Magnet design through physics informed machine learning

High-performance magnets play a key role in green technologies, including sustainable energy production and clean transport. In order to achieve the climate policy goal of two degrees, rapid electrification of the powertrain is required. Climate policy has a significant impact on the demand for critical materials. The average annual neodymium demand for energy technologies, cars and appliances is expected to increase eightfold between 2015 and 2050. Neodymium and heavy rare earth elements such as terbium and dysprosium are important for the operation of permanent magnets at high temperatures. To address the supply risk of rare-earth elements, magnets are being developed that can both eliminate the use of terbium and dysprosium and reduce the neodymium content. These goals require new strategies for materials design. There is a need to tune the materials composition, to control the grain structure, and to combine different materials at the device level. In this project we aim to develop machine learning methods that assist materials and device development by integrating physical models over all relevant length scales. Guidelines for magnet and device production will be computed taking into account the element supply and raw material costs. In this project a world-leading research group in computational magnetism and a global automotive manufacturer will work together. Excellent computational tools have been developed for the simulation of magnetic materials at various length scales. The applicant is author of micromagnetic software that treats magnetization processes on a mesoscopic level. His software is used world-wide by universities, research institutions, and companies for magnet data storage, magnetic sensors, and permanent magnetic materials design. At all length scale, the simulation of magnetic materials is resource intensive. The problem size is limited and simulations are time consuming. Therefore, numerical optimization that takes into account the material properties at the different length is hardly applied. Machine learning techniques can bridge the length scales. Once trained, machine learning models are fast and can be used for multiparameter optimization. A high magnetization and a high magnetocrystalline anisotropy are essential prerequisites for a permanent magnet material. We will create a machine learning model that maps chemical composition to magnetization and anisotropy, which are input parameters for micromagnetic simulations. Coercive fields of core-shell grains will be computed for various materials combinations and geometrical features on massively parallel hardware. We will train a gradient boost regressor that links geometry and rare-earth content to the coercive field of a single multiphase grain. The single grain model is the building block of a reduced order model for magnetization reversal that takes into account magnetic interactions between the grains of the magnet. A further speed-up for computing magnetization curves will be achieved by a neural network model for domain evolution in latent space. The domain evolution model will be tested by comparing simulation results with measured first order reversal curve diagrams. Coarse graining gives the effective permeability tensor to be used in a quasi-static Maxwell solver. At the macroscale a convolutional neural network model will be developed for fast magnetic field estimation. The optimization potential of the proposed methodology is two-fold: Multi-phase optimization gives the chemical compounds and geometry of a core-shell grain at the microscopic level. At the device level multi-material optimization assigns high coercive (and expensive) materials only to those regions that are subject to strong demagnetizing fields.