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Adaptive energy reference for machine-learning models of the electronic density of states

Physical Review Materials 2025年第1期9卷 013802-013802页

作者： Wei Bin How Sanggyu Chong Federico Grasselli Kevin K. Huguenin-Dumittan Laboratory of Computational Science and Modeling IMX École Polytechnique Fédérale de Lausanne Lausanne 1015 Switzerland

The electronic density of states (DOS) provides information regarding the distribution of electronic energy levels in a material, and can be used to approximate its optical and electronic properties and therefore guide computational materials design. Given its usefulness and relative simplicity, it has been one of the first electronic properties used as a target for machine-learning approaches going beyond interatomic potentials. A subtle but important point, well appreciated in the condensed matter community but usually overlooked in the construction of data-driven models, is that for bulk configurations the absolute energy reference of single-particle energy levels is ill-defined. Only energy differences matter, and quantities derived from the DOS are typically independent of the absolute alignment. We introduce an adaptive scheme that optimizes the energy reference of each structure as part of the training process and show that it consistently improves the quality of machine-learning models compared to traditional choices of energy reference for different classes of materials and different model architectures. On a practical level, we trace the improved performance to the ability of this self-aligning scheme to match the most prominent features in the DOS. More broadly, we believe that this paper highlights the importance of incorporating insights on the nature of the physical target into the definition of the architecture and of the appropriate figures of merit for machine-learning models, translating into better transferability and overall performance.

关键词： Electronic density of states

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Machine Learning for Online Multiscale Model Reduction for Poroelasticity Problem in Heterogeneous Media

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Lobachevskii Journal of Mathematics 2024年第11期45卷 5437-5451页

作者： Tyrylgin, A. Bai, H. Yang, Y. Laboratory of Computational Technologies for Modeling Multiphysical and Multiscale Permafrost Processes North-Eastern Federal University Yakutsk 677000 Russian Federation North-Caucasus Center for Mathematical Research North-Caucasus Federal University Stavropol 355017 Russian Federation School of Mathematics and Computational Science Xiangtan University Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Hunan Xiangtan 411105 China School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan Xiangtan 411105 China

In this study, we address the poroelasticity problem in heterogeneous media, which involves a coupled system of equations for fluid pressures and displacements. This problem is crucial in geomechanics for modeling the interaction between fluid flow and deformation in porous media, with applications spanning oil and gas reservoirs, groundwater systems, and geothermal energy production. We introduce an innovative approach by integrating machine learning techniques to train online multiscale basis functions, enhancing the Generalized Multiscale Finite Element Method (GMsFEM). This methodology allows for an adaptive and efficient representation of both macroscopic and local heterogeneities in the system, significantly reducing computational costs. The offline multiscale basis functions are precomputed using local spectral problems, while the online basis functions are dynamically updated using machine learning models trained on local residual data. This approach ensures rapid error reduction and robust convergence, leveraging the computational efficiency of machine learning. We demonstrate the effectiveness of this method through numerical experiments, showcasing its potential in advancing the simulation and modeling of poroelasticity problems in heterogeneous media. © Pleiades Publishing, Ltd. 2024.

关键词： basis functions Darcy equation displacement heterogeneous media machine learning multiscale methods online GMsFEM poroelasticity

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Thermal conductivity of Li3PS4 solid electrolytes with ab initio accuracy

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Physical Review Materials 2024年第6期8卷 065403-065403页

作者： Davide Tisi Federico Grasselli Lorenzo Gigli Michele Ceriotti Laboratory of Computational Science and Modeling Institut des Matériaux École Polytechnique Fédérale de Lausanne Lausanne 1015 Switzerland

The vast amount of computational studies on electrical conduction in solid-state electrolytes is not mirrored by comparable efforts addressing thermal conduction, which has been scarcely investigated despite its relevance to thermal management and (over)heating of batteries. The reason for this lies in the complexity of the calculations: on one hand, the diffusion of ionic charge carriers makes lattice methods formally unsuitable, due to the lack of equilibrium atomic positions needed for normal-mode expansion. On the other hand, the prohibitive cost of large-scale molecular dynamics (MD) simulations of heat transport in large systems at ab initio levels has hindered the use of MD-based methods. In this paper, we leverage recently developed machine-learning potentials targeting different ab initio functionals (PBEsol, r2SCAN, PBE0) and a state-of-the-art formulation of the Green-Kubo theory of heat transport in multicomponent systems to compute the thermal conductivity of a promising solid-state electrolyte, Li3PS4, in all its polymorphs (α, β, and γ). By comparing MD estimates with lattice methods on the low-temperature, nondiffusive γ−Li3PS4, we highlight strong anharmonicities and negligible nuclear quantum effects, hence further justifying MD-based methods even for nondiffusive phases. Finally, for the ion-conducting α and β phases, where the multicomponent Green-Kubo MD approach is mandatory, our simulations indicate a weak temperature dependence of the thermal conductivity, a glass-like behavior due to the effective local disorder characterizing these Li-diffusing phases.

关键词： Solid-state batteries Thermal conductivity Lithium-ion batteries Boltzmann theory Hybrid functionals Linear response theory Machine learning

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Thermodynamics and dielectric response of BaTiO_(3)by data-driven modeling

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npj computational Materials 2022年第1期8卷 1998-2014页

作者： Lorenzo Gigli Max Veit Michele Kotiuga Giovanni Pizzi Nicola Marzari Michele Ceriotti Laboratory of Computational Science and Modeling(COSMO) Institute of MaterialsÉcole Polytechnique Fédérale de LausanneCH-1015LausanneSwitzerland Theory and Simulation of Materials(THEOS)and National Centre for Computational Design and Discovery of Novel Materials(MARVEL) École Polytechnique Fédérale de LausanneCH-1015LausanneSwitzerland

modeling ferroelectric materials from first principles is one of the successes of density-functional theory and the driver of much development effort,requiring an accurate description of the electronic processes and the thermodynamic equilibrium that drive the spontaneous symmetry breaking and the emergence of macroscopic *** demonstrate the development and application of an integrated machine learning model that describes on the same footing structural,energetic,and functional properties of barium titanate(BaTiO_(3)),a prototypical *** model uses ab initio calculations as a reference and achieves accurate yet inexpensive predictions of energy and polarization on time and length scales that are not accessible to direct ab initio *** predictions allow us to assess the microscopic mechanism of the ferroelectric *** presence of an order-disorder transition for the Ti off-centered states is the main driver of the ferroelectric transition,even though the coupling between symmetry breaking and cell distortions determines the presence of intermediate,partly-ordered ***,we thoroughly probe the static and dynamical behavior of BaTiO_(3)across its phase diagram without the need to introduce a coarse-grained description of the ferroelectric ***,we apply the polarization model to calculate the dielectric response properties of the material in a full ab initio manner,again reproducing the correct qualitative experimental behavior.

关键词： transition ferroelectric dielectric

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modeling the ferroelectric phase transition in barium titanate with DFT accuracy and converged sampling

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Physical Review B 2024年第2期110卷 024101-024101页

作者： Lorenzo Gigli Alexander Goscinski Michele Ceriotti Gareth A. Tribello Laboratory of Computational Science and Modeling Institut des Matériaux Division of Chemistry and Chemical Engineering Centre for Quantum Materials and Technologies (CQMT) School of Mathematics and Physics

The accurate description of the structural and thermodynamic properties of ferroelectrics has been one of the most remarkable achievements of density functional theory (DFT). However, running large simulation cells with DFT is computationally demanding, while simulations of small cells are often plagued with nonphysical effects that are a consequence of the system's finite size. To avoid these finite-size effects one is thus often forced to use empirical models that describe the physics of the material in terms of effective interaction terms, that are fitted using the results from DFT. In this study we use a machine-learning (ML) potential trained on DFT, in combination with accelerated sampling techniques, to converge the thermodynamic properties of barium titanate (BTO) with first-principles accuracy and a full atomistic description. Our results indicate that the predicted Curie temperature depends strongly on the choice of DFT functional and system size, because of emergent long-range directional correlations in the local dipole fluctuations. Our findings demonstrate how the combination of ML models and traditional bottom-up modeling allow one to investigate emergent phenomena with the accuracy of first-principles calculations over the large size and time scales afforded by empirical models.

关键词： Ferroelectric phase transition Ferroelectricity Phase transitions Phase transitions by order Thermodynamics Ferroelectrics Functional materials Density functional theory Machine learning Materials modeling Molecular dynamics

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BALLORG: State-of-the-art Image Restoration using Block-augmented Lagrangian and Low-rank Gradients

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IEIE Transactions on Smart Processing and Computing 2023年第1期12卷 1-8页

作者： Tojo, Laya Devi, Manju Maik, Vivek Gurushankar Department of Electronics and Communication The Oxford College of Engineering Bangalore560068 India Department of Electronics and Communication Engineering SRM Institute of Science and Technology Kattankulathur Tamil Nadu Chennai India Laboratory of Computational Modeling of Drugs Higher Medical and Biological School South Ural State University Chelyabinsk454080 Russia

In this paper, we propose a blind image deblurring algorithm using block-augmented Lagrangian and low-rank priors (BALLORG) as a non-learning method that can give better results without the complexity of learning-based methods. The proposed algorithm achieves faster convergence within 20 iterations than conventional methods. Regularization priors are used in the form of gradients and sparse low-rank matrices, and recursive rank improvements result in better deblurring performance. The steepest descent in minimization is maintained through weight selection for penalty and regularization parameters. The block processing introduces local and global optimization, leading to better visual quality outputs. The proposed method has excellent performance in terms of the PSNR, SSIM, and FSIM matrix, which is on par with or better than that of other state-of-the-art learning and non-learning-based approaches. © 2023 Institute of Electronics and Information Engineers. All rights reserved.

关键词： Constrained optimization

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The dark side of the forces: assessing non-conservative force models for atomistic machine learning

arXiv

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arXiv 2024年

作者： Bigi, Filippo Langer, Marcel F. Ceriotti, Michele Laboratory of Computational Science and Modeling IMX Ecole Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland

The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, have revolutionized the fields of computational chemistry and materials discovery. In this domain, rigorous enforcement of symmetry and conservation laws has traditionally been considered essential. For this reason, interatomic forces are usually computed as the derivatives of the potential energy, ensuring energy conservation. Several recent works have questioned this physically constrained approach, suggesting that directly predicting the forces yields a better trade-off between accuracy and computational efficiency – and that energy conservation can be learned during training. This work investigates the applicability of such non-conservative models in microscopic simulations. We identify and demonstrate several fundamental issues, from ill-defined convergence of geometry optimization to instability in various types of molecular dynamics. Contrary to the case of rotational symmetry, energy conservation is hard to learn, monitor, and correct for. The best approach to exploit the acceleration afforded by direct force prediction might be to use it in tandem with a conservative model, reducing – rather than eliminating – the additional cost of backpropagation, but avoiding the pathological behavior associated with non-conservative forces. Copyright © 2024, The Authors. All rights reserved.

关键词： Molecular dynamics

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Adaptive energy reference for machine-learning models of the electronic density of states

arXiv

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arXiv 2024年

作者： How, Wei Bin Chong, Sanggyu Grasselli, Federico Huguenin-Dumittan, Kevin K. Ceriotti, Michele Laboratory of Computational Science and Modeling IMX École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland

The electronic density of states (DOS) provides information regarding the distribution of electronic energy levels in a material, and can be used to approximate its optical and electronic properties and therefore guide computational materials design. Given its usefulness and relative simplicity, it has been one of the first electronic properties used as target for machine-learning approaches going beyond interatomic potentials. A subtle but important point, well appreciated in the condensed matter community but usually overlooked in the construction of data-driven models, is that for bulk configurations the absolute energy reference of single-particle energy levels is ill defined. Only energy differences matter, and quantities derived from the DOS are typically independent of the absolute alignment. We introduce an adaptive scheme that optimizes the energy reference of each structure as part of the training process, and show that it consistently improves the quality of machine-learning models compared to traditional choices of energy reference, for different classes of materials and different model architectures. On a practical level, we trace the improved performance to the ability of this self-aligning scheme to match the most prominent features in the DOS. More broadly, we believe that this paper highlights the importance of incorporating insights on the nature of the physical target into the definition of the architecture and of the appropriate figures of merit for machine-learning models, that translate in better transferability and overall performance. Copyright © 2024, The Authors. All rights reserved.

关键词： Electronic density of states

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Prediction rigidities for data-driven chemistry

arXiv

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arXiv 2024年

作者： Chong, Sanggyu Bigi, Filippo Grasselli, Federico Loche, Philip Kellner, Matthias Ceriotti, Michele Laboratory of Computational Science and Modeling Institute of Materials École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland

The widespread application of machine learning (ML) to the chemical sciences is making it very important to understand how the ML models learn to correlate chemical structures with their properties, and what can be done to improve the training efficiency whilst guaranteeing interpretability and transferability. In this work, we demonstrate the wide utility of prediction rigidities, a family of metrics derived from the loss function, in understanding the robustness of ML model predictions. We show that the prediction rigidities allow the assessment of the model not only at the global level, but also on the local or the component-wise level at which the intermediate (e.g. atomic, body-ordered, or range-separated) predictions are made. We leverage these metrics to understand the learning behavior of different ML models, and to guide efficient dataset construction for model training. We finally implement the formalism for a ML model targeting a coarse-grained system to demonstrate the applicability of the prediction rigidities to an even broader class of atomistic modeling problems. Copyright © 2024, The Authors. All rights reserved.

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Efficient SVV stabilized triangular spectral element methods for incompressible flows of high Reynolds numbers

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Advances in Aerodynamics 2022年第1期4卷 58-77页

作者： Lizhen Chen Tao Tang Chuanju Xu Beijing Computational Science Research Center Beijing100193People’s Republic of China Division of Science and Technology BNU-HKBU United International CollegeZhuhaiGuangdongPeople’s Republic of China Guangdong Provincial Key Laboratory of Computational Science and Material Design Southern University of Science and TechnologyShenzhenPeople’s Republic of China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamen361005People’s Republic of China

In this paper,we propose a spectral vanishing viscosity method for the triangular spectral element computation of high Reynolds number incompressible *** can be regarded as an extension of a similar stabilization technique for the standard spectral element *** difficulty of this extension lies in the fact that a suitable definition of spectral vanishing viscosity operator in non-structured elements does not exist,and it is not clear that if a suitably defined spectral vanishing viscosity provides desirable dissipation for the artificially accumulated *** main contribution of the paper includes:1)a well-defined spectral vanishing viscosity operator is proposed for non-standard spectral element methods for the Navier-Stokes equations based on triangular or tetrahedron partitions;2)an evaluation technique is introduced to efficiently implement the stabilization term without extra computational cost;3)the accuracy and efficiency of the proposed method is carefully examined through several numerical *** numerical results show that the proposed method not only preserves the exponential convergence,but also produces improved accuracy when applied to the unsteady Navier-Stokes equations having smooth ***,the stabilized triangular spectral element method efficiently stabilizes the simulation of high Reynolds incompressible flows.

关键词： Navier-Stokes equations Triangular spectral element method Spectral vanishing viscosity

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