Using Covariance Matrix Adaptation Evolutionary Strategy to boost the search accuracy in hierarchic memetic computations

Many global optimization problems arising naturally in science and engineering exhibit some form of intrinsic ill-posedness, such as multimodality and insensitivity. Severe ill-posedness precludes the use of standard regularization techniques and necessitates more specialized approaches, usually comprised of two separate stages - global phase, that determines the problem's modality and provides rough approximations of the solutions, and a local phase, which re fines these approximations. In this work, we attempt to improve one of the most efficient currently known approaches - Hierarchic Memetic Strategy (HMS) - by incorporating the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) into its local phase. CMA-ES is a stochastic optimization algorithm that in some sense mimics the behavior of population-based evolutionary algorithms without explicitly evolving the population. This way, it avoids, to an extent, the associated cost of multiple evaluations of the objective function. We compare the performance of the HMS on relatively simple multimodal benchmark problems and on an engineering problem. To do so, we consider two con gurations: the CMA-ES and the standard SEA (Simple Evolutionary Algorithm). The results demonstrate that the HMS with CMA-ES in the local phase requires less objective function evaluations to provide the same accuracy, making this approach more efficient than the standard SEA

An Agent-Oriented Hierarchic Strategy for Solving Inverse Problems

The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is dynamically adjusted for each inverse search step. The computational cost is further decreased by the strategy employed for solution inter-processing and fitness deterioration. The HMS efficiency is compared with the results of a standard evolutionary technique, as well as with the multi-start strategy on benchmarks that exhibit typical inverse problems' difficulties. Finally, an HMS application to a real-life engineering problem leading to the identification of oil deposits by inverting magnetotelluric measurements is presented. The HMS applicability to the inversion of magnetotelluric data is also mathematically verified

Ab initio study of the relationship between spontaneous polarization and p-type doping in quasi-freestanding graphene on H-passivated SiC surfaces

Quasi-free standing graphene (QFG) obtained by the intercalation of a hydrogen layer between a SiC surface and the graphene is recognized as an excellent candidate for the development of graphene based technology. In addition, the recent proposal of a direct equivalence between the $p$-type doping typically found for these systems and the spontaneous polarization (SP) associated to the particular SiC polytype, opens the possibility of tuning the number of carriers in the Dirac cones without the need of external gate voltages. However, first principles calculations which could confirm at the atomic scale the effect of the SP are lacking mainly due to the difficulty of combining a bulk property such as the SP with the surface confined graphene doping. Here we develop an approach based on standard density functional theory (DFT) slab calculations in order to quantify the effect of the SP on the QFG doping level. First, we present an accurate scheme to estimate the SPs by exploiting the dependence of the slab's dipole moment with its thickness. Next, and in order to circumvent the DFT shortcomings associated to polar slab geometries, a double gold layer is attached at the C-terminated bottom of the slab which introduces a metal induced gap state that pins the chemical potential inside the gap thus allowing a meaningful comparison of the QFG dopings among different polytypes. Furthermore, the slab dipole can be removed after adjusting the Au-Au interlayer distances. Our results confirm that the SP does indeed induce a substantial p-doping of the Dirac cones which can be as large as a few hundreds of meV depending on the hexagonality of the polytype. The evolution of the doping with the slab thickness reveals that several tens of SiC bilayers are required to effectively remove the depolarization field and recover the macroscopic regime whereby the graphene doping should equal the SP

A multi-objective memetic inverse solver reinforced by local optimization methods

We propose a new memetic strategy that can solve the multi-physics, complex inverse problems, formulated as the multi-objective optimization ones, in which objectives are misfits between the measured and simulated states of various governing processes. The multi-deme structure of the strategy allows for both, intensive, relatively cheap exploration with a moderate accuracy and more accurate search many regions of Pareto set in parallel. The special type of selection operator prefers the coherent alternative solutions, eliminating artifacts appearing in the particular processes. The additional accuracy increment is obtained by the parallel convex searches applied to the local scalarizations of the misfit vector. The strategy is dedicated for solving ill-conditioned problems, for which inverting the single physical process can lead to the ambiguous results. The skill of the selection in artifact elimination is shown on the benchmark problem, while the whole strategy was applied for identification of oil deposits, where the misfits are related to various frequencies of the magnetic and electric waves of the magnetotelluric measurement

Multi-objective hierarchic memetic solver for inverse parametric problems

We propose a multi-objective approach for solving challenging inverse parametric problems. The objectives are misfits for several physical descriptions of a phenomenon under consideration, whereas their domain is a common set of admissible parameters. The resulting Pareto set, or parameters close to it, constitute various alternatives of minimizing individual misfits. A special type of selection applied to the memetic solution of the multi-objective problem narrows the set of alternatives to the ones that are sufficiently coherent. The proposed strategy is exemplified by solving a real-world engineering problem consisting of the magnetotelluric measurement inversion that leads to identification of oil deposits located about 3 km under the Earth's surface, where two misfit functions are related to distinct frequencies of the electric and magnetic waves

Fast parallel IGA-ADS solver for time-dependent Maxwell's equations

We propose a simulator for time-dependent Maxwell's equations with linear computational cost. We employ B-spline basis functions as considered in the isogeometric analysis (IGA). We focus on non-stationary Maxwell's equations defined on a regular patch of elements. We employ the idea of alternating-directions splitting (ADS) and employ a second-order accurate time-integration scheme for the time-dependent Maxwell's equations in a weak form. After discretization, the resulting stiffness matrix exhibits a Kronecker product structure. Thus, it enables linear computational cost LU factorization. Additionally, we derive a formulation for absorbing boundary conditions (ABCs) suitable for direction splitting. We perform numerical simulations of the scattering problem (traveling pulse wave) to verify the ABC. We simulate the radiation of electromagnetic (EM) waves from the dipole antenna. We verify the order of the time integration scheme using a manufactured solution problem. We then simulate magnetotelluric measurements. Our simulator is implemented in a shared memory parallel machine, with the GALOIS library supporting the parallelization. We illustrate the parallel efficiency with strong and weak scalability tests corresponding to non-stationary Maxwell simulations.EXPERTIA (KK-2021/00048) SIGZE (KK-2021/00095) PDC2021-121093-I0

On round-off error for adaptive finite element methods

Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called 'radical meshes'. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix. © 2012 Published by Elsevier Ltd

A Simulation Method for the Computation of the E

We propose a set of numerical methods for the computation of the frequency-dependent eff ective primary wave velocity of heterogeneous rocks. We assume the rocks' internal microstructure is given by micro-computed tomography images. In the low/medium frequency regime, we propose to solve the acoustic equation in the frequency domain by a Finite Element Method (FEM). We employ a Perfectly Matched Layer to truncate the computational domain and we show the need to repeat the domain a su cient number of times to obtain accurate results. To make this problem computationally tractable, we equip the FEM with non-fitting meshes and we precompute multiple blocks of the sti ffness matrix. In the high-frequency range, we solve the eikonal equation with a Fast Marching Method. Numerical results con rm the validity of the proposed methods and illustrate the e ffect of density, porosity, and the size and distribution of the pores on the e ective compressional wave velocity