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INTW: A versatile modular environment for advanced treatment of electronic structure and electron-phonon related properties 一个多功能的模块化环境,用于电子结构和电子-声子相关特性的高级处理
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-16 DOI: 10.1016/j.cpc.2025.109991
Haritz Garai-Marin , María Blanco-Rey , Idoia G. Gurtubay , Jon Lafuente-Bartolome , Asier Eiguren
<div><div>We present <span>INTW</span>, a modular software environment designed for advanced electronic structure calculations. Developed in Fortran95, <span>INTW</span> is capable of reading self-consistent field (SCF) results, such as electron energies, wave functions, and potentials, generated by the <span>Quantum ESPRESSO</span> and <span>SIESTA</span> codes. Using these SCF results as input, <span>INTW</span> provides a suite of specialized subroutines and functions for the computation of various electron- and phonon-related physical properties, facilitating detailed analysis of material properties at the quantum level. <span>INTW</span> particularly stands out in its treatment of symmetry, fully exploiting it even when dealing with electron spinor wave functions. Furthermore, it can efficiently work with both localized basis set codes, such as <span>SIESTA</span>, and plane-wave codes like <span>Quantum ESPRESSO</span>. These capabilities make <span>INTW</span> unique, offering a versatile approach that effectively combines the use of symmetry with both localized basis sets and plane-wave methods.</div><div><strong>Program summary</strong></div><div><em>Program Title:</em> <span>INTW</span></div><div><em>CPC Library link to program files:</em> (to be added by Technical Editor)</div><div><em>Developer’s repository link:</em> <span><span>https://github.com/eiguren/intw</span><svg><path></path></svg></span></div><div><em>Code Ocean capsule:</em> (to be added by Technical Editor)</div><div><em>Licensing provisions:</em> GPL-3.0-or-later</div><div><em>Programming language:</em> Fortran95</div><div><em>Nature of problem:</em></div><div>Accessing advanced electronic structure problems, such as the anisotropic electron-phonon interaction on the Fermi surface, requires efficient treatment of the data generated by general-purpose codes such as <span>Quantum ESPRESSO</span> and <span>SIESTA</span>. Moreover, fully exploiting symmetry operations is challenging but offers significant efficiency gains and qualitative benefits. The problem is to provide a modular framework that enables such calculations in a flexible, symmetry-aware, and computationally efficient environment set of tools.</div><div><em>Solution method:</em></div><div>Electron and phonon states are calculated only in the irreducible Brillouin zone provided by <span>Quantum ESPRESSO</span> and <span>SIESTA</span>. <span>INTW</span> interfaces with these codes to generate electron (spinor) states and phonon induced (spinor) potentials at arbitrary momenta using symmetry operations. <span>INTW</span> efficiently calculates the nearest-neighbor overlap matrices for Wannier functions by exploiting symmetry. In <span>SIESTA</span>, phonons are calculated using the supercell method, although <span>INTW</span> computes only the irreducible atomic displacements needed to construct the force-constant matrix. The electron-phonon matrix elements are computed either (1) by Fourier interpolation of the
我们提出了INTW,一个模块化的软件环境,专为先进的电子结构计算。在Fortran95中开发的INTW能够读取自一致场(SCF)结果,如电子能量,波函数和势,由Quantum ESPRESSO和SIESTA代码产生。利用这些SCF结果作为输入,INTW提供了一套专门的子程序和函数,用于计算各种电子和声子相关的物理特性,促进了量子水平上材料特性的详细分析。INTW在处理对称性方面尤其突出,即使在处理电子旋量波函数时也充分利用了对称性。此外,它可以有效地处理局部基集码(如SIESTA)和平面波码(如Quantum ESPRESSO)。这些能力使INTW独一无二,提供了一种通用的方法,有效地将对称性与局部基集和平面波方法相结合。项目摘要项目名称:INTWCPC库链接到程序文件:(由技术编辑添加)开发人员存储库链接:https://github.com/eiguren/intwCode海洋胶囊:(由技术编辑添加)许可条款:gpl -3.0-or-later编程语言:fortran95问题的性质:访问高级电子结构问题,例如费米表面上的各向异性电子-声子相互作用,需要对通用代码(如Quantum ESPRESSO和SIESTA)生成的数据进行有效处理。此外,充分利用对称操作是具有挑战性的,但可以提供显著的效率提高和质量效益。问题是提供一个模块化框架,使这种计算能够在一个灵活的、对称感知的、计算效率高的工具环境集中进行。解决方法:电子和声子态仅在量子ESPRESSO和SIESTA提供的不可约布里渊区计算。INTW接口与这些代码产生电子(旋量)状态和声子诱导(旋量)势在任意动量使用对称操作。INTW利用对称性,有效地计算了万尼尔函数的最近邻重叠矩阵。在SIESTA中,声子是使用超级单体方法计算的,尽管INTW只计算构建力常数矩阵所需的不可约原子位移。电子-声子矩阵单元的计算要么(1)通过声子势的傅里叶插值,要么(2)使用矩阵元素的万尼尔插值技术。用对称三角网格处理费米表面以计算电子-声子相关性质。附加说明,包括限制和不寻常的功能:INTW包更像是一个模块化结构的环境,旨在方便访问电子结构理论中的复杂问题,而不是专注于计算特定的材料属性。用于计算电子-声子矩阵元素、声子插值、万尼尔函数和费米表面性质的实用程序作为在此环境中通用使用的示例,用户可以将其作为实现新实用程序的模板。INTW同时使用SIESTA代码(使用局部原子基集)和Quantum ESPRESSO(作为平面波代码实现)进行操作。
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引用次数: 0
Rapid variable resolution particle initialization for complex geometries 复杂几何图形的快速变分辨率粒子初始化
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-16 DOI: 10.1016/j.cpc.2025.109992
Navaneet Villodi, Prabhu Ramachandran
The accuracy of meshless methods like Smoothed Particle Hydrodynamics (SPH) is highly dependent on the quality of the particle distribution. Existing particle initialization techniques often struggle to simultaneously achieve adaptive resolution, handle intricate boundaries, and efficiently generate well-packed distributions inside and outside a boundary. This work presents a fast and robust particle initialization method that achieves these goals using standard SPH building blocks. Our approach enables simultaneous initialization of fluid and solid regions, supports arbitrary geometries, and achieves high-quality, quasi-uniform particle arrangements without complex procedures like surface bonding. Extensive results in both 2D and 3D demonstrate that the obtained particle distributions exhibit good boundary conformity, low spatial disorder, and minimal density variation, all with significantly reduced computational cost compared to existing approaches. This work paves the way for automated particle initialization to accurately model flow in and around bodies with meshless methods, particularly with SPH.
平滑粒子流体动力学(SPH)等无网格方法的精度在很大程度上取决于粒子分布的质量。现有的粒子初始化技术往往难以同时实现自适应分辨率,处理复杂的边界,并有效地在边界内外生成良好的分布。这项工作提出了一种快速和鲁棒的粒子初始化方法,使用标准SPH构建块实现这些目标。我们的方法可以同时初始化流体和固体区域,支持任意几何形状,并实现高质量的准均匀颗粒排列,而无需表面粘合等复杂程序。2D和3D的大量结果表明,所获得的粒子分布具有良好的边界一致性,低空间无序性和最小的密度变化,与现有方法相比,所有这些都大大降低了计算成本。这项工作为自动粒子初始化铺平了道路,通过无网格方法精确地模拟物体内部和周围的流动,特别是SPH。
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引用次数: 0
Fantômas unconfined: global QCD fits with Bézier parameterizations Fantômas unconstrained:全局QCD与bsamizier参数化拟合
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-14 DOI: 10.1016/j.cpc.2025.109969
Lucas Kotz , Aurore Courtoy , T.J. Hobbs , Pavel Nadolsky , Fredrick Olness , Maximiliano Ponce-Chavez , Varada Purohit
Fantômas is a C++ toolkit for exploring the parametrization dependence of parton distribution functions (PDFs) and other correlator functions in quantum chromodynamics (QCD). Fantômas facilitates the generation of adaptable polynomial parametrizations for PDFs, called metamorphs, to find best-fit PDF solutions and quantify the epistemic uncertainty associated with the parametrizations during their fitting. The method employs Bézier curves as universal approximators for a variety of PDF shapes. Integrated into the xFitter framework for the global QCD analysis, Fantômas provides a foundation for general models of PDFs, while reducing the computational time compared to the approaches utilizing traditional polynomial parametrizations as well as providing an interpretable alternative to neural-network-based models. This paper outlines the structure and practical usage of the Fantômas toolkit, including its inputs, outputs, and implementation within xFitter. It also provides a practical example of using Fantômas for uncertainty quantification as well as the combination of PDF fits into a single ensemble.
Fantômas是一个c++工具包,用于探索量子色动力学(QCD)中部子分布函数(pdf)和其他相关函数的参数化依赖。Fantômas有助于生成PDF的自适应多项式参数化,称为变形,以找到最适合的PDF解,并在拟合期间量化与参数化相关的认知不确定性。该方法采用bsamizier曲线作为各种PDF形状的通用逼近器。集成到xFitter框架中用于全局QCD分析,Fantômas为pdf的一般模型提供了基础,同时与使用传统多项式参数化的方法相比减少了计算时间,并提供了基于神经网络的模型的可解释替代方案。本文概述了Fantômas工具包的结构和实际用法,包括它的输入、输出和xFitter中的实现。它还提供了一个使用Fantômas进行不确定度量化的实际示例,以及PDF适合于单个集成的组合。
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引用次数: 0
Efficient GPU-accelerated training of a neuroevolution potential with analytical gradients 高效gpu加速训练与分析梯度的神经进化潜能
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-13 DOI: 10.1016/j.cpc.2025.109994
Hongfu Huang , Junhao Peng , Kaiqi Li , Jian Zhou , Zhimei Sun
Machine-learning interatomic potentials (MLIPs) such as neuroevolution potentials (NEP) combine quantum-mechanical accuracy with computational efficiency significantly accelerate atomistic dynamic simulations. Trained by derivative-free optimization, the normal NEP achieves good accuracy, but suffers from inefficiency due to the high-dimensional parameter search. To overcome this problem, we present a gradient-optimized NEP (GNEP) training framework employing explicit analytical gradients and the Adam optimizer. This approach greatly improves training efficiency and convergence speedily while maintaining accuracy. By applying GNEP to the training of Sb-Te material systems (datasets include crystalline, liquid, and disordered phases), the fitting time has been substantially reduced—often by orders of magnitude—compared to the NEP training framework. The fitted potentials are validated by DFT reference calculations, demonstrating satisfactory agreement in equation of state and radial distribution functions. These results confirm that GNEP retains high predictive accuracy and transferability while considerably improved computational efficiency.
机器学习原子间势(MLIPs),如神经进化势(NEP),将量子力学精度与计算效率相结合,显著加速了原子动态模拟。通过无导数优化训练,普通NEP具有良好的精度,但由于高维参数搜索而存在效率低下的问题。为了克服这个问题,我们提出了一个梯度优化的NEP (GNEP)训练框架,使用显式分析梯度和Adam优化器。该方法在保持训练精度的同时,大大提高了训练效率和收敛速度。通过将GNEP应用于Sb-Te材料系统的训练(数据集包括晶体、液体和无序相),与NEP训练框架相比,拟合时间大大减少——通常是数量级上的减少。通过DFT参考计算验证了拟合势,在状态方程和径向分布函数中表现出令人满意的一致性。这些结果证实,GNEP保持了较高的预测精度和可转移性,同时大大提高了计算效率。
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引用次数: 0
Adaptive equilibration of molecular dynamics simulations 分子动力学模拟的自适应平衡
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-11 DOI: 10.1016/j.cpc.2025.109989
Luciano G. Silvestri, Zachary A. Johnson, Michael S. Murillo
We present a systematic framework for shortening and automating molecular dynamics equilibration through improved position initialization methods and uncertainty quantification analysis, using the Yukawa one-component plasma as an exemplar system. Our comprehensive evaluation of seven initialization approaches (uniform random, uniform random with rejection, Halton and Sobol sequences, perfect and perturbed lattices, and a Monte Carlo pair distribution method) demonstrates that initialization significantly impacts equilibration efficiency, with microfield distribution analysis providing diagnostic insights into thermal behaviors. Our results establish that initialization method selection is relatively inconsequential at low coupling strengths, while physics-informed methods demonstrate superior performance at high coupling strengths, reducing equilibration time. We establish direct relationships between temperature stability and uncertainties in transport properties (diffusion coefficient and viscosity), comparing thermostating protocols including ON-OFF versus OFF-ON duty cycles, Berendsen versus Langevin thermostats, and thermostat coupling strengths. Our findings demonstrate that weaker thermostat coupling generally requires fewer equilibration cycles, and OFF-ON thermostating sequences outperform ON-OFF approaches for most initialization methods. The methodology implements temperature forecasting as a quantitative metric for system thermalization, enabling users to determine equilibration adequacy based on specified uncertainty tolerances in desired output properties, thus transforming equilibration from a heuristic process to a rigorously quantifiable procedure with clear termination criteria.
本文以汤川单组分等离子体为例,通过改进位置初始化方法和不确定性量化分析,提出了缩短和自动化分子动力学平衡的系统框架。我们对7种初始化方法(均匀随机、均匀随机带抑制、Halton和Sobol序列、完美晶格和摄动晶格以及蒙特卡罗对分布方法)的综合评估表明,初始化显著影响平衡效率,微场分布分析为热行为提供了诊断性见解。我们的研究结果表明,初始化方法的选择在低耦合强度下相对无关紧要,而物理信息方法在高耦合强度下表现出优异的性能,减少了平衡时间。我们建立了温度稳定性与输运性质(扩散系数和粘度)的不确定性之间的直接关系,比较了恒温方案,包括ON-OFF与OFF-ON占空比、Berendsen与Langevin恒温器以及恒温器耦合强度。我们的研究结果表明,较弱的恒温器耦合通常需要较少的平衡周期,并且对于大多数初始化方法来说,OFF-ON恒温序列优于ON-OFF方法。该方法将温度预测作为系统热化的定量度量,使用户能够根据期望输出特性的指定不确定性容差确定平衡是否充足,从而将平衡从启发式过程转变为具有明确终止标准的严格量化过程。
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引用次数: 0
Pyrometheus: Symbolic abstractions for XPU and automatically differentiated computation of combustion kinetics and thermodynamics XPU的符号抽象和燃烧动力学和热力学的自动微分计算
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-11 DOI: 10.1016/j.cpc.2025.109987
Esteban Cisneros–Garibay , Henry Le Berre , Dimitrios Adam , Spencer H. Bryngelson , Jonathan B. Freund
The cost of combustion simulations is often dominated by the evaluation of net production rates of chemical species and mixture thermodynamics (thermochemistry). Execution on computing accelerators (XPUs) such as graphics processing units (GPUs) can greatly reduce this cost. Established thermochemistry software is not readily portable to such devices, as it sacrifices valuable analytical forms that enable differentiation, sensitivity analysis, and implicit time integration. Symbolic abstractions are developed with corresponding transformations that enable computation on accelerators and automatic differentiation by avoiding premature specification of detail. The software package Pyrometheus is introduced as an implementation of these abstractions and their transformations for combustion thermochemistry. The formulation facilitates code generation from the symbolic representation of a specific thermochemical mechanism in multiple target languages, including Python, C++, and Fortran. The generated code processes array-valued expressions, but does not specify their semantics. The semantics are provided by compatible array libraries, including NumPy, Pytato, and Google JAX. Thus, the generated code retains a symbolic representation of the thermochemistry, which enables computation on accelerators and CPUs and facilitates automatic differentiation. The design and operation of the symbolic abstractions and their companion tool, Pyrometheus, are discussed throughout. Roofline demonstrations show that the computation of chemical source terms within MFC, a Fortran-based flow solver we link to Pyrometheus, is performant.
燃烧模拟的成本通常由化学物质和混合物热力学(热化学)的净产率的评估所主导。在图形处理单元(gpu)等计算加速器(xpu)上执行可以大大降低此成本。现有的热化学软件不容易移植到这样的设备上,因为它牺牲了有价值的分析形式,使微分、灵敏度分析和隐式时间积分成为可能。符号抽象与相应的转换一起开发,通过避免过早地规范细节,可以在加速器上进行计算和自动区分。介绍了Pyrometheus软件包,作为这些抽象及其在燃烧热化学中的转换的实现。该公式便于用多种目标语言(包括Python、c++和Fortran)从特定热化学机制的符号表示生成代码。生成的代码处理数组值表达式,但不指定其语义。语义由兼容的数组库提供,包括NumPy、Pytato和谷歌JAX。因此,生成的代码保留了热化学的符号表示,这使得能够在加速器和cpu上进行计算并促进自动微分。符号抽象及其配套工具Pyrometheus的设计和操作贯穿始终。rooline演示表明,在MFC(我们链接到Pyrometheus的基于fortran的流求解器)中计算化学源项是有效的。
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引用次数: 0
SOFIA: Singularities of Feynman integrals automatized 费曼积分奇点的自动化
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-10 DOI: 10.1016/j.cpc.2025.109970
Miguel Correia , Mathieu Giroux , Sebastian Mizera
We introduce
, a Mathematica package that automatizes the computation of singularities of Feynman integrals, based on new theoretical understanding of their analytic structure. Given a Feynman diagram,
generates a list of potential singularities along with a candidate symbol alphabet. The package also provides a comprehensive set of tools for analyzing the analytic properties of Feynman integrals and related objects, such as cosmological and energy correlators. We showcase its capabilities by reproducing known results and predicting singularities and symbol alphabets of Feynman integrals at and beyond the high-precision frontier.

Program Summary

Program title: SOFIA (Singularities of Feynman Integrals Automatized)
CPC Library link to program files: https://doi.org/10.17632/3nnz2mr5wx.1
Developer’s repository link: https://github.com/StrangeQuark007/SOFIA [1]
Licensing provisions: MIT license
Programming language: Mathematica 13 or higher
Supplementary material: The example file SOFIA_examples.nb in SOFIA GitHub [1].
Nature of problem: This paper makes a significant contribution to perturbative computations in particle physics and related fields, by introducing a novel computer package analyzing the singularity structure of these integrals. In practice, this information can be leveraged to derive differential equations, the solutions of which enable efficient computation of the Feynman integrals, a crucial step that has been a major bottleneck in high-precision QCD computations. We believe this paper pushes the field of Feynman integrals into a new direction. The key insights that enabled this work were based on applications of cutting-edge techniques from algebraic geometry. The versatility of the package we introduce means it can be also used in other applications, including computations of cosmological and energy-energy correlators, as well as post-Minkowski expansion of gravitational potentials.
Solution method: Based on new theoretical insights, it provides an easy-to-use open-source tool for multi-loop computations in perturbation theory. In the paper, we demonstrated it can be used in diverse applications, including perturbative Standard Model computations, computations of cosmological and energy-energy correlators, as well as post-Minkowski expansions of gravitational potentials. Given the high degree of automation and broad scope of applications, we think the paper would be a good fit in CPC.
基于对费曼积分分析结构的新的理论认识,我们介绍了一个Mathematica软件包,它可以自动计算费曼积分的奇点。给定一个费曼图,生成一个潜在奇点列表以及候选符号字母表。该软件包还提供了一套全面的工具,用于分析费曼积分和相关对象的解析特性,如宇宙学和能量相关器。我们通过再现已知结果和预测费曼积分的奇点和符号字母来展示其能力,并超越高精度边界。程序摘要程序标题:SOFIA(费曼积分的奇点自动化)CPC库链接到程序文件:https://doi.org/10.17632/3nnz2mr5wx.1Developer的存储库链接:https://github.com/StrangeQuark007/SOFIA[1]许可条款:MIT许可编程语言:Mathematica 13或更高版本补充材料:示例文件SOFIA_examples。在索菲亚GitHub b[1]。问题性质:本文通过引入一种新的计算机包来分析这些积分的奇异结构,对粒子物理和相关领域的微扰计算做出了重大贡献。在实践中,可以利用这些信息来推导微分方程,其解可以有效地计算费曼积分,这是高精度QCD计算的主要瓶颈。我们相信本文将费曼积分领域推向了一个新的方向。使这项工作得以实现的关键见解是基于代数几何尖端技术的应用。我们介绍的包的多功能性意味着它也可以用于其他应用,包括宇宙学和能量-能量相关器的计算,以及后闵可夫斯基引力势的扩展。求解方法:基于新的理论见解,为微扰理论中的多环计算提供了一个易于使用的开源工具。在本文中,我们证明了它可以用于各种应用,包括微扰标准模型计算,宇宙学和能量-能量相关器的计算,以及引力势的后闵可夫斯基展开。鉴于自动化程度高,应用范围广,我们认为该论文将非常适合CPC。
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引用次数: 0
Verification of a hybrid kinetic-gyrokinetic model using the advanced semi-Lagrange code ssV 基于先进半拉格朗日代码ssV的混合动力学-陀螺动力学模型验证
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-10 DOI: 10.1016/j.cpc.2025.109980
Sreenivasa chary Thatikonda , F.N. De Oliveira-Lopes , A. Mustonen , K. Pommois , D. Told , F. Jenko
The super simple Vlasov (ssV) code was developed to study instabilities, turbulence, and reconnection in weakly magnetized plasmas, such as the solar wind in the dissipation range and the edge of fusion plasmas. The ssV code overcomes the limitations of standard gyrokinetic theory by using a hybrid kinetic-gyrokinetic model that incorporates fully kinetic ions and gyrokinetic electrons. This hybrid kinetic-gyrokinetic model enables accurate modeling in regimes characterized by steep gradients and high-frequency dynamics. To achieve this, ssV implements a set of semi-Lagrangian numerical schemes, including Positive Flux Conservative (PFC), Flux Conservative fifth-order (FCV), FCV with Umeda limiters, and a Semi-Lagrangian Monotonicity-Preserving fifth-order scheme (SLMP5). Benchmark problems such as Landau damping, ion-acoustic waves, ion Bernstein waves, and kinetic Alfvén waves were employed to evaluate the schemes. The SLMP5 scheme consistently delivered the best overall accuracy and numerical stability performance. The code also addresses well-known electromagnetic gyrokinetic simulation issues, such as the Ampère cancellation problem, using carefully chosen velocity-space resolutions and accurate integral evaluation.
开发了超简单的Vlasov (ssV)代码,用于研究弱磁化等离子体的不稳定性、湍流性和重联性,如耗散范围内的太阳风和聚变等离子体的边缘。ssV代码通过使用包含完全动力学离子和旋转动力学电子的混合动力学-旋转动力学模型克服了标准回旋动力学理论的局限性。这种混合动力学-陀螺动力学模型能够在陡坡和高频动力学特征的情况下精确建模。为了实现这一点,ssV实现了一组半拉格朗日数值格式,包括正通量保守(PFC)、通量保守五阶(FCV)、带梅达限制器的FCV和半拉格朗日保持单调的五阶格式(SLMP5)。采用朗道阻尼、离子声波、离子伯恩斯坦波和动力学alfvsamn波等基准问题对方案进行了评价。SLMP5方案始终提供最佳的整体精度和数值稳定性性能。该代码还解决了众所周知的电磁陀螺动力学模拟问题,如安普瑞抵消问题,使用精心选择的速度空间分辨率和精确的积分评估。
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引用次数: 0
Physics-informed multiresolution wavelet neural network method for solving partial differential equations 求解偏微分方程的多分辨率小波神经网络方法
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-09 DOI: 10.1016/j.cpc.2025.109986
Feng Han , Jianguo Wang , Guoliang Peng , Xueting Shi
In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate unknown functions, then substituting the MWNN into PDEs and training the MWNN by least-squares algorithm. We apply the proposed method to various problems, including stationary/nonstationary advection, diffusion and advection-diffusion problems, and linear/nonlinear time-dependent problems. Numerical experiments show that the PIMWNN method can achieve higher accuracy and faster speed than Physics Informed Neural Networks (PINNs). Moreover, the PIMWNN method can handle different boundary conditions easily and solve the time-dependent problems efficiently. The proposed method is expected to solve the spectral bias problem in network training. These characteristics show the great potential of the PIMWNN method used in the field of numerical solving methods for PDEs.
提出了一种基于物理信息的多分辨率小波神经网络(PIMWNN)求解偏微分方程的方法。该方法利用多分辨率小波神经网络(MWNN)对未知函数进行近似,然后将多分辨率小波神经网络代入偏微分方程中,利用最小二乘算法对其进行训练。我们将提出的方法应用于各种问题,包括平稳/非平稳平流,扩散和平流扩散问题,以及线性/非线性时间相关问题。数值实验表明,PIMWNN方法比物理信息神经网络(pinn)具有更高的精度和更快的速度。此外,该方法可以方便地处理不同的边界条件,并能有效地解决时变问题。该方法有望解决网络训练中的频谱偏置问题。这些特点显示了PIMWNN方法在偏微分方程数值求解领域的巨大潜力。
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引用次数: 0
GridapROMs.jl: Efficient reduced order modelling in the Julia programming language GridapROMs。jl: Julia编程语言中的高效降阶建模
IF 3.4 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Pub Date : 2025-12-09 DOI: 10.1016/j.cpc.2025.109985
Nicholas Mueller, Santiago Badia
In this paper, we introduce GridapROMs, a Julia-based library for the numerical approximation of parameterized partial differential equations (PDEs) using a comprehensive suite of linear reduced order models (ROMs). The library is designed to be extendable and productive, leveraging an expressive high-level API built on the Gridap PDE solver backend, while achieving high performance through Julia’s just-in-time compiler and advanced lazy evaluation techniques. GridapROMs is PDE-agnostic, enabling its application to a wide range of problems, including linear, nonlinear, single-field, multi-field, steady, and unsteady equations. This work details the library’s key innovations, implementation principles, and core components, providing usage examples and demonstrating its capabilities by solving a fluid dynamics problem modeled by the Navier-Stokes equations in a 3D geometry. Program summary Program Title: GridapROMs.jl (version 1.0) CPC Library link to program files: https://doi.org/10.17632/h27nszy8bt.1 Developer’s repository link: https://github.com/Gridap/GridapROMs.jl Licensing provisions: MIT license Programming language: Julia Nature of problem: Numerical simulation of parameterized PDEs, including linear, nonlinear, single-field, multi-field, steady, and unsteady problems. Classical full-order models are computationally expensive, requiring intensive computations for each parameter configuration. Solution method: GridapROMs approximates the parameter-to-solution map using linear reduced order models. It constructs a reduced basis from the tangent hyperplane to the solution manifold and applies a (Petrov-)Galerkin projection to the full-order equations. Nonaffine parameter dependencies in the residual and/or Jacobian are efficiently handled using hyper-reduction techniques.
在本文中,我们介绍了GridapROMs,一个基于julia的库,用于使用一套全面的线性降阶模型(ROMs)对参数化偏微分方程(PDEs)进行数值逼近。该库被设计为可扩展和高效的,利用构建在Gridap PDE求解器后端的富有表现力的高级API,同时通过Julia的即时编译器和高级惰性评估技术实现高性能。GridapROMs是pde不可知的,使其应用于广泛的问题,包括线性,非线性,单场,多场,稳态和非定常方程。这项工作详细介绍了图书馆的关键创新,实现原则和核心组件,提供了使用示例,并通过解决三维几何中的Navier-Stokes方程建模的流体动力学问题来展示其功能。节目名称:GridapROMs。jl(版本1.0)CPC库链接到程序文件:https://doi.org/10.17632/h27nszy8bt.1开发人员的存储库链接:https://github.com/Gridap/GridapROMs.jl许可条款:MIT许可编程语言:Julia问题性质:参数化偏微分方程的数值模拟,包括线性,非线性,单场,多场,稳定和非稳态问题。经典的全阶模型计算成本很高,需要对每个参数配置进行密集的计算。求解方法:GridapROMs使用线性降阶模型逼近参数到解映射。构造了从切超平面到解流形的约简基,并对全阶方程应用了(Petrov-)伽辽金投影。残差和/或雅可比矩阵中的非仿射参数依赖使用超约简技术有效地处理。
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Computer Physics Communications
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