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Conservative mixed Discontinuous Galerkin finite element method with full decoupling strategy for incompressible MHD problems

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Communications in Nonlinear Science and Numerical Simulation 2025年 147卷

作者： Huang, Huayi Huang, Yunqing Tang, Qili Yin, Lina Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China

In this research, we propose a mixed Discontinuous Galerkin (DG) finite element method (FEM) for the numerical solution of incompressible magnetohydrodynamics (MHD) problems, ensuring the divergence-free condition for the velocity field. Our proposed methodology is characterized by its energy stability. Subsequently, we construct a novel finite element discretization scheme, for which we establish the theoretical framework of energy stability. Furthermore, we incorporate a preconditioning strategy that facilitates the development of an alternative positive definite, fully decoupled linearization approach. A significant advantage of this scheme is its ability to circumvent the complexities associated with solving saddle point problems at each time step. We demonstrate the uniqueness and convergence of the solutions within this fully decoupled, block-structured linear system. This theoretical validation is complemented by a series of numerical experiments that substantiate the effectiveness and accuracy of our proposed method. © 2.2. Elsevier B.V.

关键词： Finite element method

The OpenLAM Challenges

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arXiv 2025年

作者： Peng, Anyang Liu, Xinzijian Guo, Ming-Yu Zhang, Linfeng Wang, Han AI for Science Institute Beijing100080 China DP Technology Beijing100080 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China School of Chemistry Sun Yat-sen University Guangzhou510006 China

Inspired by the success of Large Language Models (LLMs), the development of Large Atom Models (LAMs) has gained significant momentum in scientific computation. Since 2.2., the Deep Potential team has been actively pretraining LAMs and launched the OpenLAM Initiative to develop an open-source foundation model spanning the periodic table. A core objective is establishing comprehensive benchmarks for reliable LAM evaluation, addressing limitations in existing datasets. As a first step, the LAM Crystal Philately competition has collected over 19.8 million valid structures, including 1 million on the OpenLAM convex hull, driving advancements in generative modeling and materials science applications. Copyright © 2.2., The Authors. All rights reserved.

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Discovering dense hydrogen solid at 12.0K with deep variational free energy approach

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arXiv 2025年

作者： Dong, Xinyang Xie, Hao Chen, Yixiao Liang, Wenshuo Zhang, Linfeng Wang, Lei Wang, Han Beijing National Laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing100190 China AI for Science Institute Beijing100080 China Department of Astrophysics University of Zürich Winterthurerstrasse 190 Zürich8057 Switzerland Princeton University PrincetonNJ08544 United States DP Technology Beijing100080 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China

We perform deep variational free energy calculations to investigate the dense hydrogen system at 12.0 K and high pressures. In this computational framework, neural networks are used to model the free energy through the proton Boltzmann distribution and the electron wavefunction. By directly minimizing the free energy, our results reveal the emergence of a crystalline order associated with the center of mass of hydrogen molecules at approximately 180 GPa. This transition from atomic liquid to a molecular solid is marked by discontinuities in both the pressure and thermal entropy. Additionally, we discuss the broader implications and limitations of these findings in the context of recent studies of dense hydrogen under similar conditions. Copyright © 2.2., The Authors. All rights reserved.

关键词： Molecules

Sachdev-Ye-Kitaev charging advantage as a random walk on graphs

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Physical Review B 2025年第7期111卷 075138-075138页

作者： Francisco Divi Jeff Murugan Dario Rosa ICTP South American Institute for Fundamental Research Instituto de Física Teórica UNESP - Universidade Estadual Paulista Rua Dr. Bento Teobaldo Ferraz 271 01140-070 São Paulo SP Brazil Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town South Africa The National Institute for Theoretical and Computational Sciences Private Bag X1 Matieland South Africa

We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size N and the facilitation of operator delocalization by specific graph structures. A graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes.

关键词： Quantum chaos

Leveraging recurrence in neural network wavefunctions for large-scale simulations of Heisenberg antiferromagnets: the square lattice

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arXiv 2025年

作者： Schuyler Moss, M. Wiersema, Roeland Hibat-Allah, Mohamed Carrasquilla, Juan Melko, Roger G. Department of Physics and Astronomy University of Waterloo OntarioN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Center for Computational Quantum Physics Flatiron Institute 162 Fifth Avenue New YorkNY10010 United States Department of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Vector Institute MaRS Centre TorontoONM5G 1M1 Canada Institute for Theoretical Physics ETH Zürich 8093 Switzerland

Machine-learning-based variational Monte Carlo simulations are a promising approach for targeting quantum many body ground states, especially in two dimensions and in cases where the ground state is known to have a non-trivial sign structure. While many state-of-the-art variational energies have been reached with these methods for finite-size systems, little work has been done to use these results to extract information about the target state in the thermodynamic limit. In this work, we employ recurrent neural networks (RNNs) as a variational ansätze, and leverage their recurrent nature to simulate the ground states of progressively larger systems through iterative retraining. This transfer learning technique allows us to simulate spin-12.systems on lattices with more than 1,000 spins without beginning optimization from scratch for each system size, thus reducing the demands for computational resources. In this study, we focus on the square-lattice antiferromagnetic Heisenberg model (SLAHM), where it is possible to carefully benchmark our results. We show that we are able to systematically improve the accuracy of the results from our simulations by increasing the training time, and obtain results for finite-sized lattices that are in good agreement with the literature values. Furthermore, we use these results to extract accurate estimates of the ground-state properties in the thermodynamic limit. This work demonstrates that RNN wavefunctions can be used to accurately study quantum many-body physics in the thermodynamic limit. Copyright © 2.2., The Authors. All rights reserved.

关键词： Ground state

Developed ‘laminar’ bubbly flow with non-uniform bubble sizes

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Science China(Technological Sciences) 2001年第1期44卷 47-54页

作者： LUO Rui 1. Department of Thermal Engineering Tsinghua University 100084 Beijing China 2. Institute of Applied Physics and Computational Mathematics 100088 Beijing China

Bubbles with different sizes have different dynamic and kinetic behavior in a two-phase bubbly flow. A common two-fluid model based on the uniform bubble size assumption is not suitable for a bubbly flow with non-uniform bubble sizes. To deal with non-uniform bubbly flows, a multi-fluid model is established, with which bubbles are divided into several groups according to their sizes and a set of basic equations is derived for each group of bubbles with almost the same size. Through analyzing the bubble-bubble and bubble-pipe wall interactions, two new constitutive laws for the wall-force and pressure difference between the liquid phase and interface are developed to close the averaged basic equations. The respective phase distributions for each group of bubbles measured by a specially designed three-dimensional photographic method are used to check the model. Comparison between model-predicted values and experimental data shows that the model can describe laminar bubbly flow with non-uniform bubble sizes.

关键词： multi-fluid model non-uniform bubbly flow phase distribution

Discovery of High-Temperature Superconducting Ternary Hydrides via Deep Learning

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arXiv 2025年

作者： Wang, Xiaoyang Zhang, Chengqian Wang, Zhenyu Liu, Hanyu Lv, Jian Wang, Han Weinan, E. Ma, Yanming National Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China Key Laboratory of Material Simulation Methods & Software of Ministry of Education State Key Laboratory of Superhard Materials College of Physics Jilin University Changchun130012 China International Center of Future Science Jilin University Changchun130012 China HEDPS CAPT College of Engineering Peking University Beijing100871 China AI for Science Institute Beijing100080 China Center for Machine Learning Research Peking University Beijing100871 China School of Mathematical Sciences Peking University Beijing100871 China

The discovery of novel high-temperature superconductor materials holds transformative potential for a wide array of technological applications. However, the combinatorially vast chemical and configurational search space poses a significant bottleneck for both experimental and theoretical investigations. In this study, we employ the design of high-temperature ternary superhydride superconductors as a representative case to demonstrate how this challenge can be well addressed through a deep-learning-driven theoretical framework. This framework integrates high-throughput crystal structure exploration, physics-informed screening, and accurate prediction of superconducting critical temperatures. Our approach enabled the exploration of approximately 36 million ternary hydride structures across a chemical space of 2. elements, leading to the identification of 144 potential high-Tc superconductors with predicted Tc > 2.0 K and superior thermodynamic stability at 2.0 GPa. Among these, 12. compounds spanning 2. novel structural prototypes are reported for the first time, representing a significant expansion of the known structural landscape for hydride superconductors. This work not only greatly expands the known repertoire of high-Tc hydride superconductors but also establishes a scalable and efficient methodology for navigating the complex landscape of multinary hydrides. © 2.2., CC BY.

关键词： High temperature superconductors

Component-based parallel programming for peta-scale particle simulations

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Component-based parallel programming for peta-scale particle...

8th International Joint conference on Software Technologies, ICSOFT 2.13

作者： Cao, Xiaolin Mo, Zeyao Zhang, Aiqing Institute of Applied Physics and Computational Mathematics No. 2 East Fenghao Road Beijing China

ISBN: (纸本)9789898565686

A major parallel programming challenge in scientific computing is to hide parallel computing details of data distribution and communication. Component-based approaches are often used in practice to encapsulate these computer science details and shield them from domain experts. In this paper, we present our component-based parallel programming approach for large-scale particle simulations. Our approach encapsulates parallel computing details in parallel integrator components on top of a patch-based data structure in JASMIN infrastructure. It enables domain programmers to "think parallel, write sequential". They only need to assemble necessary components and write serial numerical kernels on a patch invoked by components. Using this approach, two real application programs have been developed to support the petascale simulations with billons of particles on tens of thousands of processor cores. Copyright © 2.13 SCITEPRESS.

关键词： Parallel programming

HiPro-CodeGen: Automatic programming for parallel numerical simulations 9

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HiPro-CodeGen: Automatic programming for parallel numerical ...

9th International Conference on Software Engineering and Applications, ICSOFT-EA 2.14

作者： Li, Liao Cuiping, Jing Wei, Wang Aiqing, Zhang Zhang, Yang Institute of Applied Physics and Computational Mathematics No. 2 East Fenghao Road Beijing China

ISBN: (纸本)9789897580369

HiPro-CodeGen is a code generation engine designed for numerical simulation development. Its central objective is to produce a parallel software framework with standard structure for an application developed on JASMIN, a domain-specific computational framework. The unique parallel part and all interfaces of the application are generated and implementation of sequential subroutines is the only part of the code left to be written manually for a programmer. The design and implementation of the code generation engine is introduced which combines numerical mathematics with component-based programming to create ontological models for parallel simulations. A hybrid programming method is proposed on the work mechanism of the engine which combines graphical and textual approaches to hide parallel programming and object-oriented programming from developers. A real application is presented to show the effectiveness and efficiency of the engine.

关键词： Parallel programming