applying an ensemble Kalman type update to the highdimensional Eulerian flow field. We present some initial results from this hybrid filter and compare those to results from a standard ensemble Kalman filter and an ensemble run without assimilation. 1
A Survey of Implicit Particle Filters for Data Assimilation
"... Abstract The implicit particle filter is a sequential Monte Carlo method for data assimilation. The idea is to focus the particles onto the high probability regions of the target probability density function (pdf) so that the number of particles required for a good approximation of this pdf remains ..."
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Abstract The implicit particle filter is a sequential Monte Carlo method for data assimilation. The idea is to focus the particles onto the high probability regions of the target probability density function (pdf) so that the number of particles required for a good approximation of this pdf remains manageable, even if the dimension of the state space is large. We explain how this idea is implemented, discuss special cases of practical importance, and work out the relations of the implicit particle filter with other data assimilation methods. We illustrate the theory with four examples. 1
Path Integral Formulation of Stochastic Optimal Control with Generalized Costs?
"... Abstract: Path integral control solves a class of stochastic optimal control problems with a Monte Carlo (MC) method for an associated HamiltonJacobiBellman (HJB) equation. The MC approach avoids the need for a global grid of the domain of the HJB equation and, therefore, path integral control is ..."
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Abstract: Path integral control solves a class of stochastic optimal control problems with a Monte Carlo (MC) method for an associated HamiltonJacobiBellman (HJB) equation. The MC approach avoids the need for a global grid of the domain of the HJB equation and, therefore, path integral control is in principle applicable to control problems of moderate to large dimension. The class of problems path integral control can solve, however, is defined by requirements on the cost function, the noise covariance matrix and the control input matrix. We relax the requirements on the cost function by introducing a new state that represents an augmented running cost. In our new formulation the cost function can contain stochastic integral terms and linear control costs, which are important in applications in engineering, economics and finance. We find an efficient numerical implementation of our gridfree MC approach and demonstrate its performance and usefulness in examples from hierarchical electric load management. The dimension of one of our examples is large enough to make classical gridbased HJB solvers impractical. 1.
Implicit sampling for path integral control, Monte Carlo localization and online SLAM. in review
, 2013
"... The applicability and usefulness of implicit sampling in stochastic optimal control, stochastic localization, and simultaneous localization and mapping (SLAM), is explored; implicit sampling is a recentlydeveloped variationallyenhanced sampling method. The theory is illustrated with examples, and ..."
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The applicability and usefulness of implicit sampling in stochastic optimal control, stochastic localization, and simultaneous localization and mapping (SLAM), is explored; implicit sampling is a recentlydeveloped variationallyenhanced sampling method. The theory is illustrated with examples, and it is found that implicit sampling is significantly more efficient than current Monte Carlo methods in test problems for all three applications. 1
Smallnoise analysis and symmetrization of implicit Monte Carlo samplers
, 2014
"... Implicit samplers are algorithms for producing independent, weighted samples from multivariate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis s ..."
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Implicit samplers are algorithms for producing independent, weighted samples from multivariate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algorithms that leads to improved (implicit) sampling schemes at a relatively small additional cost. Computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems. 1
application to geomagnetic data assimilation
"... Implicit particle filtering for models with partial noise, and an ..."