336,212 research outputs found
Accuracy and transferability of Gaussian approximation potential models for tungsten
We introduce interatomic potentials for tungsten in the bcc crystal phase and its defects within the Gaussian approximation potential framework, fitted to a database of first-principles density functional theory calculations. We investigate the performance of a sequence of models based on databases of increasing coverage in configuration space and showcase our strategy of choosing representative small unit cells to train models that predict properties observable only using thousands of atoms. The most comprehensive model is then used to calculate properties of the screw dislocation, including its structure, the Peierls barrier and the energetics of the vacancy-dislocation interaction. All software and raw data are available at www.libatoms.org
Approximately bisimilar symbolic models for nonlinear control systems
Control systems are usually modeled by differential equations describing how
physical phenomena can be influenced by certain control parameters or inputs.
Although these models are very powerful when dealing with physical phenomena,
they are less suitable to describe software and hardware interfacing the
physical world. For this reason there is a growing interest in describing
control systems through symbolic models that are abstract descriptions of the
continuous dynamics, where each "symbol" corresponds to an "aggregate" of
states in the continuous model. Since these symbolic models are of the same
nature of the models used in computer science to describe software and
hardware, they provide a unified language to study problems of control in which
software and hardware interact with the physical world. Furthermore the use of
symbolic models enables one to leverage techniques from supervisory control and
algorithms from game theory for controller synthesis purposes. In this paper we
show that every incrementally globally asymptotically stable nonlinear control
system is approximately equivalent (bisimilar) to a symbolic model. The
approximation error is a design parameter in the construction of the symbolic
model and can be rendered as small as desired. Furthermore if the state space
of the control system is bounded the obtained symbolic model is finite. For
digital control systems, and under the stronger assumption of incremental
input-to-state stability, symbolic models can be constructed through a suitable
quantization of the inputs.Comment: Corrected typo
Solving, Estimating and Selecting Nonlinear Dynamic Models without the Curse of Dimensionality
We present a comprehensive framework for Bayesian estimation of structural nonlinear dynamic economic models on sparse grids. TheSmolyak operator underlying the sparse grids approach frees global approximation from the curse of dimensionality and we apply it to a Chebyshev approximation of the model solution. The operator also eliminates the curse from Gaussian quadrature and we use it for the integrals arising from rational expectations and in three new nonlinear state space filters. The filters substantially decrease the computational burden compared to the sequential importance resampling particle filter. The posterior of the structural parameters is estimated by a new Metropolis-Hastings algorithm with mixing parallel sequences. The parallel extension improves the global maximization property of the algorithm, simplifies the choice of the innovation variances, allows for unbiased convergence diagnostics and for a simple implementation of the estimation on parallel computers. Finally, we provide all algorithms in the open source software JBendge4 for the solution and estimation of a general class of models.Dynamic Stochastic General Equilibrium (DSGE) Models, Bayesian Time Series Econometrics, Curse of Dimensionality
Latent Gaussian modeling and INLA: A review with focus on space-time applications
Bayesian hierarchical models with latent Gaussian layers have proven very
flexible in capturing complex stochastic behavior and hierarchical structures
in high-dimensional spatial and spatio-temporal data. Whereas simulation-based
Bayesian inference through Markov Chain Monte Carlo may be hampered by slow
convergence and numerical instabilities, the inferential framework of
Integrated Nested Laplace Approximation (INLA) is capable to provide accurate
and relatively fast analytical approximations to posterior quantities of
interest. It heavily relies on the use of Gauss-Markov dependence structures to
avoid the numerical bottleneck of high-dimensional nonsparse matrix
computations. With a view towards space-time applications, we here review the
principal theoretical concepts, model classes and inference tools within the
INLA framework. Important elements to construct space-time models are certain
spatial Mat\'ern-like Gauss-Markov random fields, obtained as approximate
solutions to a stochastic partial differential equation. Efficient
implementation of statistical inference tools for a large variety of models is
available through the INLA package of the R software. To showcase the practical
use of R-INLA and to illustrate its principal commands and syntax, a
comprehensive simulation experiment is presented using simulated non Gaussian
space-time count data with a first-order autoregressive dependence structure in
time
JBendge: An Object-Oriented System for Solving, Estimating and Selecting Nonlinear Dynamic Models
We present an object-oriented software framework allowing to specify, solve, and estimate nonlinear dynamic general equilibrium (DSGE) models. The imple- mented solution methods for nding the unknown policy function are the standard linearization around the deterministic steady state, and a function iterator using a multivariate global Chebyshev polynomial approximation with the Smolyak op- erator to overcome the course of dimensionality. The operator is also useful for numerical integration and we use it for the integrals arising in rational expecta- tions and in nonlinear state space lters. The estimation step is done by a parallel Metropolis-Hastings (MH) algorithm, using a linear or nonlinear lter. Implemented are the Kalman, Extended Kalman, Particle, Smolyak Kalman, Smolyak Sum, and Smolyak Kalman Particle lters. The MH sampling step can be interactively moni- tored and controlled by sequence and statistics plots. The number of parallel threads can be adjusted to benet from multiprocessor environments. JBendge is based on the framework JStatCom, which provides a standardized ap- plication interface. All tasks are supported by an elaborate multi-threaded graphical user interface (GUI) with project management and data handling facilities.Dynamic Stochastic General Equilibrium (DSGE) Models, Bayesian Time Series Econometrics, Java, Software Development
A Petri Net Tool for Software Performance Estimation Based on Upper Throughput Bounds
Functional and non-functional properties analysis (i.e., dependability, security, or performance) ensures that requirements are fulfilled during the design phase of software systems. However, the Unified Modelling Language (UML), standard de facto in industry for software systems modelling, is unsuitable for any kind of analysis but can be tailored for specific analysis purposes through profiling. For instance, the MARTE profile enables to annotate performance data within UML models that can be later transformed to formal models (e.g., Petri nets or Timed Automatas) for performance evaluation. A performance (or throughput) estimation in such models normally relies on a whole exploration of the state space, which becomes unfeasible for large systems. To overcome this issue upper throughput bounds are computed, which provide an approximation to the real system throughput with a good complexity-accuracy trade-off. This paper introduces a tool, named PeabraiN, that estimates the performance of software systems via their UML models. To do so, UML models are transformed to Petri nets where performance is estimated based on upper throughput bounds computation. PeabraiN also allows to compute other features on Petri nets, such as the computation of upper and lower marking place bounds, and to simulate using an approximate (continuous) method. We show the applicability of PeabraiN by evaluating the performance of a building closed circuit TV system
TMB: Automatic Differentiation and Laplace Approximation
TMB is an open source R package that enables quick implementation of complex
nonlinear random effect (latent variable) models in a manner similar to the
established AD Model Builder package (ADMB, admb-project.org). In addition, it
offers easy access to parallel computations. The user defines the joint
likelihood for the data and the random effects as a C++ template function,
while all the other operations are done in R; e.g., reading in the data. The
package evaluates and maximizes the Laplace approximation of the marginal
likelihood where the random effects are automatically integrated out. This
approximation, and its derivatives, are obtained using automatic
differentiation (up to order three) of the joint likelihood. The computations
are designed to be fast for problems with many random effects (~10^6) and
parameters (~10^3). Computation times using ADMB and TMB are compared on a
suite of examples ranging from simple models to large spatial models where the
random effects are a Gaussian random field. Speedups ranging from 1.5 to about
100 are obtained with increasing gains for large problems. The package and
examples are available at http://tmb-project.org
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