39,881 research outputs found
Variational Algorithms for Nonlinear Smoothing Applications
A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided
ON THE DYNAMICS OF COMMERCIAL FISHING AND PARAMETER IDENTIFICATION
This paper has two main objectives. The first is to develop a dynamic model of commercial fisheries different from most existing models that assume optimizing behavior. The industry is assumed to have a well-defined index of performance. Based upon this index, the decision to invest or not is made. We do not, however, assume that the industry or firm is efficient or optimal in its operations. The second is that a new approach of fitting model dynamics to time series data is employed to simultaneously estimate the poorly known initial conditions and parameters of nonlinear fisheries dynamics. The approach is a data assimilation technique known as the variational adjoint method. Estimation of the poorly known initial conditions is one of the attractive features of the variational adjoint method.Resource /Energy Economics and Policy,
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data
While nonlinear stochastic partial differential equations arise naturally in
spatiotemporal modeling, inference for such systems often faces two major
challenges: sparse noisy data and ill-posedness of the inverse problem of
parameter estimation. To overcome the challenges, we introduce a strongly
regularized posterior by normalizing the likelihood and by imposing physical
constraints through priors of the parameters and states. We investigate joint
parameter-state estimation by the regularized posterior in a physically
motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate
reconstruction. The high-dimensional posterior is sampled by a particle Gibbs
sampler that combines MCMC with an optimal particle filter exploiting the
structure of the SEBM. In tests using either Gaussian or uniform priors based
on the physical range of parameters, the regularized posteriors overcome the
ill-posedness and lead to samples within physical ranges, quantifying the
uncertainty in estimation. Due to the ill-posedness and the regularization, the
posterior of parameters presents a relatively large uncertainty, and
consequently, the maximum of the posterior, which is the minimizer in a
variational approach, can have a large variation. In contrast, the posterior of
states generally concentrates near the truth, substantially filtering out
observation noise and reducing uncertainty in the unconstrained SEBM
Variational System Identification for Nonlinear State-Space Models
This paper considers parameter estimation for nonlinear state-space models,
which is an important but challenging problem. We address this challenge by
employing a variational inference (VI) approach, which is a principled method
that has deep connections to maximum likelihood estimation. This VI approach
ultimately provides estimates of the model as solutions to an optimisation
problem, which is deterministic, tractable and can be solved using standard
optimisation tools. A specialisation of this approach for systems with additive
Gaussian noise is also detailed. The proposed method is examined numerically on
a range of simulated and real examples focusing on the robustness to parameter
initialisation; additionally, favourable comparisons are performed against
state-of-the-art alternatives
Variational approach for learning Markov processes from time series data
Inference, prediction and control of complex dynamical systems from time
series is important in many areas, including financial markets, power grid
management, climate and weather modeling, or molecular dynamics. The analysis
of such highly nonlinear dynamical systems is facilitated by the fact that we
can often find a (generally nonlinear) transformation of the system coordinates
to features in which the dynamics can be excellently approximated by a linear
Markovian model. Moreover, the large number of system variables often change
collectively on large time- and length-scales, facilitating a low-dimensional
analysis in feature space. In this paper, we introduce a variational approach
for Markov processes (VAMP) that allows us to find optimal feature mappings and
optimal Markovian models of the dynamics from given time series data. The key
insight is that the best linear model can be obtained from the top singular
components of the Koopman operator. This leads to the definition of a family of
score functions called VAMP-r which can be calculated from data, and can be
employed to optimize a Markovian model. In addition, based on the relationship
between the variational scores and approximation errors of Koopman operators,
we propose a new VAMP-E score, which can be applied to cross-validation for
hyper-parameter optimization and model selection in VAMP. VAMP is valid for
both reversible and nonreversible processes and for stationary and
non-stationary processes or realizations
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