Alexander Khrabry, Louis E. S. Hoffenberg, Igor D. Kaganovich, Yuri Barsukov, David B. Graves
Accurate Gibbs free energies of Fe clusters are required for predictive modeling of Fe cluster growth during condensation of a cooling vapor. We present a straightforward method of calculating free energies of cluster formation using the data provided by molecular dynamics (MD) simulations. We apply this method to calculate free energies of Fe clusters having from 2 to 100 atoms. The free energies are verified by comparing to an MD-simulated equilibrium cluster size distribution in a sub-saturated vapor. We show that these free energies differ significantly from those obtained with a commonly used spherical cluster approximation - which relies on a surface tension coefficient of a flat surface. The spherical cluster approximation can be improved by using a cluster size-dependent Tolman correction for the surface tension. The values for the Tolman length and effective surface tension were derived, which differ from the commonly used experimentally measured surface tension based on the potential energy. This improved approximation does not account for geometric magic number effects responsible for spikes and troughs in densities of neighbor cluster sizes. Nonetheless, it allows to model cluster formation from a cooling vapor and accurately reproduce the condensation timeline, overall shape of the cluster size distribution, average cluster size, and the distribution width. Using a constant surface tension coefficient resulted in distorted condensation dynamics and inaccurate cluster size distributions. The analytical expression for cluster nucleation rate from classical nucleation theory (CNT) was updated to account for the size-dependence of cluster surface tension.
{"title":"Gibbs free energies of Fe clusters can be approximated by Tolman correction to accurately model cluster nucleation and growth","authors":"Alexander Khrabry, Louis E. S. Hoffenberg, Igor D. Kaganovich, Yuri Barsukov, David B. Graves","doi":"arxiv-2408.16693","DOIUrl":"https://doi.org/arxiv-2408.16693","url":null,"abstract":"Accurate Gibbs free energies of Fe clusters are required for predictive\u0000modeling of Fe cluster growth during condensation of a cooling vapor. We\u0000present a straightforward method of calculating free energies of cluster\u0000formation using the data provided by molecular dynamics (MD) simulations. We\u0000apply this method to calculate free energies of Fe clusters having from 2 to\u0000100 atoms. The free energies are verified by comparing to an MD-simulated\u0000equilibrium cluster size distribution in a sub-saturated vapor. We show that\u0000these free energies differ significantly from those obtained with a commonly\u0000used spherical cluster approximation - which relies on a surface tension\u0000coefficient of a flat surface. The spherical cluster approximation can be\u0000improved by using a cluster size-dependent Tolman correction for the surface\u0000tension. The values for the Tolman length and effective surface tension were\u0000derived, which differ from the commonly used experimentally measured surface\u0000tension based on the potential energy. This improved approximation does not\u0000account for geometric magic number effects responsible for spikes and troughs\u0000in densities of neighbor cluster sizes. Nonetheless, it allows to model cluster\u0000formation from a cooling vapor and accurately reproduce the condensation\u0000timeline, overall shape of the cluster size distribution, average cluster size,\u0000and the distribution width. Using a constant surface tension coefficient\u0000resulted in distorted condensation dynamics and inaccurate cluster size\u0000distributions. The analytical expression for cluster nucleation rate from\u0000classical nucleation theory (CNT) was updated to account for the\u0000size-dependence of cluster surface tension.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yangjun Qin, Xiao Wan, Liuhua Mu, Zhicheng Zong, Tianhao Li, Nuo Yang
The influence of hydrated cation-{pi} interaction forces on the adsorption and filtration capabilities of graphene-based membrane materials is significant. However, the lack of interaction potential between hydrated Cs+ and graphene limits the scope of adsorption studies. Here, it is developed that a deep neural network potential function model to predict the interaction force between hydrated Cs+ and graphene. The deep potential has DFT-level accuracy, enabling accurate property prediction. This deep potential is employed to investigate the properties of the graphene surface solution, including the density distribution, mean square displacement, and vibrational power spectrum of water. Furthermore, calculations of the molecular orbital electron distributions indicate the presence of electron migration in the molecular orbitals of graphene and hydrated Cs+, resulting in a strong electrostatic interaction force. The method provides a powerful tool to study the adsorption behavior of hydrated cations on graphene surfaces and offers a new solution for handling radionuclides.
{"title":"Deep potential for interaction between hydrated Cs+ and graphene","authors":"Yangjun Qin, Xiao Wan, Liuhua Mu, Zhicheng Zong, Tianhao Li, Nuo Yang","doi":"arxiv-2408.15797","DOIUrl":"https://doi.org/arxiv-2408.15797","url":null,"abstract":"The influence of hydrated cation-{pi} interaction forces on the adsorption\u0000and filtration capabilities of graphene-based membrane materials is\u0000significant. However, the lack of interaction potential between hydrated Cs+\u0000and graphene limits the scope of adsorption studies. Here, it is developed that\u0000a deep neural network potential function model to predict the interaction force\u0000between hydrated Cs+ and graphene. The deep potential has DFT-level accuracy,\u0000enabling accurate property prediction. This deep potential is employed to\u0000investigate the properties of the graphene surface solution, including the\u0000density distribution, mean square displacement, and vibrational power spectrum\u0000of water. Furthermore, calculations of the molecular orbital electron\u0000distributions indicate the presence of electron migration in the molecular\u0000orbitals of graphene and hydrated Cs+, resulting in a strong electrostatic\u0000interaction force. The method provides a powerful tool to study the adsorption\u0000behavior of hydrated cations on graphene surfaces and offers a new solution for\u0000handling radionuclides.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gustavo R. Pérez-Lemus, Yinan Xu, Yezhi Jin, Pablo F. Zubieta Rico, Juan J. de Pablo
Machine-learned interatomic potentials (MILPs) are rapidly gaining interest for molecular modeling, as they provide a balance between quantum-mechanical level descriptions of atomic interactions and reasonable computational efficiency. However, questions remain regarding the stability of simulations using these potentials, as well as the extent to which the learned potential energy function can be extrapolated safely. Past studies have reported challenges encountered when MILPs are applied to classical benchmark systems. In this work, we show that some of these challenges are related to the characteristics of the training datasets, particularly the inclusion of rigid constraints. We demonstrate that long stability in simulations with MILPs can be achieved by generating unconstrained datasets using unbiased classical simulations if the fast modes are correctly sampled. Additionally, we emphasize that in order to achieve precise energy predictions, it is important to resort to enhanced sampling techniques for dataset generation, and we demonstrate that safe extrapolation of MILPs depends on judicious choices related to the system's underlying free energy landscape and the symmetry features embedded within the machine learning models.
{"title":"The Importance of Learning without Constraints: Reevaluating Benchmarks for Invariant and Equivariant Features of Machine Learning Potentials in Generating Free Energy Landscapes","authors":"Gustavo R. Pérez-Lemus, Yinan Xu, Yezhi Jin, Pablo F. Zubieta Rico, Juan J. de Pablo","doi":"arxiv-2408.16157","DOIUrl":"https://doi.org/arxiv-2408.16157","url":null,"abstract":"Machine-learned interatomic potentials (MILPs) are rapidly gaining interest\u0000for molecular modeling, as they provide a balance between quantum-mechanical\u0000level descriptions of atomic interactions and reasonable computational\u0000efficiency. However, questions remain regarding the stability of simulations\u0000using these potentials, as well as the extent to which the learned potential\u0000energy function can be extrapolated safely. Past studies have reported\u0000challenges encountered when MILPs are applied to classical benchmark systems.\u0000In this work, we show that some of these challenges are related to the\u0000characteristics of the training datasets, particularly the inclusion of rigid\u0000constraints. We demonstrate that long stability in simulations with MILPs can\u0000be achieved by generating unconstrained datasets using unbiased classical\u0000simulations if the fast modes are correctly sampled. Additionally, we emphasize\u0000that in order to achieve precise energy predictions, it is important to resort\u0000to enhanced sampling techniques for dataset generation, and we demonstrate that\u0000safe extrapolation of MILPs depends on judicious choices related to the\u0000system's underlying free energy landscape and the symmetry features embedded\u0000within the machine learning models.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Paul Fuchs, Stephan Thaler, Sebastien Röcken, Julija Zavadlav
Neural Networks (NNs) are promising models for refining the accuracy of molecular dynamics, potentially opening up new fields of application. Typically trained bottom-up, atomistic NN potential models can reach first-principle accuracy, while coarse-grained implicit solvent NN potentials surpass classical continuum solvent models. However, overcoming the limitations of costly generation of accurate reference data and data inefficiency of common bottom-up training demands efficient incorporation of data from many sources. This paper introduces the framework chemtrain to learn sophisticated NN potential models through customizable training routines and advanced training algorithms. These routines can combine multiple top-down and bottom-up algorithms, e.g., to incorporate both experimental and simulation data or pre-train potentials with less costly algorithms. chemtrain provides an object-oriented high-level interface to simplify the creation of custom routines. On the lower level, chemtrain relies on JAX to compute gradients and scale the computations to use available resources. We demonstrate the simplicity and importance of combining multiple algorithms in the examples of parametrizing an all-atomistic model of titanium and a coarse-grained implicit solvent model of alanine dipeptide.
神经网络（NN）是提高分子动力学精确度的有前途的模型，有可能开辟新的应用领域。通常自下而上训练的原子论 NN 势模型可以达到第一原理精度，而粗粒度隐式溶剂 NN 势则超越了经典的连续介质模型。然而，要克服精确参考数据生成成本高昂和普通自下而上训练数据效率低的限制，就必须有效地整合多种来源的数据。本文介绍了 chemtrain 框架，通过可定制的训练程序和先进的训练算法来学习复杂的 NN 电位模型。这些训练程序可以结合多种自上而下和自下而上的算法，例如，结合实验数据和模拟数据，或使用低成本算法预训练电位。 chemtrain 提供了面向对象的高级接口，简化了自定义程序的创建。在底层，chemtrain 依靠 JAX 计算梯度，并根据可用资源的使用情况对计算进行扩展。我们以钛的全原子模型参数化和丙氨酸二肽的粗粒度隐式溶剂模型为例，展示了多种算法组合的简便性和重要性。
{"title":"chemtrain: Learning Deep Potential Models via Automatic Differentiation and Statistical Physics","authors":"Paul Fuchs, Stephan Thaler, Sebastien Röcken, Julija Zavadlav","doi":"arxiv-2408.15852","DOIUrl":"https://doi.org/arxiv-2408.15852","url":null,"abstract":"Neural Networks (NNs) are promising models for refining the accuracy of\u0000molecular dynamics, potentially opening up new fields of application. Typically\u0000trained bottom-up, atomistic NN potential models can reach first-principle\u0000accuracy, while coarse-grained implicit solvent NN potentials surpass classical\u0000continuum solvent models. However, overcoming the limitations of costly\u0000generation of accurate reference data and data inefficiency of common bottom-up\u0000training demands efficient incorporation of data from many sources. This paper\u0000introduces the framework chemtrain to learn sophisticated NN potential models\u0000through customizable training routines and advanced training algorithms. These\u0000routines can combine multiple top-down and bottom-up algorithms, e.g., to\u0000incorporate both experimental and simulation data or pre-train potentials with\u0000less costly algorithms. chemtrain provides an object-oriented high-level\u0000interface to simplify the creation of custom routines. On the lower level,\u0000chemtrain relies on JAX to compute gradients and scale the computations to use\u0000available resources. We demonstrate the simplicity and importance of combining\u0000multiple algorithms in the examples of parametrizing an all-atomistic model of\u0000titanium and a coarse-grained implicit solvent model of alanine dipeptide.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fanjie Xu, Wentao Guo, Feng Wang, Lin Yao, Hongshuai Wang, Fujie Tang, Zhifeng Gao, Linfeng Zhang, Weinan E, Zhong-Qun Tian, Jun Cheng
The study of structure-spectrum relationships is essential for spectral interpretation, impacting structural elucidation and material design. Predicting spectra from molecular structures is challenging due to their complex relationships. Herein, we introduce NMRNet, a deep learning framework using the SE(3) Transformer for atomic environment modeling, following a pre-training and fine-tuning paradigm. To support the evaluation of NMR chemical shift prediction models, we have established a comprehensive benchmark based on previous research and databases, covering diverse chemical systems. Applying NMRNet to these benchmark datasets, we achieve state-of-the-art performance in both liquid-state and solid-state NMR datasets, demonstrating its robustness and practical utility in real-world scenarios. This marks the first integration of solid and liquid state NMR within a unified model architecture, highlighting the need for domainspecific handling of different atomic environments. Our work sets a new standard for NMR prediction, advancing deep learning applications in analytical and structural chemistry.
{"title":"Towards a Unified Benchmark and Framework for Deep Learning-Based Prediction of Nuclear Magnetic Resonance Chemical Shifts","authors":"Fanjie Xu, Wentao Guo, Feng Wang, Lin Yao, Hongshuai Wang, Fujie Tang, Zhifeng Gao, Linfeng Zhang, Weinan E, Zhong-Qun Tian, Jun Cheng","doi":"arxiv-2408.15681","DOIUrl":"https://doi.org/arxiv-2408.15681","url":null,"abstract":"The study of structure-spectrum relationships is essential for spectral\u0000interpretation, impacting structural elucidation and material design.\u0000Predicting spectra from molecular structures is challenging due to their\u0000complex relationships. Herein, we introduce NMRNet, a deep learning framework\u0000using the SE(3) Transformer for atomic environment modeling, following a\u0000pre-training and fine-tuning paradigm. To support the evaluation of NMR\u0000chemical shift prediction models, we have established a comprehensive benchmark\u0000based on previous research and databases, covering diverse chemical systems.\u0000Applying NMRNet to these benchmark datasets, we achieve state-of-the-art\u0000performance in both liquid-state and solid-state NMR datasets, demonstrating\u0000its robustness and practical utility in real-world scenarios. This marks the\u0000first integration of solid and liquid state NMR within a unified model\u0000architecture, highlighting the need for domainspecific handling of different\u0000atomic environments. Our work sets a new standard for NMR prediction, advancing\u0000deep learning applications in analytical and structural chemistry.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142204157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shun Nanjo, Arifin, Hayato Maeda, Yoshihiro Hayashi, Kan Hatakeyama-Sato, Ryoji Himeno, Teruaki Hayakawa, Ryo Yoshida
Machine learning has rapidly advanced the design and discovery of new materials with targeted applications in various systems. First-principles calculations and other computer experiments have been integrated into material design pipelines to address the lack of experimental data and the limitations of interpolative machine learning predictors. However, the enormous computational costs and technical challenges of automating computer experiments for polymeric materials have limited the availability of open-source automated polymer design systems that integrate molecular simulations and machine learning. We developed SPACIER, an open-source software program that integrates RadonPy, a Python library for fully automated polymer property calculations based on all-atom classical molecular dynamics into a Bayesian optimization-based polymer design system to overcome these challenges. As a proof-of-concept study, we successfully synthesized optical polymers that surpass the Pareto boundary formed by the tradeoff between the refractive index and Abbe number.
{"title":"SPACIER: On-Demand Polymer Design with Fully Automated All-Atom Classical Molecular Dynamics Integrated into Machine Learning Pipelines","authors":"Shun Nanjo, Arifin, Hayato Maeda, Yoshihiro Hayashi, Kan Hatakeyama-Sato, Ryoji Himeno, Teruaki Hayakawa, Ryo Yoshida","doi":"arxiv-2408.05135","DOIUrl":"https://doi.org/arxiv-2408.05135","url":null,"abstract":"Machine learning has rapidly advanced the design and discovery of new\u0000materials with targeted applications in various systems. First-principles\u0000calculations and other computer experiments have been integrated into material\u0000design pipelines to address the lack of experimental data and the limitations\u0000of interpolative machine learning predictors. However, the enormous\u0000computational costs and technical challenges of automating computer experiments\u0000for polymeric materials have limited the availability of open-source automated\u0000polymer design systems that integrate molecular simulations and machine\u0000learning. We developed SPACIER, an open-source software program that integrates\u0000RadonPy, a Python library for fully automated polymer property calculations\u0000based on all-atom classical molecular dynamics into a Bayesian\u0000optimization-based polymer design system to overcome these challenges. As a\u0000proof-of-concept study, we successfully synthesized optical polymers that\u0000surpass the Pareto boundary formed by the tradeoff between the refractive index\u0000and Abbe number.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schr"{o}dinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born-Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, Schr"{o}dingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a rotationally equivariant total wavefunction ansatz that includes both nuclear and electronic coordinates. This strategy not only allows for the efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections through a single training process. Comparison with benchmarks of atomic and molecular systems demonstrates its accuracy and efficiency.
通过将各种基于神经网络（NN）的波函数解析与变异蒙特卡洛方法相结合，机器学习的最新进展促进了电子薛定谔方程（SE）的精确数值求解。然而，这些基于神经网络的方法都是基于天生-奥本海默近似（BOA）的，需要对每个核构型进行昂贵的计算训练。在这项工作中，我们提出了一种新颖的 NN 架构--Schr"{o}dingerNet，通过定义一个旨在均衡整个系统局部能量的损失函数来求解全电子-核 SE。这种策略不仅可以在采样良好的核构型空间内的任何几何形状上高效、准确地生成连续势能面，还可以通过单一训练过程纳入非BOA 修正。与原子和分子系统基准的比较证明了它的准确性和效率。
{"title":"SchrödingerNet: A Universal Neural Network Solver for The Schrödinger Equation","authors":"Yaolong Zhang, Bin Jiang, Hua Guo","doi":"arxiv-2408.04497","DOIUrl":"https://doi.org/arxiv-2408.04497","url":null,"abstract":"Recent advances in machine learning have facilitated numerically accurate\u0000solution of the electronic Schr\"{o}dinger equation (SE) by integrating various\u0000neural network (NN)-based wavefunction ansatzes with variational Monte Carlo\u0000methods. Nevertheless, such NN-based methods are all based on the\u0000Born-Oppenheimer approximation (BOA) and require computationally expensive\u0000training for each nuclear configuration. In this work, we propose a novel NN\u0000architecture, Schr\"{o}dingerNet, to solve the full electronic-nuclear SE by\u0000defining a loss function designed to equalize local energies across the system.\u0000This approach is based on a rotationally equivariant total wavefunction ansatz\u0000that includes both nuclear and electronic coordinates. This strategy not only\u0000allows for the efficient and accurate generation of a continuous potential\u0000energy surface at any geometry within the well-sampled nuclear configuration\u0000space, but also incorporates non-BOA corrections through a single training\u0000process. Comparison with benchmarks of atomic and molecular systems\u0000demonstrates its accuracy and efficiency.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a space-time multigrid method based on tensor-product space-time finite element discretizations. The method is facilitated by the matrix-free capabilities of the {ttfamily deal.II} library. It addresses both high-order continuous and discontinuous variational time discretizations with spatial finite element discretizations. The effectiveness of multigrid methods in large-scale stationary problems is well established. However, their application in the space-time context poses significant challenges, mainly due to the construction of suitable smoothers. To address these challenges, we develop a space-time cell-wise additive Schwarz smoother and demonstrate its effectiveness on the heat and acoustic wave equations. The matrix-free framework of the {ttfamily deal.II} library supports various multigrid strategies, including $h$-, $p$-, and $hp$-refinement across spatial and temporal dimensions. Extensive empirical evidence, provided through scaling and convergence tests on high-performance computing platforms, demonstrate high performance on perturbed meshes and problems with heterogeneous and discontinuous coefficients. Throughputs of over a billion degrees of freedom per second are achieved on problems with more than a trillion global degrees of freedom. The results prove that the space-time multigrid method can effectively solve complex problems in high-fidelity simulations and show great potential for use in coupled problems.
{"title":"A Space-Time Multigrid Method for Space-Time Finite Element Discretizations of Parabolic and Hyperbolic PDEs","authors":"Nils Margenberg, Peter Munch","doi":"arxiv-2408.04372","DOIUrl":"https://doi.org/arxiv-2408.04372","url":null,"abstract":"We present a space-time multigrid method based on tensor-product space-time\u0000finite element discretizations. The method is facilitated by the matrix-free\u0000capabilities of the {ttfamily deal.II} library. It addresses both high-order\u0000continuous and discontinuous variational time discretizations with spatial\u0000finite element discretizations. The effectiveness of multigrid methods in\u0000large-scale stationary problems is well established. However, their application\u0000in the space-time context poses significant challenges, mainly due to the\u0000construction of suitable smoothers. To address these challenges, we develop a\u0000space-time cell-wise additive Schwarz smoother and demonstrate its\u0000effectiveness on the heat and acoustic wave equations. The matrix-free\u0000framework of the {ttfamily deal.II} library supports various multigrid\u0000strategies, including $h$-, $p$-, and $hp$-refinement across spatial and\u0000temporal dimensions. Extensive empirical evidence, provided through scaling and\u0000convergence tests on high-performance computing platforms, demonstrate high\u0000performance on perturbed meshes and problems with heterogeneous and\u0000discontinuous coefficients. Throughputs of over a billion degrees of freedom\u0000per second are achieved on problems with more than a trillion global degrees of\u0000freedom. The results prove that the space-time multigrid method can effectively\u0000solve complex problems in high-fidelity simulations and show great potential\u0000for use in coupled problems.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stefaan S. P. Hessmann, Kristof T. Schütt, Niklas W. A. Gebauer, Michael Gastegger, Tamio Oguchi, Tomoki Yamashita
Global optimization of crystal compositions is a significant yet computationally intensive method to identify stable structures within chemical space. The specific physical properties linked to a three-dimensional atomic arrangement make this an essential task in the development of new materials. We present a method that efficiently uses active learning of neural network force fields for structure relaxation, minimizing the required number of steps in the process. This is achieved by neural network force fields equipped with uncertainty estimation, which iteratively guide a pool of randomly generated candidates towards their respective local minima. Using this approach, we are able to effectively identify the most promising candidates for further evaluation using density functional theory (DFT). Our method not only reliably reduces computational costs by up to two orders of magnitude across the benchmark systems Si16 , Na8Cl8 , Ga8As8 and Al4O6 , but also excels in finding the most stable minimum for the unseen, more complex systems Si46 and Al16O24 . Moreover, we demonstrate at the example of Si16 that our method can find multiple relevant local minima while only adding minor computational effort.
{"title":"Accelerating crystal structure search through active learning with neural networks for rapid relaxations","authors":"Stefaan S. P. Hessmann, Kristof T. Schütt, Niklas W. A. Gebauer, Michael Gastegger, Tamio Oguchi, Tomoki Yamashita","doi":"arxiv-2408.04073","DOIUrl":"https://doi.org/arxiv-2408.04073","url":null,"abstract":"Global optimization of crystal compositions is a significant yet\u0000computationally intensive method to identify stable structures within chemical\u0000space. The specific physical properties linked to a three-dimensional atomic\u0000arrangement make this an essential task in the development of new materials. We\u0000present a method that efficiently uses active learning of neural network force\u0000fields for structure relaxation, minimizing the required number of steps in the\u0000process. This is achieved by neural network force fields equipped with\u0000uncertainty estimation, which iteratively guide a pool of randomly generated\u0000candidates towards their respective local minima. Using this approach, we are\u0000able to effectively identify the most promising candidates for further\u0000evaluation using density functional theory (DFT). Our method not only reliably\u0000reduces computational costs by up to two orders of magnitude across the\u0000benchmark systems Si16 , Na8Cl8 , Ga8As8 and Al4O6 , but also excels in finding\u0000the most stable minimum for the unseen, more complex systems Si46 and Al16O24 .\u0000Moreover, we demonstrate at the example of Si16 that our method can find\u0000multiple relevant local minima while only adding minor computational effort.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study investigates the application of Factorization Machines with Quantum Annealing (FMQA) to address the crystal structure problem (CSP) in materials science. FMQA is a black-box optimization algorithm that combines machine learning with annealing machines to find samples to a black-box function that minimize a given loss. The CSP involves determining the optimal arrangement of atoms in a material based on its chemical composition, a critical challenge in materials science. We explore FMQA's ability to efficiently sample optimal crystal configurations by setting the loss function to the energy of the crystal configuration as given by a predefined interatomic potential. Further we investigate how well the energies of the various metastable configurations, or local minima of the potential, are learned by the algorithm. Our investigation reveals FMQA's potential in quick ground state sampling and in recovering relational order between local minima.
{"title":"Machine learning supported annealing for prediction of grand canonical crystal structures","authors":"Yannick Couzinie, Yuya Seki, Yusuke Nishiya, Hirofumi Nishi, Taichi Kosugi, Shu Tanaka, Yu-ichiro Matsushita","doi":"arxiv-2408.03556","DOIUrl":"https://doi.org/arxiv-2408.03556","url":null,"abstract":"This study investigates the application of Factorization Machines with\u0000Quantum Annealing (FMQA) to address the crystal structure problem (CSP) in\u0000materials science. FMQA is a black-box optimization algorithm that combines\u0000machine learning with annealing machines to find samples to a black-box\u0000function that minimize a given loss. The CSP involves determining the optimal\u0000arrangement of atoms in a material based on its chemical composition, a\u0000critical challenge in materials science. We explore FMQA's ability to\u0000efficiently sample optimal crystal configurations by setting the loss function\u0000to the energy of the crystal configuration as given by a predefined interatomic\u0000potential. Further we investigate how well the energies of the various\u0000metastable configurations, or local minima of the potential, are learned by the\u0000algorithm. Our investigation reveals FMQA's potential in quick ground state\u0000sampling and in recovering relational order between local minima.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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