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Multiphysics simulations of microstructure influence on hysteresis and eddy current losses of electrical steel

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arXiv 2025年

作者： Kühn, Patrick Yang, Yangyiwei Chen, Guanyu Foster, Shanelle N. Egger, Herbert Xu, Bai-Xiang Mechanics of Functional Materials Division Institute of Materials Science Technische Universität Darmstadt Darmstadt64287 Germany Department of Electrical and Computer Engineering Michigan State University MI48824 United States Johann Radon Institute for Computational and Applied Mathematics Linz Austria Institute for Numerical Mathematics Johannes Kepler University Linz Austria

Improving efficiency of electrical machines requires fundamental knowledge on the mechanisms behind magnetic and eddy current losses of the magnetic core materials, with Fe-Si alloy as a prototype. These losses are intrinsically influenced by the microstructure of the materials. This necessitates physics-based, microstructure-informed multiscale simulations. In the present paper, we utilised micromagnetic simulations and computational homogenization methods to calculate the effective hysteresis and effective conductivities of Fe-Si electrical steels. To demonstrate the methodology, binder-jet printed electrical steel material samples with different microstructure were investigated. The microstructure samples were digitized based on both the descriptor-based synthetic reconstruction and SEM-image-based digitization. More samples were generated with varying microstructure features such as grain size and grain boundary phases. The micromagnetic simulations were then performed to investigate the magnetic hysteresis and hysteresis loss. The eddy current loss was also evaluated by using the effective conductivity through computational homogenization. By performing parameter research on a series of synthetic microstructures, effects of average grain size and grain boundary (GB) phase thickness on the hysteresis loss and eddy current loss were unveiled. An average grain size around 120 µm has the lowest hysteresis loss, although the eddy current loss increases with the grain size. Increasing GB-phase thickness helps reduce both losses. Results indicate the potential to decrease loss of magnetic core materials by microstructure optimization. © 2025, CC BY.

关键词： Silicon alloys

Multilevel Monte Carlo for a class of Partially Observed Processes in Neuroscience

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arXiv 2023年

作者： Maama, Mohamed Jasra, Ajay Kamatani, Kengo Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia School of Data Science The Chinese University of Hong Kong CN Shenzhen China Institute of Statistical Mathematics Tokyo190-0014 Japan

In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we focus upon the case of neuroscience. The data are assumed to be observed regularly in time and driven by the SDE model with unknown parameters. In practice the SDE may not have an analytically tractable solution and this leads naturally to a time-discretization. We adapt the multilevel Markov chain Monte Carlo method of [15], which works with a hierarchy of time discretizations and show empirically and theoretically that this is preferable to using one single time discretization. The improvement is in terms of the computational cost needed to obtain a pre-specified numerical error. Our approach is illustrated on models applied to examples of Bayesian inference problems using both simulated and real observed data from neuroscience. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

A Flow Artist for High-Dimensional Cellular Data

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A Flow Artist for High-Dimensional Cellular Data

IEEE Workshop on Machine Learning for Signal Processing

作者： Kincaid MacDonald Dhananjay Bhaskar Guy Thampakkul Nhi Nguyen Joia Zhang Michael Perlmutter Ian Adelstein Smita Krishnaswamy Department of Mathematics Yale University Department of Genetics Yale School of Medicine Department of Computer Science Yale University Department of Mathematics Pomona College Applied Mathematics Program Yale University Department of Statistics University of Washington Department of Mathematics Boise State University Computational Biology and Bioinformatics Program Yale University

We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in high-throughput biology such as single-cell transcriptomics. Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i.e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field. Here we present FlowArtist, a neural network that embeds points while jointly learning a vector field around the points. The combination allows FlowArtist to better separate and visualize velocity-informed structures. Our results, on toy datasets and single-cell RNA velocity data, illustrate the value of utilizing coordinate and velocity information in tandem for embedding and visualizing high-dimensional data.

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A PRIORI AND A POSTERIORI ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN TIME-DISCRETE METHODS VIA MAXIMAL REGULARITY

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arXiv 2024年

作者： Akrivis, Georgios Larsson, Stig Department of Computer Science and Engineering University of Ioannina Ioannina451 10 Greece Institute of Applied and Computational Mathematics FORTH Crete Heraklion700 13 Greece Department of Mathematical Sciences Chalmers University of Technology University of Göteborg Göteborg Sweden

The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori error estimates of optimal order under optimal regularity assumptions. The analysis is set in the maximal regularity framework of UMD Banach spaces. Similar results were proved in an earlier work, based on the consistency analysis of Radau IIA methods. The present error analysis, which is based on variational techniques, is of independent interest, but the main motivation is that it extends to nonlinear parabolic equations;in contrast to the earlier work. Both autonomous and nonautonomous linear equations are *** Codes 65M12, 65M15 © 2024, CC BY.

关键词： Galerkin methods

Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation

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arXiv 2024年

作者： An, Dong Childs, Andrew M. Lin, Lin Ying, Lexing Beijing International Center for Mathematical Research Peking University China Joint Center for Quantum Information and Computer Science University of Maryland College Park United States Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Department of Mathematics University of California Berkeley United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley United States Challenge Institute for Quantum Computation University of California Berkeley United States Department of Mathematics Stanford University United States Institute for Computational and Mathematical Engineering Stanford University United States

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are well studied, eigenvalue transformations are distinct, especially for non-normal matrices. We propose an efficient quantum algorithm for performing a class of eigenvalue transformations that can be expressed as a certain type of matrix Laplace transformation. This allows us to significantly extend the recently developed linear combination of Hamiltonian simulation (LCHS) method [An, Liu, Lin, Phys. Rev. Lett. 131, 150603, 2023;An, Childs, Lin, arXiv:2312.03916] to represent a wider class of eigenvalue transformations, such as powers of the matrix inverse, A-k, and the exponential of the matrix inverse, e-A-1. The latter can be interpreted as the solution of a mass-matrix differential equation of the form Au′(t) = -u(t). We demonstrate that our eigenvalue transformation approach can solve this problem without explicitly inverting A, reducing the computational complexity. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

MAKE HASTE SLOWLY: A THEORY OF EMERGENT STRUCTURED MIXED SELECTIVITY IN FEATURE LEARNING RELU NETWORKS

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arXiv 2025年

作者： Jarvis, Devon Klein, Richard Rosman, Benjamin Saxe, Andrew M. School of Computer Science and Applied Mathematics University of the Witwatersrand South Africa Machine Intelligence and Neural Discovery Institute University of the Witwatersrand South Africa Gatsby Computational Neuroscience Unit Sainsbury Wellcome Centre UCL United Kingdom CIFAR Azrieli Global Scholar CIFAR Canada

In spite of finite dimension ReLU neural networks being a consistent factor behind recent deep learning successes, a theory of feature learning in these models remains elusive. Currently, insightful theories still rely on assumptions including the linearity of the network computations, unstructured input data and architectural constraints such as infinite width or a single hidden layer. To begin to address this gap we establish an equivalence between ReLU networks and Gated Deep Linear Networks, and use their greater tractability to derive dynamics of learning. We then consider multiple variants of a core task reminiscent of multi-task learning or contextual control which requires both feature learning and nonlinearity. We make explicit that, for these tasks, the ReLU networks possess an inductive bias towards latent representations which are not strictly modular or disentangled but are still highly structured and reusable between contexts. This effect is amplified with the addition of more contexts and hidden layers. Thus, we take a step towards a theory of feature learning in finite ReLU networks and shed light on how structured mixed-selective latent representations can emerge due to a bias for node-reuse and learning speed. © 2025, CC BY.

关键词： Multi-task learning

Fine-Grained Synonymous Codon Usage Patterns and their Potential Role in Functional Protein Production

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Fine-Grained Synonymous Codon Usage Patterns and their Poten...

2021 IEEE International Conference on Bioinformatics and Biomedicine, BIBM 2021

作者： Babjac, Ashley Li, Jun Emrich, Scott University of Tennessee Department of Electrical Engineering and Computer Science KnoxvilleTN37996 United States University of Notre Dame Department of Applied and Computational Mathematics and Statistics Notre DameIN46556 United States

ISBN: (纸本)9781665401265

Multiple computational models exist that leverage the idea that some codons are 'preferred' to others when producing functional proteins. In this work, we aim to address the following two questions: (i) do proteins have similar codon usage subprofiles?, (ii) if so, can they be associated to specific Gene Ontology (GO) terms? To answer these questions, we analyze two different data sets E. coli and S. cerevisiae (yeast). For both, we use codon usage profiles that have been linked to protein co-translational folding and perform unsupervised clustering. Significantly, our clusters determine biologically meaningful patterns consistent with previously published observations. Our results suggest that codon patterns have potential to be incorporated into more complex deep learning-inspired frameworks in future work to better understand and predict functional protein production in a cell. © 2021 IEEE.

关键词： Proteins

A Novel Perspective on Brain Tumor Classification Using Hybrid Algorithm

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A Novel Perspective on Brain Tumor Classification Using Hybr...

computer, Electronics & Electrical Engineering & their Applications (IC2E3), International Conference on

作者： R. Jayanthi A. Hepzibah Christinal R. Hephzibah T. Shekinah Chandrajit Bajaj D. Abraham Chandy Department of Mathematics Karunya University Coimbatore India Department of Computer Science and Engineering Loyola – ICAM College of Engineering and Technology Chennai Computational Applied Mathematics Chair in Visualization University of Texas Austin Department of Electronics and Communication Engineering Karunya University Coimbatore India

Brain tumor classification is a critical task in medical imaging, where the early and accurate detection of brain tumors is crucial for patient treatment and survival. In recent years, Machine Learning techniques have emerged as a promising approach for automated brain tumor classification. In this paper, we investigate the performance of three ML classifiers – Support Vector Machine, Naïve Bayes, and an ensemble of SVM and Naïve Bayes – for the two-class classification of brain tumor data into a tumor and no tumor classes. Our experiments demonstrate that the ensemble of SVM and Naïve Bayes classifier achieved an accuracy of 97% outperforming the other classifiers. These results indicate that our ensemble classifier can be a powerful tool for the accurate and efficient classification of brain tumor data, potentially leading to improved patient outcomes.

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A framework for fully autonomous design of materials via multiobjective optimization and active learning: challenges and next steps

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arXiv 2023年

作者： Chang, Tyler H. Elias, Jakob R. Wild, Stefan M. Chaudhuri, Santanu Libera, Joseph A. Mathematics and Computer Science Division Argonne National Laboratory United States Applied Materials Division Argonne National Laboratory United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory United States Department of Civil Materials and Environmental Engineering University of Illinois Chicago United States

In order to deploy machine learning in a real-world self-driving laboratory where data acquisition is costly and there are multiple competing design criteria, systems need to be able to intelligently sample while balancing performance trade-offs and constraints. For these reasons, we present an active learning process based on multiobjective black-box optimization with continuously updated machine learning models. This workflow is built on open-source technologies for real-time data streaming and modular multiobjective optimization software development. We demonstrate a proof of concept for this workflow through the autonomous operation of a continuous-flow chemistry laboratory, which identifies ideal manufacturing conditions for the electrolyte 2,2,2-trifluoroethyl methyl carbonate. Copyright © 2023, The Authors. All rights reserved.

关键词： Multiobjective optimization