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Land cover classification plays a critical role in describing Earth's surface characteristics. However, these classifications can be affected by uncertainties introduced by variability in investigator interpretations. While land cover classification mapping is becoming easier due to the emergence of cloud geospatial platforms, such uncertainty is often overlooked. This study aimed to create a robust land cover classification map by reducing inter-investigator variability from independent investigators' maps using a Bayesian inference framework. In Saitama City, Japan, as a case study, 44 investigators used a point-based visual interpretation method via Google Earth Engine to collect stratified reference samples across four different land cover classes: Forest, Agriculture, Urban, and Water. These samples were then used to train a random forest classifier, resulting in the creation of individual classification maps. We quantified pixel-level discrepancies in these maps arising from inherent inter-investigator variability. To address them, we developed a Bayesian inference framework to produce a unified classification map. This framework updates the classification probability based on a Dirichlet distribution and yielded an overall accuracy of 0.851 for independent validation samples, an improvement over the average accuracy of 0.728 for the individual maps. We further improved the results by introducing K-Medoids to group the most reliable maps as the input for Bayesian inference, achieving an overall accuracy of 0.858, the highest among all approaches tested. Our approach also effectively reduced salt-and-pepper noise, which is often found in individual classification maps. This research underscores the intrinsic uncertainties present in land cover classification maps attributable to investigator variations and introduces a potential solution to mitigate these variations., Comment: 17 pages, 7 figures

This work introduces a latent space method to calculate the demagnetization reversal process of multigrain permanent magnets. The algorithm consists of two deep learning models based on neural networks. The embedded Stoner-Wohlfarth method is used as a reduced order model for computing samples to train and test the machine learning approach. The work is a proof of concept of the method since the used microstructures are simple and the only varying parameters are the magnetic anisotropy axes of the hard magnetic grains. A convolutional autoencoder is used for nonlinear dimensionality reduction, in order to reduce the required amount of training samples for predicting the hysteresis loops. We enriched the loss function with physical information about the underlying problem which increases the accuracy of the machine learning approach. A deep learning regressor is operating in the latent space of the autoencoder. The predictor takes a series of previously encoded magnetization states and outputs the next magnetization state along the hysteresis curve. To predict the complete demagnetization loop, we apply a recursive learning scheme.

We demonstrate the use of model order reduction and neural networks for estimating the hysteresis properties of nanocrystalline permanent magnets from microstructure. With a data-driven approach, we learn the demagnetization curve from data-sets created by grain growth and micromagnetic simulations. We show that the granular structure of a magnet can be encoded within a low-dimensional latent space. Latent codes are constructed using a variational autoencoder. The mapping of structure code to hysteresis properties is a multi-target regression problem. We apply deep neural network and use parameter sharing, in order to predict anchor points along the demagnetization curves from the magnet's structure code. The method is applied to study the magnetic properties of nanocrystalline permanent magnets. We show how new grain structures can be generated by interpolation between two points in the latent space and how the magnetic properties of the resulting magnets can be predicted., Comment: 17 pages, 8 figures

In this paper, we address the problem that standard stochastic Landau-Lifshitz-Gilbert (sLLG) simulations typically produce results that show unphysical mesh-size dependence. The root cause of this problem is that the effects of spin wave fluctuations are ignored in sLLG. We propose to represent the effect of these fluctuations by a "FUll-Spinwave-Scaled Stochastic LLG", or FUSSS LLG method. In FUSSS LLG, the intrinsic parameters of the sLLG simulations are first scaled by scaling factors that integrate out the spin wave fluctuations up to the mesh size, and the sLLG simulation is then performed with these scaled parameters. We developed FUSSS LLG by studying the Ferromagnetic Resonance (FMR) in Nd$_2$Fe$_{14}$B cubes. The nominal scaling greatly reduced the mesh size dependence relative to sLLG. We further discovered that adjusting one scaling exponent by less than 10% delivered fully mesh-size-independent results for the FMR peak. We then performed three tests and validations of our FUSSS LLG with this modified scaling. 1) We studied the same FMR but with magnetostatic fields included. 2) We simulated the total magnetization of the Nd$_2$Fe$_{14}$B cube. 3) We studied the effective, temperature- and sweeping rate-dependent coercive field of the cubes. In all three cases we found that FUSSS LLG delivered essentially mesh-size-independent results, which tracked the theoretical expectations better than unscaled sLLG. Motivated by these successful validations, we propose that FUSSS LLG provides marked, qualitative progress towards accurate, high precision modeling of micromagnetics in hard, permanent magnets., Comment: 9 pages, 6 figures, 1 table

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the solutions to a class of problems. We demonstrate this idea by estimating the coercive field of permanent magnets which depends on the width and strength of local defects. When the neural network incorporates the physics of magnetization reversal, training can be achieved in an unsupervised way. There is no need to generate labeled training data. The presented test cases have been rigorously studied in the past. Thus, a detailed and easy comparison with analytical solutions is made. We show that a single deep neural network can learn the solution of partial differential equations for an entire class of problems., Comment: 18 pages, 11 figures

We propose a data-assimilation method for evaluating the finite-temperature magnetization of a permanent magnet over a high-dimensional composition space. Based on a general framework for constructing a predictor from two data sets including missing values, a practical scheme for magnetic materials is formulated in which a small number of experimental data in limited composition space are integrated with a larger number of first-principles calculation data. We apply the scheme to (Nd$_{1-\alpha-\beta-\gamma}$Pr$_{\alpha}$La$_{\beta}$Ce$_{\gamma}$)$_{2}$(Fe$_{1-\delta-\zeta}$Co$_{\delta}$Ni$_{\zeta}$)$_{14}$B. The magnetization in the whole $(\alpha, \beta, \gamma, \delta, \zeta)$ space at arbitrary temperature is obtained. It is shown that the Co doping does not enhance the magnetization at low temperatures, whereas the magnetization increases with increasing $\delta$ above 320 K., Comment: 11 pages, 7 figures

We investigated the atomic fill site probability distributions across supercell structures of RT12-xTi (R=Nd, Sm, T=Fe, Co). We use a combined molecular dynamics and Boltzmann distribution approach to extrapolate the probability distributions for Ti substitution from lower to higher temperatures with an equilibrium condition to assess how temperature affects the predictability of the structures fill path. It was found that the Nd and Sm based Fe systems have the highest filling probability path at lower temperatures but the cohesive energy change due to Ti substitution in Sm and Nd based crystals indicates that a more stable system could be achieved with a combination Co and Fe in the transition metal site., Comment: 5 pages, 4 figures, 2 tables

We demonstrate how micromagnetic simulations can be employed in order to characterize and analyze the magnetic microstructure of nanocomposites. For the example of nanocrystalline Nd$-$Fe$-$B, which is a potential material for future permanent-magnet applications, we have compared three different models for the micromagnetic analysis of this material class: (i) a description of the nanocomposite microstructure in terms of Stoner-Wohlfarth particles with and without the magnetodipolar interaction; (ii) a model based on the core-shell representation of the nanograins; (iii) the latter model including a contribution of superparamagnetic clusters. The relevant parameter spaces have been systematically scanned with the aim to establish which micromagnetic approach can most adequately describe experimental data for this material. According to our results, only the last, most sophisticated model is able to provide an excellent agreement with the measured hysteresis loop. The presented methodology is generally applicable to multiphase magnetic nanocomposites and it highligths the complex interrelationship between the microstructure, magnetic interactions, and the macroscopic magnetic properties.

We report the results of a comparative study of the magnetic microstructure of textured and isotropic $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}/\alpha$-$\mathrm{Fe}$ nanocomposites using magnetometry, transmission electron microscopy, synchrotron x-ray diffraction, and, in particular, magnetic small-angle neutron scattering (SANS). Analysis of the magnetic neutron data of the textured specimen and computation of the correlation function of the spin misalignment SANS cross section suggests the existence of inhomogeneously magnetized regions on an intraparticle nanometer length scale, about $40-50 \, \mathrm{nm}$ in the remanent state. Possible origins for this spin disorder are discussed: it may originate in thin grain-boundary layers (where the materials parameters are different than in the $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}$ grains), or it may reflect the presence of crystal defects (introduced via hot pressing), or the dispersion in the orientation distribution of the magnetocrystalline anisotropy axes of the $\mathrm{Nd}_2\mathrm{Fe}_{14}\mathrm{B}$ grains. X-ray powder diffraction data reveal a crystallographic texture in the direction perpendicular to the pressing direction -- a finding which might be related to the presence of a texture in the magnetization distribution, as inferred from the magnetic SANS data.

The coercive field of permanent magnets decreases with increasing grain size. The grain size dependence of coercivity is explained by a size dependent demagnetizing factor. In Dy free Nd$_2$Fe$_{14}$B magnets the size dependent demagnetizing factor ranges from 0.2 for a grain size of 55 nm to 1.22 for a grain size of 8300 nm. The comparison of experimental data with micromagnetic simulations suggests that the grain size dependence of the coercive field in hard magnets is due to the non-uniform magnetostatic field in polyhedral grains.

The coercive field and angular dependence of the coercive field of single-grain Nd$_{2}$Fe$_{14}$B permanent magnets are computed using finite element micromagnetics. It is shown that the thickness of surface defects plays a critical role in determining the reversal process. For small defect thicknesses reversal is heavily driven by nucleation, whereas with increasing defect thickness domain wall de-pinning becomes more important. This change results in an observable shift between two well-known behavioral models. A similar trend is observed in experimental measurements of bulk samples, where a Nd-Cu infiltration process has been used to enhance coercivity by modifying the grain boundaries. When account is taken of the imperfect grain alignment of real magnets, the single-grain computed results appears to closely match experimental behaviour.