Ensemble Kalman filter for neural network based one-shot inversion

We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simultaneously in a one-shot sense when estimating the unknown parameters from data, i.e. the neural network is trained only for the unknown parameter. By establishing a link to the Bayesian approach to inverse problems, an algorithmic framework is developed which ensures the feasibility of the parameter estimate w.r. to the forward model. We propose an efficient, derivative-free optimization method based on variants of the ensemble Kalman inversion. Numerical experiments show that the ensemble Kalman filter for neural network based one-shot inversion is a promising direction combining optimization and machine learning techniques for inverse problems

A Covariance Matrix Adaptation Evolution Strategy for Direct Policy Search in Reproducing Kernel Hilbert Space

The covariance matrix adaptation evolution strategy (CMA-ES) is an efficient derivative-free optimization algorithm. It optimizes a black-box objective function over a well defined parameter space. In some problems, such parameter spaces are defined using function approximation in which feature functions are manually defined. Therefore, the performance of those techniques strongly depends on the quality of chosen features. Hence, enabling CMA-ES to optimize on a more complex and general function class of the objective has long been desired. Specifically, we consider modeling the input space for black-box optimization in reproducing kernel Hilbert spaces (RKHS). This modeling leads to a functional optimization problem whose domain is a function space that enables us to optimize in a very rich function class. In addition, we propose CMA-ES-RKHS, a generalized CMA-ES framework, that performs black-box functional optimization in the RKHS. A search distribution, represented as a Gaussian process, is adapted by updating both its mean function and covariance operator. Adaptive representation of the function and covariance operator is achieved with sparsification techniques. We evaluate CMA-ES-RKHS on a simple functional optimization problem and bench-mark reinforcement learning (RL) domains. For an application in RL, we model policies for MDPs in RKHS and transform a cumulative return objective as a functional of RKHS policies, which can be optimized via CMA-ES-RKHS. This formulation results in a black-box functional policy search framework

Identification of Hemodynamically Optimal Coronary Stent Designs Based on Vessel Caliber

Coronary stent design influences local patterns of wall shear stress (WSS) that are associated with neointimal growth, restenosis, and the endothelialization of stent struts. The number of circumferentially repeating crowns NC for a given stent de- sign is often modified depending on the target vessel caliber, but the hemodynamic implications of altering NC have not previously been studied. In this investigation, we analyzed the relationship between vessel diameter and the hemodynamically optimal NC using a derivative-free optimization algorithm coupled with computational fluid dynamics. The algorithm computed the optimal vessel diameter, defined as minimizing the area of stent-induced low WSS, for various configurations (i.e., NC) of a generic slotted-tube design and designs that resemble commercially available stents. Stents were modeled in idealized coronary arteries with a vessel diameter that was allowed to vary between 2 and 5 mm. The results indicate that the optimal vessel diameter increases for stent configurations with greater NC, and the designs of current commercial stents incorporate a greater NC than hemodynamically optimal stent designs. This finding suggests that reducing the NC of current stents may improve the hemodynamic environment within stented arteries and reduce the likelihood of excessive neointimal growth and thrombus formation

A Derivative Free Optimization method for reservoir characterization inverse problem

International audienceReservoir characterization inverse problem aims at building reservoir models consistent with available production and seismic data for better forecasting of the production of a field. These observed data (pressures, oil/water/gas rates at the wells and 4D seismic data) are compared with simulated data to determine unknown petrophysical properties of the reservoir. The underlying optimization problem is usually formulated as the minimization of a least-squares objective function composed of two terms : the production data and the seismic data mismatch. In practice, this problem is often solved by nonlinear optimization methods, such as Sequential Quadratic Programming methods with derivatives approximated by finite differences. In applications involving 4D seismic data, the use of the classical Gauss-Newton algorithm is often infeasible because the computation of the Jacobian matrix is CPU time consuming and its storage is impossible for large datasets like seismic-related ones. Consequently, this optimization problem requires dedicated techniques: derivatives are not available, the associated forward problems are CPU time consuming and some constraints may be introduced to handle a priori information. We propose a derivative free optimization method under constraints based on trust region approach coupled with local quadratic interpolating models of the cost function and of non linear constraints. Results obtained with this method on a synthetic reservoir application with the joint inversion of production data and 4D seismic data are presented. Its performance is compared with a classical SQP method (quasi-Newton approach based on classical BFGS approximation of the Hessian of the objective function with derivatives approximated by finite differences) in terms of number of simulations of the forward problem

Approaches to accommodate remeshing in shape optimization

This study proposes novel optimization methodologies for the optimization of problems that reveal non-physical step discontinuities. More specifically, it is proposed to use gradient-only techniques that do not use any zeroth order information at all for step discontinuous problems. A step discontinuous problem of note is the shape optimization problem in the presence of remeshing strategies, since changes in mesh topologies may - and normally do - introduce non-physical step discontinuities. These discontinuities may in turn manifest themselves as non-physical local minima in which optimization algorithms may become trapped. Conventional optimization approaches for step discontinuous problems include evolutionary strategies, and design of experiment (DoE) techniques. These conventional approaches typically rely on the exclusive use of zeroth order information to overcome the discontinuities, but are characterized by two important shortcomings: Firstly, the computational demands of zero order methods may be very high, since many function values are in general required. Secondly, the use of zero order information only does not necessarily guarantee that the algorithms will not terminate in highly unfit local minima. In contrast, the methodologies proposed herein use only first order information, rather than only zeroth order information. The motivation for this approach is that associated gradient information in the presence of remeshing remains accurately and uniquely computable, notwithstanding the presence of discontinuities. From a computational effort point of view, a gradient-only approach is of course comparable to conventional gradient based techniques. In addition, the step discontinuities do not manifest themselves as local minima.Thesis (PhD)--University of Pretoria, 2010.Mechanical and Aeronautical Engineeringunrestricte

Derivative-Free Robust Optimization for Circuit Design

In this paper, we introduce a framework for derivative-free robust opti- mization based on the use of an efficient derivative-free optimization routine for mixed-integer nonlinear problems. The proposed framework is employed to find a robust optimal design of a particular integrated circuit (namely a DC–DC converter commonly used in portable electronic devices). The proposed robust optimization ap- proach outperforms the traditional statistical approach as it is shown in the numerical result