Search results for "Automatic differentiation"
showing 10 items of 12 documents
From optimization to algorithmic differentiation: a graph detour
2021
This manuscript highlights the work of the author since he was nominated as "Chargé de Recherche" (research scientist) at Centre national de la recherche scientifique (CNRS) in 2015. In particular, the author shows a thematic and chronological evolution of his research interests:- The first part, following his post-doctoral work, is concerned with the development of new algorithms for non-smooth optimization.- The second part is the heart of his research in 2020. It is focused on the analysis of machine learning methods for graph (signal) processing.- Finally, the third and last part, oriented towards the future, is concerned with (automatic or not) differentiation of algorithms for learnin…
Automatic differentiation of melanoma from dysplastic nevi.
2015
International audience; Malignant melanoma causes the majority of deaths related to skin cancer. Nevertheless, it is the most treatable one, depending on its early diagnosis. The early prognosis is a challenging task for both clinicians and dermatologist, due to the characteristic similarities of melanoma with other skin lesions such as dysplastic nevi. In the past decades, several computerized lesion analysis algorithms have been proposed by the research community for detection of melanoma. These algorithms mostly focus on differentiating melanoma from benign lesions and few have considered the case of melanoma against dysplastic nevi. In this paper, we consider the most challenging task a…
An Automatic Differentiation Based Approach to the Level Set Method
2015
This paper discusses an implementation of the parametric level set method. Adjoint approach is used to perform the sensitivity analysis, but contrary to standard implementations, the state problem is differentiated in its discretized form. The required partial derivatives are computed using tools of automatic differentiation, which avoids the need to derive the adjoint problem from the governing partial differential equation. The augmented Lagrangian approach is used to enforce volume constraints, and a gradient based optimization method is used to solve the subproblems. Applicability of the method is demonstrated by repeating well known compliance minimization studies of a cantilever beam …
Geometric optimal control : homotopic methods and applications
2012
This work is about geometric optimal control applied to celestial and quantum mechanics. We first dealt with the minimum fuel consumption problem of transfering a satellite around the Earth. This brought to the creation of the code HamPath which permits first of all to solve optimal control problem for which the command law is smooth. It is based on the Pontryagin Maximum Principle (PMP) and on the notion of conjugate point. This program combines shooting method, differential homotopic methods and tools to compute second order optimality conditions. Then we are interested in quantum control. We study first a system which consists in two different particles of spin 1/2 having two different r…
Implementation of sparse forward mode automatic differentiation with application to electromagnetic shape optimization
2011
In this paper, we present the details of a simple lightweight implementation of the so-called sparse forward mode automatic differentiation (AD) in the C++programming language. Our implementation and the well-known ADOL-C tool (which utilizes taping and compression techniques) are used to compute Jacobian matrices of two nonlinear systems of equations from the MINPACK-2 test problem collection. Timings of the computations are presented and discussed. Moreover, we perform the shape sensitivity analysis of a time-harmonic Maxwell equation solver using our implementation and the tapeless mode of ADOL-C, which implements the dense forward mode AD. It is shown that the use of the sparse forward …
On shape differentiation of discretized electric field integral equation
2013
Abstract This work presents shape derivatives of the system matrix representing electric field integral equation discretized with Raviart–Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in an excellent agreement. Furthermore, the derived formulas are employed to analyze shape sensitivity of the input impedance of a planar inverted F-antenna, and the results are compared to those obtained using a finite difference approximation.
Continuous optimal control sensitivity analysis with AD
2000
In order to apply a parametric method to a minimum time control problem in celestial mechanics, a sensitivity analysis is performed. The analysis is continuous in the sense that it is done in the infinite dimensional control setting. The resulting sufficient second order condition is evaluated by means of automatic differentiation, while the associated sensitivity derivative is computed by continuous reverse differentiation. The numerical results are given for several examples of orbit transfer, also illustrating the advantages of automatic differentiation over finite differences for the computation of gradients on the discretized problem.
Optimisation non-lisse pour l'estimation de composants immunitaires cellulaires dans un environnement tumoral
2021
In this PhD proposal we will investigate new regularization methods of inverse problems that provide an absolute quantification of immune cell subpopulations. The mathematical aspect of this PhD proposal is two-fold. The first goal is to enhance the underlying linear model through a more refined construction of the expression matrix. The second goal is, given this linear model, to derive the best possible estimator. These two issues can be treated in a decoupled way, which is the standard for existing methods such as Cibersort, or as a coupled optimization problem (which is known as blind deconvolution in signal processing).
Algorithmic differentiation for cloud schemes (IFS Cy43r3) using CoDiPack (v1.8.1)
2019
Abstract. Numerical models in atmospheric sciences not only need to approximate the flow equations on a suitable computational grid, they also need to include subgrid effects of many non-resolved physical processes. Among others, the formation and evolution of cloud particles is an example of such subgrid processes. Moreover, to date there is no universal mathematical description of a cloud, hence many cloud schemes have been proposed and these schemes typically contain several uncertain parameters. In this study, we propose the use of algorithmic differentiation (AD) as a method to identify parameters within the cloud scheme, to which the output of the cloud scheme is most sensitive. We il…
Canonical Retina-to-Cortex Vision Model Ready for Automatic Differentiation
2020
Canonical vision models of the retina-to-V1 cortex pathway consist of cascades of several Linear+Nonlinear layers. In this setting, parameter tuning is the key to obtain a sensible behavior when putting all these multiple layers to work together. Conventional tuning of these neural models very much depends on the explicit computation of the derivatives of the response with regard to the parameters. And, in general, this is not an easy task. Automatic differentiation is a tool developed by the deep learning community to solve similar problems without the need of explicit computation of the analytic derivatives. Therefore, implementations of canonical visual neuroscience models that are ready…