Computer Physics Communications最新文献

{"title":"Graspg – An extension to Grasp2018 based on configuration state function generators","authors":"Ran Si , Yanting Li , Kai Wang , Chongyang Chen , Gediminas Gaigalas , Michel Godefroid , Per Jönsson","doi":"10.1016/j.cpc.2025.109604","DOIUrl":"10.1016/j.cpc.2025.109604","url":null,"abstract":"<div><div>The <span>Graspg</span> program package is an extension to <span>Grasp</span>2018 (Froese Fischer et al. (2019) <span><span>[1]</span></span>) based on configuration state function generators (CSFGs). The generators keep spin-angular integrations at a minimum and reduce substantially the execution time and the memory requirement for large-scale multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (CI) atomic structure calculations. The package includes the improvements reported in Li (2023) <span><span>[8]</span></span> in terms of redesigned and efficient constructions of direct and exchange potentials and Lagrange multipliers. In addition, further parallelization of the diagonalization procedure has been implemented. Tools have been developed for predicting configuration state functions (CSFs) that are unimportant and can be discarded for large MCDHF or CI calculations based on results from smaller calculations, thus providing efficient methods for <em>a priori</em> condensation. The package provides a seamless interoperability with <span>Grasp2018</span>. From extensive test runs and benchmarking, we have demonstrated reductions in the execution time and disk file sizes with factors of 37 and 98, respectively, for MCDHF calculations based on large orbital sets compared to corresponding <span>Grasp2018</span> calculations. For CI calculations, reductions of the execution time with factors over 200 have been attained. With a sensible use of the new possibilities for <em>a priori</em> condensation, CI calculations with nominally hundreds of millions of CSFs can be handled.</div><div><strong>PROGRAM SUMMARY</strong></div><div><em>Program Title:</em> <span>Graspg</span></div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/7b5kbhy3v9.1</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> MIT License</div><div><em>Programming language:</em> Fortran 95</div><div><em>Nature of problem:</em> Prediction of atomic energy levels using a multiconfiguration Dirac–Hartree–Fock approach.</div><div><em>Solution method:</em> The computational method is the same as in <span>Grasp2018</span> [1] except that configuration state function generators (CSFGs) have been introduced, a concept that substantially reduces the execution times and memory requirements for large-scale calculations [2]. The method also relies on redesigned and more efficient constructions of direct and exchange potentials and Lagrange multipliers, along with additional parallelization of the diagonalization procedure as detailed in [3].</div><div><em>Additional comments including restrictions and unusual features:</em> 1. provides a seamless interoperability with <span>Grasp</span>2018, 2. options to limit the Breit interaction, 3. includes tools for predicting CSFs that are unimportant and can be discarded for large MCDHF or CI calculations based on the results from smaller calculations","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109604"},"PeriodicalIF":7.2,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discovery and inversion of the viscoelastic wave equation in inhomogeneous media","authors":"Su Chen ,&nbsp;Yi Ding ,&nbsp;Hiroe Miyake ,&nbsp;Xiaojun Li","doi":"10.1016/j.cpc.2025.109599","DOIUrl":"10.1016/j.cpc.2025.109599","url":null,"abstract":"<div><div>In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and noisy datasets and are not suitable for varying coefficients. To address this issue, we propose a hybrid framework that combines two alternating direction optimization phases: discovery and embedding. The discovery phase employs current well-developed sparse regression techniques to preliminarily identify governing equations from observations. The embedding phase implements a recurrent convolutional neural network (RCNN), enabling efficient processes for time-space iterations involved in discretized forms of wave equation. The RCNN model further optimizes the imperfect sparse regression results to obtain more accurate functional terms and coefficients. Through alternating update of discovery-embedding phases, essential physical equations can be robustly identified from noisy and low-resolution measurements. To assess the performance of proposed framework, numerical experiments are conducted on various scenarios involving wave equation in elastic/viscoelastic and homogeneous/inhomogeneous media. The results demonstrate that the proposed method exhibits excellent robustness and accuracy, even when faced with high levels of noise and limited data availability in both spatial and temporal domains.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109599"},"PeriodicalIF":7.2,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143791760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluation of the generalized Fermi-Dirac integral and its derivatives for moderate/large values of the parameters. New version announcement","authors":"Amparo Gil ,&nbsp;Andrzej Odrzywołek ,&nbsp;Javier Segura ,&nbsp;Nico M. Temme","doi":"10.1016/j.cpc.2025.109605","DOIUrl":"10.1016/j.cpc.2025.109605","url":null,"abstract":"<div><div>A revised version of the Matlab implementations of the expansions for the Fermi-Dirac integral and its derivatives is presented. In the new version, our functions for computing the Kummer functions <span><math><mi>M</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></span> and <span><math><mi>U</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>)</mo></math></span> are incorporated into the software. The algorithms for computing the Kummer functions are described in [1,2]. In this way, the implementations of the expansions for the Fermi-Dirac integral can be used in earlier Matlab versions and can be easily adapted to GNU Octave. The efficiency of the computations is also greatly improved.</div></div><div><h3>New version program summary</h3><div><em>Program Title:</em> FermiDiracExpans</div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/sk34wtcxhh.2</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> GPLv3</div><div><em>Programming language:</em> Matlab</div><div><em>Journal reference of previous version:</em> Comput. Phys. Commun. 283 (2023) 108563</div><div><em>Does the new version supersede the previous version?:</em> Yes</div><div><em>Reasons for the new version:</em> With the new version, the implementations of the expansions for the Fermi-Dirac integral can be used in earlier Matlab versions and can be easily adapted to GNU Octave. The efficiency of the computations is also greatly improved.</div><div><em>Summary of revisions:</em> The built-in Matlab functions <span>kummerU</span> and <span>hypergeom</span> are replaced by our functions <span>Uabx</span> and <span>Mabx</span>, respectively. These functions improve both the accuracy and efficiency of the built-in Matlab functions for computing the Kummer functions. A few relations satisfied by the Kummer functions are used to adapt the expressions in the expansions involving Kummer functions with negative parameters into expressions with real positive parameters and arguments, as used in our algorithms for Kummer functions.</div><div><em>Nature of problem:</em> The evaluation of the relativistic Fermi-Dirac function and its partial derivatives is needed in different problems in applied and theoretical physics, such as stellar astrophysics, plasma physics or electronics.</div><div><em>Solution method:</em> Convergent and asymptotic expansions are provided to approximate the relativistic Fermi-Dirac function and its derivatives for moderate/large values of its parameters.</div></div><div><h3>References</h3><div><ul><li><span>[1]</span><span><div>A. Gil, D. Ruiz-Antolin, J. Segura, N.M. Temme, Numer. Algorithms 94 (2023) 669–679.</div></span></li><li><span>[2]</span><span><div>A. Gil, D. Ruiz-Antolin, J. Segura, N.M. Temme, Lecture Notes in Computer Science, vol. 14477, Springer, Cham, 2025.</div></span></li></ul></div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109605"},"PeriodicalIF":7.2,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Directional finite difference method for directly solving 3D gyrokinetic field equations with enhanced accuracy","authors":"Min-Gu Yoo ,&nbsp;Weixing Wang ,&nbsp;Edward Startsev ,&nbsp;Stephane Either","doi":"10.1016/j.cpc.2025.109597","DOIUrl":"10.1016/j.cpc.2025.109597","url":null,"abstract":"<div><div>The gyrokinetic (GK) field equation is a three-dimensional (3D) elliptic equation, but it is often simplified to a set of two-dimensional (2D) equations by assuming that the field does not vary along a specific direction. However, this simplification can introduce inevitable 0th-order numerical errors, as nonlinear mode coupling in toroidal geometry can produce undesirable harmonic modes that violate the assumption. In this work, we propose a novel directional finite difference method (FDM) with a local coordinate transformation to better resolve the target field of interest. The directional FDM can accurately solve 3D GK field equations without simplifications, which can overcome the limitations of conventional methods. The accuracy and efficiency of different FDMs are analyzed in great detail for a variety of geometries, from simple 2D Cartesian coordinates to realistic 3D curvilinear coordinates. The 0th-order numerical errors of simplified 2D GK equations were found to be more problematic for low-harmonic modes and low aspect ratio geometries such as spherical tokamaks. On the other hand, the directional 3D FDM can accurately resolve a much wider range of harmonic modes aligned to the direction of interest, including the low-harmonic modes. We demonstrate that the directional 3D FDM is a highly effective algorithm for solving the 3D GK field equations, achieving accuracy improvements of 10 to 100 times or more, particularly for low-harmonic modes in spherical tokamaks.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109597"},"PeriodicalIF":7.2,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143786147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An OpenFOAM-based solver for modeling low Mach number turbulent flows at high pressure with real-fluid effects","authors":"Danh Nam Nguyen ,&nbsp;Chun Sang Yoo","doi":"10.1016/j.cpc.2025.109600","DOIUrl":"10.1016/j.cpc.2025.109600","url":null,"abstract":"<div><div>Numerical simulations of non-reacting/reacting flows at supercritical pressure near the critical points with real-fluid models in OpenFOAM often encounter instability and divergence issues unless the solution algorithm incorporates special techniques. In this paper, we develop a novel pressure-based solver, <em>realFluidFoam</em>, tailored for simulations of subsonic turbulent flows at transcritical and supercritical conditions in OpenFOAM. The <em>realFluidFoam</em> solver utilizes unique algorithms to enhance the stability and convergency while taking into account real-fluid effects. Its source code and implementation details are provided to facilitate a comprehensive understanding of integrating real-fluid models into fluid flow simulations in OpenFOAM. The <em>realFluidFoam</em> solver is validated against experimental data by performing large-eddy simulations (LESs) of liquid nitrogen injection and coaxial liquid nitrogen/preheated hydrogen injection under transcritical and supercritical conditions. The LES results show a satisfactory agreement with the experimental data, verifying that the <em>realFluidFoam</em> solver can accurately simulate transcritical and supercritical turbulent fluid flows over the wide range of pressure, especially near the critical points.</div></div><div><h3>Program summary</h3><div><em>Program Title:</em> realFluidFoam</div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/btzj8b7b8j.1</span><svg><path></path></svg></span></div><div><em>Developer's repository link (OpenFOAM-6 ver.):</em> <span><span>https://github.com/danhnam11/realFluidFoam-6</span><svg><path></path></svg></span></div><div><em>Developer's repository link (OpenFOAM-8 ver.):</em> <span><span>https://github.com/danhnam11/realFluidFoam-8</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> GPLv3</div><div><em>Programming language:</em> C++</div><div><em>Nature of problem:</em> Instability and divergence problems are often encountered in simulations of subsonic fluid flows under high pressure conditions near critical points (i.e., transcritical and supercritical conditions) using real-fluid models in OpenFOAM due to pseudo-boiling effects and high density stratifications.</div><div><em>Solution method:</em> A pressure-based solution method with a modified PIMPLE algorithm is employed to improve the stability while a fast and robust coupling Newton-Bisection algorithm is utilized to guarantee the convergency of fluid flow simulations under transcritical and supercritical conditions in OpenFOAM.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109600"},"PeriodicalIF":7.2,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An efficient three-dimensional mesh quality optimization method based on gradient-enhanced probabilistic model","authors":"Longwei Deng ,&nbsp;Junhui Yin ,&nbsp;Qing He ,&nbsp;Xinyu Cao ,&nbsp;Chaoyang Zhang ,&nbsp;Junhao Cui ,&nbsp;Bin Li","doi":"10.1016/j.cpc.2025.109602","DOIUrl":"10.1016/j.cpc.2025.109602","url":null,"abstract":"<div><div>As a cornerstone of numerical simulations, mesh generation establishes the initial discrete model required for simulations, and the quality of the mesh significantly impacts the accuracy of the analysis results. However, the initial mesh elements generated by automated mesh generators often do not meet the stringent requirements of numerical simulations due to their poor mesh quality. This paper proposes an efficient three-dimensional tetrahedral mesh quality optimization method based on gradient-enhanced probabilistic model. The proposed method includes a preprocessing step that first solves for the steepest descent direction and optimal step length of nodes, allowing for the rapid optimization of early node movement and placement, subsequently completing the initial relocation of nodes. By establishing a probabilistic model for determining the optimal node positions and creating a memoryless stochastic process, the method ensures good convergence speed and accuracy as the node positions approach their optimal solutions. Therefore, the proposed method not only accelerates the overall optimization efficiency but also enhances mesh quality, achieving a balanced improvement between smoothing efficiency and mesh quality. This paper validates the proposed method on both three-dimensional tetrahedral meshes and surface meshes, and develops a parallel version, demonstrating the method's broad applicability and strong optimization capability. Through ablation study and comparisons with classic methods, it is shown that the proposed method outperforms traditional methods in both optimization efficiency and mesh quality. The GitHub repository link is: <span><span>https://github.com/suyi-92/EMeshOptimization.git</span><svg><path></path></svg></span>. And the input files can be found at: <span><span>https://drive.google.com/drive/folders/1ziiWzmorx82NiVJPxWI0yoBrPpk_Lzrg?usp=sharing</span><svg><path></path></svg></span></div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109602"},"PeriodicalIF":7.2,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143783911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Direct minimization on the complex Stiefel manifold in Kohn-Sham density functional theory for finite and extended systems","authors":"Kai Luo ,&nbsp;Tingguang Wang ,&nbsp;Xinguo Ren","doi":"10.1016/j.cpc.2025.109596","DOIUrl":"10.1016/j.cpc.2025.109596","url":null,"abstract":"<div><div>Direct minimization method on the complex Stiefel manifold in Kohn-Sham density functional theory is formulated to treat both finite and extended systems in a unified manner. This formulation is well-suited for scenarios where straightforward iterative diagonalization becomes challenging, especially when the Aufbau principle is not applicable. We present the theoretical foundation and numerical implementation of the Riemannian conjugate gradient (RCG) within a localized non-orthogonal basis set. Riemannian Broyden-Fletcher-Goldfarb-Shanno (RBFGS) method is tentatively implemented. Extensive testing compares the performance of the proposed methods and highlights that the quasi-Newton method is more efficient. However, for extended systems, the computational time required grows rapidly with respect to the number of <strong>k</strong>-points.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109596"},"PeriodicalIF":7.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DeepFlame 2.0: A new version for fully GPU-native machine learning accelerated reacting flow simulations under low-Mach conditions","authors":"Runze Mao ,&nbsp;Xinyu Dong ,&nbsp;Xuan Bai ,&nbsp;Ziheng Wu ,&nbsp;Guanlin Dang ,&nbsp;Han Li ,&nbsp;Zhi X. Chen","doi":"10.1016/j.cpc.2025.109595","DOIUrl":"10.1016/j.cpc.2025.109595","url":null,"abstract":"<div><div>This paper presents <em>DeepFlame</em> v2.0, a significant computational framework upgrade designed for high-performance combustion simulations on GPU-based heterogeneous architectures. The updated version implements a comprehensive CUDA-accelerated architecture incorporating fundamental combustion modelling components, including: implicit/explicit finite volume method (FVM) discretisation schemes, chemical kinetics integrators, thermophysical property models, and subgrid-scale closures for both fluid dynamics and combustion processes. The redesigned code supports diverse boundary conditions and discretisation schemes for broad applicability across combustion configurations. Key performance optimisations integrate advanced CUDA features including data coalescing techniques, CUDA Graphs for kernel scheduling, and NCCL-based multi-GPU communication. Validation studies employing the fully-implicit low-Mach solver demonstrate two-order-of-magnitude acceleration compared to conventional CPU implementations across canonical test cases, while maintaining numerical accuracy.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109595"},"PeriodicalIF":7.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"QUANTUM ESPRESSO implementation of the RPA-based functional","authors":"Angel Rosado,&nbsp;Mario Benites,&nbsp;Efstratios Manousakis","doi":"10.1016/j.cpc.2025.109594","DOIUrl":"10.1016/j.cpc.2025.109594","url":null,"abstract":"<div><div>We detail our implementation of the random-phase-approximation based functional (RPAF) derived in Ref. <span><span>[1]</span></span> for the QUANTUM ESPRESSO (QE) package. We also make available in the <em>Computer Physics Communications</em> library the source files which are required in order to apply this functional within QE. We also provide the corresponding RPAF projector augmented wave (PAW) and ultrasoft pseudopotentials for most elements. Lastly, we benchmark the performance of the RPAF by calculating the equilibrium lattice constant and bulk modulus of a set of the same 60 crystals used by other authors to benchmark other functionals for both PAW and ultrasoft pseudopotentials. We find that the RPAF performs better overall as compared to the other most popular functionals.</div></div><div><h3>Program summary</h3><div><em>Program Title:</em> Implementation of RPAF functional in QUANTUM ESPRESSO</div><div><em>CPC Library link to program files:</em> <span><span>https://doi.org/10.17632/y96kpb2dpd.1</span><svg><path></path></svg></span></div><div><em>Developer's repository link:</em> <span><span>https://data.mendeley.com/datasets/bg45fjkz2t</span><svg><path></path></svg></span></div><div><em>Licensing provisions:</em> GPLv3</div><div><em>Programming language:</em> Fortran 90</div><div><em>Nature of problem:</em> To make the RPAF available to be used in DFT calculations.</div><div><em>Solution method:</em> Implementation of RPAF in QUANTUM ESPRESSO.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109594"},"PeriodicalIF":7.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fractal-constrained deep learning for super-resolution of turbulence with zero or few label data","authors":"Jiaxin Wu ,&nbsp;Min Luo ,&nbsp;Boo Cheong Khoo ,&nbsp;Dunhui Xiao ,&nbsp;Pengzhi Lin","doi":"10.1016/j.cpc.2025.109548","DOIUrl":"10.1016/j.cpc.2025.109548","url":null,"abstract":"<div><div>The super-resolution of turbulence is of paramount importance and still remains challenging due to the inefficiency of the current technologies in retaining the intrinsic physics like the multi-scale flow structures and energy cascades. To address this challenge, this work proposes a fractal-constrained deep learning super-resolution model termed SKFSR-FIC. The model is characterized by two distinctive designs: (1) a SKip-connected Feature-reuse Super-Resolution (SKFSR) network that learns and retains multi-scale flow structures and multi-frequency dynamics, achieving efficient upscaling of flow fields while reconstructing self-similar physics; (2) a fractal invariance constraint (FIC) that utilizes the self-similarities of flow properties invariant to scales to substitute label data information in super resolution, thus achieving accurate reconstruction of multi-scale dynamics and energy cascades. The SKFSR-FIC model, for the first time, leverages fractal dimensions to guide the turbulent flow reconstruction and significantly reduces the reliance on label data and, especially, achieves zero-shot (i.e., unsupervised) super-resolution that cannot be handled by existing deep learning models. The results from five self-affine fractal images and two turbulent flow cases demonstrate the enhanced efficiency (up to 2 times) and accuracy (up to 100 times) of the unsupervised SKFSR-FIC model compared to the conventional interpolation method and deep learning models. Moreover, the SKFSR network is compatible with both FIC and label data, thereby adaptively enabling unsupervised, supervised and semi-supervised learning strategies. In particular, the semi-supervised SKFSR-FIC model, even by using one snapshot, achieves the best accuracy among the three learning strategies due to the combination of physics and data.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"312 ","pages":"Article 109548"},"PeriodicalIF":7.2,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}