2,676 research outputs found
FATODE: A Library for Forward, Adjoint, and Tangent Linear Integration of ODEs
FATODE is a FORTRAN library for the integration of ordinary differential equations with direct and adjoint sensitivity analysis capabilities.
The paper describes the capabilities, implementation, code organization, and usage of this package.
FATODE implements four families of methods -- explicit Runge-Kutta for nonstiff problems and fully implicit Runge-Kutta, singly diagonally implicit Runge-Kutta, and Rosenbrock for stiff problems.
Each family contains several methods with different orders of accuracy; users can add new methods by simply providing their coefficients.
For each family the forward, adjoint, and tangent linear models are implemented.
General purpose solvers for dense and sparse linear algebra are used; users can easily incorporate problem-tailored linear algebra routines.
The performance of the package is demonstrated on several test problems.
To the best of our knowledge FATODE is the first publicly available general purpose package that offers forward and adjoint sensitivity
analysis capabilities in the context of Runge Kutta methods. A wide range of applications are expected to benefit from its use; examples include parameter estimation,
data assimilation, optimal control, and uncertainty quantification
Towards a Better Understanding of the Local Attractor in Particle Swarm Optimization: Speed and Solution Quality
Particle Swarm Optimization (PSO) is a popular nature-inspired meta-heuristic
for solving continuous optimization problems. Although this technique is widely
used, the understanding of the mechanisms that make swarms so successful is
still limited. We present the first substantial experimental investigation of
the influence of the local attractor on the quality of exploration and
exploitation. We compare in detail classical PSO with the social-only variant
where local attractors are ignored. To measure the exploration capabilities, we
determine how frequently both variants return results in the neighborhood of
the global optimum. We measure the quality of exploitation by considering only
function values from runs that reached a search point sufficiently close to the
global optimum and then comparing in how many digits such values still deviate
from the global minimum value. It turns out that the local attractor
significantly improves the exploration, but sometimes reduces the quality of
the exploitation. As a compromise, we propose and evaluate a hybrid PSO which
switches off its local attractors at a certain point in time. The effects
mentioned can also be observed by measuring the potential of the swarm
Forward-Mode Automatic Differentiation in Julia
We present ForwardDiff, a Julia package for forward-mode automatic
differentiation (AD) featuring performance competitive with low-level languages
like C++. Unlike recently developed AD tools in other popular high-level
languages such as Python and MATLAB, ForwardDiff takes advantage of
just-in-time (JIT) compilation to transparently recompile AD-unaware user code,
enabling efficient support for higher-order differentiation and differentiation
using custom number types (including complex numbers). For gradient and
Jacobian calculations, ForwardDiff provides a variant of vector-forward mode
that avoids expensive heap allocation and makes better use of memory bandwidth
than traditional vector mode. In our numerical experiments, we demonstrate that
for nontrivially large dimensions, ForwardDiff's gradient computations can be
faster than a reverse-mode implementation from the Python-based autograd
package. We also illustrate how ForwardDiff is used effectively within JuMP, a
modeling language for optimization. According to our usage statistics, 41
unique repositories on GitHub depend on ForwardDiff, with users from diverse
fields such as astronomy, optimization, finite element analysis, and
statistics.
This document is an extended abstract that has been accepted for presentation
at the AD2016 7th International Conference on Algorithmic Differentiation.Comment: 4 page
Empirical Evaluation of Contextual Policy Search with a Comparison-based Surrogate Model and Active Covariance Matrix Adaptation
Contextual policy search (CPS) is a class of multi-task reinforcement
learning algorithms that is particularly useful for robotic applications. A
recent state-of-the-art method is Contextual Covariance Matrix Adaptation
Evolution Strategies (C-CMA-ES). It is based on the standard black-box
optimization algorithm CMA-ES. There are two useful extensions of CMA-ES that
we will transfer to C-CMA-ES and evaluate empirically: ACM-ES, which uses a
comparison-based surrogate model, and aCMA-ES, which uses an active update of
the covariance matrix. We will show that improvements with these methods can be
impressive in terms of sample-efficiency, although this is not relevant any
more for the robotic domain.Comment: Supplementary material for poster paper accepted at GECCO 2019;
https://doi.org/10.1145/3319619.332193
Experimental Comparisons of Derivative Free Optimization Algorithms
In this paper, the performances of the quasi-Newton BFGS algorithm, the
NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution
Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm
Optimizers (PSO) are compared experimentally on benchmark functions reflecting
important challenges encountered in real-world optimization problems.
Dependence of the performances in the conditioning of the problem and
rotational invariance of the algorithms are in particular investigated.Comment: 8th International Symposium on Experimental Algorithms, Dortmund :
Germany (2009
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