20,496 research outputs found
Common pulse retrieval algorithm: a fast and universal method to retrieve ultrashort pulses
We present a common pulse retrieval algorithm (COPRA) that can be used for a
broad category of ultrashort laser pulse measurement schemes including
frequency-resolved optical gating (FROG), interferometric FROG, dispersion
scan, time domain ptychography, and pulse shaper assisted techniques such as
multiphoton intrapulse interference phase scan (MIIPS). We demonstrate its
properties in comprehensive numerical tests and show that it is fast, reliable
and accurate in the presence of Gaussian noise. For FROG it outperforms
retrieval algorithms based on generalized projections and ptychography.
Furthermore, we discuss the pulse retrieval problem as a nonlinear
least-squares problem and demonstrate the importance of obtaining a
least-squares solution for noisy data. These results improve and extend the
possibilities of numerical pulse retrieval. COPRA is faster and provides more
accurate results in comparison to existing retrieval algorithms. Furthermore,
it enables full pulse retrieval from measurements for which no retrieval
algorithm was known before, e.g., MIIPS measurements
Inference for Generalized Linear Models via Alternating Directions and Bethe Free Energy Minimization
Generalized Linear Models (GLMs), where a random vector is
observed through a noisy, possibly nonlinear, function of a linear transform
arise in a range of applications in nonlinear
filtering and regression. Approximate Message Passing (AMP) methods, based on
loopy belief propagation, are a promising class of approaches for approximate
inference in these models. AMP methods are computationally simple, general, and
admit precise analyses with testable conditions for optimality for large i.i.d.
transforms . However, the algorithms can easily diverge for general
. This paper presents a convergent approach to the generalized AMP
(GAMP) algorithm based on direct minimization of a large-system limit
approximation of the Bethe Free Energy (LSL-BFE). The proposed method uses a
double-loop procedure, where the outer loop successively linearizes the LSL-BFE
and the inner loop minimizes the linearized LSL-BFE using the Alternating
Direction Method of Multipliers (ADMM). The proposed method, called ADMM-GAMP,
is similar in structure to the original GAMP method, but with an additional
least-squares minimization. It is shown that for strictly convex, smooth
penalties, ADMM-GAMP is guaranteed to converge to a local minima of the
LSL-BFE, thus providing a convergent alternative to GAMP that is stable under
arbitrary transforms. Simulations are also presented that demonstrate the
robustness of the method for non-convex penalties as well
On Meshfree GFDM Solvers for the Incompressible Navier-Stokes Equations
Meshfree solution schemes for the incompressible Navier--Stokes equations are
usually based on algorithms commonly used in finite volume methods, such as
projection methods, SIMPLE and PISO algorithms. However, drawbacks of these
algorithms that are specific to meshfree methods have often been overlooked. In
this paper, we study the drawbacks of conventionally used meshfree Generalized
Finite Difference Method~(GFDM) schemes for Lagrangian incompressible
Navier-Stokes equations, both operator splitting schemes and monolithic
schemes. The major drawback of most of these schemes is inaccurate local
approximations to the mass conservation condition. Further, we propose a new
modification of a commonly used monolithic scheme that overcomes these problems
and shows a better approximation for the velocity divergence condition. We then
perform a numerical comparison which shows the new monolithic scheme to be more
accurate than existing schemes
- …