Application of heuristic optimization techniques in physics of magnetism

The progress of technical abilities of computers creates enables the use of still more elaborated computational techniques. The classical examples are here the Monte-Carlo or the Molecular Dynamics simulations which are the sensible alternative to study even quite complicated structures. In this work we want, however, to deal with the problems which may be described as the optimization questions and from the algorithmical point of view are NP-hard problems. The typical problem studied is here the searching for the ground states of different magnetic systems. In the presented paper we pay the attention to the samples described by the Ising hamiltonian and want to show the use of evolutionary algorithm not only in finding the ground state but also as a tool to look for the minimum energy state at different temperatures

Phase diagram for mixed ternary alloy from evolutionary optimization

There is an increasing interest in studying still more complicated magnetic systems. A group of ternary mixed alloys is, among them, a point of interest for as well historical as scientific reasons. The most known material belonging to this group is the famous pigment - Prussian blue. The Prussian blue analogues may be characterized by special properties, like the existence of compensation points or different magnetic phases. It is also a computationally hard problem due to a large number of possible combination of states. In this work I present the results of ground state calculations for Prussian blue analog with A lattice occupation 0.66 and p = 0 which is the simplest model. The phase diagram presented show dicrepancies with results presented earlier by other groups coming from the lower total energy obtained in the evolutionary computation

Gale duality, decoupling, parameter homotopies, and monodromy

2014 Spring.Numerical Algebraic Geometry (NAG) has recently seen significantly increased application among scientists and mathematicians as a tool that can be used to solve nonlinear systems of equations, particularly polynomial systems. With the many recent advances in the field, we can now routinely solve problems that could not have been solved even 10 years ago. We will give an introduction and overview of numerical algebraic geometry and homotopy continuation methods; discuss heuristics for preconditioning fewnomial systems, as well as provide a hybrid symbolic-numerical algorithm for computing the solutions of these types of polynomials and associated software called galeDuality; describe a software module of bertini named paramotopy that is scientific software specifically designed for large-scale parameter homotopy runs; give two examples that are parametric polynomial systems on which the aforementioned software is used; and finally describe two novel algorithms, decoupling and a heuristic that makes use of monodromy

Compositional optimization of hard-magnetic phases with machine-learning models

Machine Learning (ML) plays an increasingly important role in the discovery and design of new materials. In this paper, we demonstrate the potential of ML for materials research using hard-magnetic phases as an illustrative case. We build kernel-based ML models to predict optimal chemical compositions for new permanent magnets, which are key components in many green-energy technologies. The magnetic-property data used for training and testing the ML models are obtained from a combinatorial high-throughput screening based on density-functional theory calculations. Our straightforward choice of describing the different configurations enables the subsequent use of the ML models for compositional optimization and thereby the prediction of promising substitutes of state-of-the-art magnetic materials like Nd$_2$Fe$_{14}$B with similar intrinsic hard-magnetic properties but a lower amount of critical rare-earth elements.Comment: 12 pages, 6 figure