Journal of Computational Physics最新文献

{"title":"PE-RWP: A deep learning framework for polynomial feature extraction of rogue wave patterns and peregrine waves localization","authors":"Zhe Lin ,&nbsp;Yong Chen","doi":"10.1016/j.jcp.2025.114243","DOIUrl":"10.1016/j.jcp.2025.114243","url":null,"abstract":"<div><div>Rogue wave (RW) patterns are nonlinear wave phenomena universally present in integrable systems. When one or more free internal parameters in the exact RW solutions of integrable systems like the nonlinear Schrödinger (NLS) equation are sufficiently large, the RW exhibit unique geometric patterns fully determined by the zero structure of the Yablonskii-Vorob’ev (Y-V) polynomial hierarchy. In this paper, we propose a deep learning-based “Polynomial Extractor for Rogue Wave Patterns” (PE-RWP). This approach replaces traditional asymptotic analysis of high-order RW solutions under large-parameter conditions, enabling automatic and precise identification of polynomial characteristics within RW patterns. We introduce a generalized polynomial hierarchy with parameters <span><math><msub><mi>γ</mi><mrow><mi>k</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span> that encompasses all Y-V polynomials relevant to RW patterns, serving as the target objective for PE-RWP. The unique dual-branch network architecture (with a regression branch for determining parameter values and a classification branch for identifying corresponding polynomial types) enables PE-RWP to effectively output this generalized polynomial hierarchy and recognize RW patterns subjected to arbitrary scaling and rotational transformations. Furthermore, as an application based on the mathematical theory of RW patterns, we leverage the Y-V polynomials output by PE-RWP to achieve unsupervised localization of Peregrine waves through deep learning methods. Finally, through extensive experimental evaluation, both problems-polynomial extraction and Peregrine wave localization-are effectively solved with high accuracy.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114243"},"PeriodicalIF":3.8,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144686015","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":"State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics","authors":"Zhuoyuan Li ,&nbsp;Bin Dong ,&nbsp;Pingwen Zhang","doi":"10.1016/j.jcp.2025.114240","DOIUrl":"10.1016/j.jcp.2025.114240","url":null,"abstract":"<div><div>Data assimilation has become a key technique for combining physical models with observational data to estimate state variables. However, classical assimilation algorithms often struggle with the high nonlinearity present in both physical and observational models. To address this challenge, a novel generative model, termed the State-Observation Augmented Diffusion (SOAD) model is proposed for data-driven assimilation. The marginal posterior associated with SOAD has been derived and then proved to match the true posterior distribution under mild assumptions, suggesting its theoretical advantages over previous score-based approaches. Experimental results also indicate that SOAD may offer improved performance compared to existing data-driven methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114240"},"PeriodicalIF":3.8,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144662639","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":"Neural chaos: A spectral stochastic neural operator","authors":"Bahador Bahmani ,&nbsp;Ioannis G. Kevrekidis ,&nbsp;Michael D. Shields","doi":"10.1016/j.jcp.2025.114233","DOIUrl":"10.1016/j.jcp.2025.114233","url":null,"abstract":"<div><div>Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. In this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114233"},"PeriodicalIF":3.8,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703340","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":"Comparison of stabilization strategies applied to scale-resolved simulations using the discontinuous Galerkin method","authors":"Amaury Bilocq,&nbsp;Maxime Borbouse,&nbsp;Nayan Levaux,&nbsp;Vincent E. Terrapon,&nbsp;Koen Hillewaert","doi":"10.1016/j.jcp.2025.114238","DOIUrl":"10.1016/j.jcp.2025.114238","url":null,"abstract":"<div><div>This study evaluates several stabilization strategies for the discontinuous Galerkin Spectral Element Method in scale-resolved simulations of compressible turbulence, with emphasis on accuracy, robustness, and computational efficiency. A novel selective entropy-stable approach (DG-ES) is introduced, which activates entropy stabilization only in localized regions to enhance robustness while minimizing dissipation. The performance of DG-ES is benchmarked against artificial viscosity (DG-AV), as well as fully entropy-stable methods based on Gauss–Legendre (ESDG-GL) and Gauss–Lobatto (ESDG-GLL) quadratures, across a range of canonical shock–turbulence interaction test cases. Results show that DG-AV performs well in scenarios involving highly mobile shocks, effectively resolving both shocks and small-scale turbulence, but its accuracy deteriorates in stationary shock configurations. Additionally, DG-AV is highly sensitive to the choice and calibration of its detector. In contrast, entropy-stable methods improve post-shock turbulence accuracy but tend to introduce spurious oscillations near shocks and incur greater computational cost. The ESDG-GL method suffers from entropy projection errors in shocklet-dominated regions, while ESDG-GLL is affected by excess dissipation due to under-integration. DG-ES achieves a favorable balance, accurately capturing turbulence with reduced sensitivity to detector calibration and maintaining competitive efficiency. However, like the ESDG-GL, it requires smaller time steps to ensure stability in the presence of strong shocks, due to the stiffness introduced by the entropy projection.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114238"},"PeriodicalIF":3.8,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654845","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":"Deep generalized Green’s function","authors":"Rixi Peng ,&nbsp;Juncheng Dong ,&nbsp;Jordan Malof ,&nbsp;Willie J. Padilla ,&nbsp;Vahid Tarokh","doi":"10.1016/j.jcp.2025.114235","DOIUrl":"10.1016/j.jcp.2025.114235","url":null,"abstract":"<div><div>The Green’s function has ubiquitous and unparalleled usage for the efficient solving of partial differential equations (PDEs) and analyzing systems governed by PDEs. However, obtaining a closed-form Green’s function for most PDEs on various domains is often impractical. Several approaches attempt to address this issue by approximating the Green’s function with numerical methods, but several challenges remain. We introduce the Deep Generalized Green’s Function (DGGF), a deep-learning approach that overcomes the challenges of problem-specific modeling, long computational times, and large data storage requirements associated with other approaches. Our method efficiently solves PDE problems using an integral solution format. It outperforms direct methods, such as FEM and physics-informed neural networks (PINNs). Additionally, our method alleviates the training burden, scales effectively to various spatial dimensions, and is demonstrated across a range of PDE types and domains. Unlike the direct Gaussian approximation of a Dirac delta function, our method can be used to solve PDEs in higher dimensions. Because our method directly addresses the singularity, it can be used to solve different PDEs without prior knowledge. Unlike BI-GreenNet, which is limited to PDEs with known expressions of the singular part of the Green’s function, our method does not require prior knowledge of the singularity. The results confirm the advantages of DGGFs and the benefits of Generalized Greens Functions as a novel and effective approach to solving PDEs without suffering from singularities.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114235"},"PeriodicalIF":3.8,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654846","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":"Probabilistic data-driven turbulence closure modeling by assimilating statistics","authors":"Sagy R. Ephrati","doi":"10.1016/j.jcp.2025.114234","DOIUrl":"10.1016/j.jcp.2025.114234","url":null,"abstract":"<div><div>A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the <em>ideal large-eddy simulation</em> model [8] and data assimilation methods. The method requires <em>a posteriori</em> measured data to define a stochastic large-eddy simulation model, which is combined with a Bayesian statistical correction enforcing user-specified statistics extracted from high-fidelity flow snapshots. Thus, it enables computationally cheap ensemble simulations by combining knowledge of the local integration error and knowledge of desired flow statistics. An example implementation of the modeling framework is given for two-dimensional Rayleigh-Bénard convection at Rayleigh number <span><math><mrow><mi>Ra</mi><mo>=</mo><msup><mn>10</mn><mn>10</mn></msup></mrow></math></span>, incorporating stochastic perturbations and an ensemble Kalman filtering step in a non-intrusive way. Physical flow dynamics are obtained, whilst kinetic energy spectra and heat flux are accurately reproduced in long-time ensemble forecasts on coarse grids for two discretizations. The model is shown to produce accurate results with as few as 20 high-fidelity flow snapshots as input data.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114234"},"PeriodicalIF":3.8,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757426","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":"Multi-plane moment-of-fluid interface reconstruction in 3D","authors":"Jacob Spainhour ,&nbsp;Mikhail Shashkov","doi":"10.1016/j.jcp.2025.114239","DOIUrl":"10.1016/j.jcp.2025.114239","url":null,"abstract":"<div><div>Moment-of-fluid (MOF) methods for interface reconstruction approximate the region occupied by material in each mesh element only through reference to its geometric moments. We present a 3D MOF method that represents the material (POM) in each cell as the convex intersection of the cell and multiple half-spaces, each selected to minimize the least-squares error between computed moments of the approximated material and provided reference moments.</div><div>This optimization problem is highly non-linear and non-convex, making the numerical result very sensitive to the initial guess.To create an effective initial guess in each cell, we construct an ellipsoid from 0th–2nd order reference moments such that its shape corresponds with that of the POM.Within this ellipsoid we inscribe a polyhedron, and initialize the minimization problem with the half-spaces defined by each of its faces.The inscribed polyhedron has minimally 4 faces, and using up to 3rd order moments permits optimization over up to 20 unknown values.We therefore define MOF methods that utilize 4, 5, or 6 half-spaces, correspondingly initialized with the faces of a single inscribed tetrahedron, triangular prism, or hexahedron.Stability of the non-linear optimization is further improved with a prepossessing step that normalizes the reference moments according to the axes of the reference ellipsoid.</div><div>Using this approach, the non-linear least-squares solver reliably converges to a near-global minimum from a single initial guess. We demonstrate accuracy and robustness using single-cell and multi-cell examples over a wide spectrum of geometry. In particular, we demonstrate our ability to exactly reproduce several important and complex features defined by up to four half-spaces, such as corners, filaments, filament tips, and embedded material in the cell.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114239"},"PeriodicalIF":3.8,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654848","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 optimally convergent parallel splitting algorithm for the multiple-network poroelasticity model","authors":"Jijing Zhao ,&nbsp;Huangxin Chen ,&nbsp;Mingchao Cai ,&nbsp;Shuyu Sun","doi":"10.1016/j.jcp.2025.114214","DOIUrl":"10.1016/j.jcp.2025.114214","url":null,"abstract":"<div><div>This paper presents a novel parallel splitting algorithm for solving quasi-static multiple-network poroelasticity (MPET) equations. By introducing a total pressure variable, the MPET system can be reformulated into a coupled Stokes-parabolic system. To efficiently solve this system, we propose a parallel splitting approach. In the first time step, a monolithic solver is used to solve all variables simultaneously. For subsequent time steps, the system is split into a Stokes subproblem and a parabolic subproblem. These subproblems are then solved in parallel using a stabilization technique. This parallel splitting approach differs from sequential or iterative decoupling, reducing computational time. The algorithm is proven to be unconditionally stable, optimally convergent, and robust across various parameter settings. These theoretical results are confirmed by numerical experiments. We also apply this parallel algorithm to simulate fluid-tissue interactions within the physiological environment of the human brain.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114214"},"PeriodicalIF":3.8,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654847","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":"A model-consistent data-driven computational strategy for PDE joint inversion problems","authors":"Kui Ren ,&nbsp;Lu Zhang","doi":"10.1016/j.jcp.2025.114232","DOIUrl":"10.1016/j.jcp.2025.114232","url":null,"abstract":"<div><div>The task of simultaneously reconstructing multiple physical coefficients in partial differential equations (PDEs) from observed data is ubiquitous in applications. In this work, we propose an integrated data-driven and model-based iterative reconstruction framework for such joint inversion problems where additional data on the unknown coefficients are supplemented for better reconstructions. Our method couples the supplementary data with the PDE model to make the data-driven modeling process consistent with the model-based reconstruction procedure. This coupling strategy allows us to characterize the impact of learning uncertainty on the joint inversion results for two typical inverse problems. Numerical evidence is provided to demonstrate the feasibility of using data-driven models to improve the joint inversion of multiple coefficients in PDEs.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114232"},"PeriodicalIF":3.8,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631821","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":"Identifying large-scale linear parameter varying systems with dynamic mode decomposition methods","authors":"Jean Panaioti Jordanou ,&nbsp;Eduardo Camponogara ,&nbsp;Eduardo Gildin","doi":"10.1016/j.jcp.2025.114230","DOIUrl":"10.1016/j.jcp.2025.114230","url":null,"abstract":"<div><div>Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven identification of such systems, the literature is quite scarce regarding the identification of LPV models for large-scale systems. Since large-scale systems are ubiquitous in practice, this work develops a methodology for the local and global identification of large-scale LPV systems based on nonintrusive reduced-order modeling. The developed method is coined as DMD-LPV for being inspired in the Dynamic Mode Decomposition (DMD). To validate the proposed identification method, we identify a system described by a discretized linear diffusion equation, with the diffusion gain defined by a polynomial over a parameter. The experiments show that the proposed method can easily identify a reduced-order LPV model of a given large-scale system without the need to perform identification in the full-order dimension, and with almost no performance decay over performing a reduction, given that the model structure is well-established.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"539 ","pages":"Article 114230"},"PeriodicalIF":3.8,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633696","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}