Journal of Computational Physics最新文献

{"title":"Modular operator superposition (MOS): A physics-guided machine learning framework for addressing the curse of dimensionality and multiscale challenges in computational fluid dynamics","authors":"Kai Liu ,&nbsp;S. Balachandar ,&nbsp;Haochen Li","doi":"10.1016/j.jcp.2025.114435","DOIUrl":"10.1016/j.jcp.2025.114435","url":null,"abstract":"<div><div>We introduce Modular Operator Superposition (MOS), a physics-guided and AI-augmented framework for efficient, scalable, and generalizable flow field modeling in high-dimensional and multiscale fluid systems. Rather than globally resolving flow fields via mesh-based discretization, MOS decomposes the system into physically meaningful flow primitives, each represented by a reusable modular operator. These operators are trained offline using a parameterized physics-informed neural network (P-PINN) in a single pre-processing step, and later composed through a physics-guided superposition strategy to approximate the full system-level mapping. The core advantage of MOS lies in its modularization strategy. By learning only small-scale flow primitives offline, MOS reduces the training cost to a fixed, minimal investment independent of system-level complexity. In the online stage, MOS dynamically solves for primitive-level interactions for any specific configuration of a system, then reconstructs the global flow field through the superposition of modular outputs. This two-stage online process, comprising both solving and inference, enables scalable and generalizable predictions. As a result, MOS addresses the curse of dimensionality by reducing high-dimensional systems to tractable compositions of modular operators and overcomes multiscale challenges through a scale-adaptive operator assembly that flexibly resolves flow features with minimal overhead. We demonstrate MOS for static and dynamic arrays of up to <span><math><mrow><mn>15</mn><mo>,</mo><mn>000</mn></mrow></math></span> cylinders in a channel cross-flow (corresponding to roughly <span><math><msup><mn>10</mn><mn>5</mn></msup></math></span> input parameters). All of these configurations are solved using a shared single-cylinder cross-flow modular operator, trained offline in 30 hours using a data-free, physics-informed machine learning strategy. In the online stage, MOS achieves end-to-end flow field prediction at 3 to 5 orders of magnitude speedup over conventional numerical solvers, while maintaining high fidelity (<span><math><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>&gt;</mo><mn>0.85</mn></mrow></math></span> for all cases). Moreover, the MOS solution format requires 3 to 5 orders of magnitude lower memory usage than conventional numerical outputs. Once solved, the solution can be queried in real-time to infer flow variables at arbitrary spatial resolutions or scattered points, enabling flexible and efficient visualization across scales. Additional tests indicate that MOS remains robust to polydispersity and translational/rotational motion of the cylinders.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"544 ","pages":"Article 114435"},"PeriodicalIF":3.8,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334204","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":"Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains","authors":"Minglei Yang ,&nbsp;Yanfang Liu ,&nbsp;Diego Del-Castillo-Negrete ,&nbsp;Yanzhao Cao ,&nbsp;Guannan Zhang","doi":"10.1016/j.jcp.2025.114434","DOIUrl":"10.1016/j.jcp.2025.114434","url":null,"abstract":"<div><div>Simulating stochastic differential equations (SDEs) in bounded domains presents significant computational challenges due to particle exit phenomena, which require the accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a hybrid diffusion model that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Specifically, the proposed hybrid diffusion model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a conditional diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. The performance of the proposed approach is demonstrated with three test cases: a simple one-dimensional problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional transport problem of interest to magnetically confined fusion plasmas.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"544 ","pages":"Article 114434"},"PeriodicalIF":3.8,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334123","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":"Randomized methods for dynamical low-rank approximation","authors":"Benjamin Carrel","doi":"10.1016/j.jcp.2025.114421","DOIUrl":"10.1016/j.jcp.2025.114421","url":null,"abstract":"<div><div>We introduce novel dynamical low-rank methods for solving large-scale matrix differential equations, motivated by algorithms from randomized numerical linear algebra. In terms of performance (ratio accuracy/cost), our methods can overperform existing dynamical low-rank techniques. Several applications to stiff differential equations demonstrate the robustness, accuracy and low variance of the new methods, despite their inherent randomness. Allowing augmentation of the range and corange, the new methods have a good potential for preserving critical physical quantities such as the energy, mass and momentum. Numerical experiments on the Vlasov-Poisson equation are particularly encouraging.</div><div>The new methods comprise two essential steps: a range estimation step followed by a post-processing step. The range estimation is achieved through a novel dynamical rangefinder method. Subsequently, we propose two methods for post-processing, leading to two time-stepping methods: dynamical randomized singular value decomposition (DRSVD) and dynamical generalized Nyström (DGN). The new methods naturally extend to the rank-adaptive framework by estimating the error via Gaussian sampling.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"544 ","pages":"Article 114421"},"PeriodicalIF":3.8,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145264822","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":"Ensemble score filter for data assimilation of two-phase flow models in porous media","authors":"Ruoyu Hu ,&nbsp;Sanjeeb Poudel ,&nbsp;Feng Bao ,&nbsp;Sanghyun Lee","doi":"10.1016/j.jcp.2025.114416","DOIUrl":"10.1016/j.jcp.2025.114416","url":null,"abstract":"<div><div>Numerical modeling and simulation of two-phase flow in porous media is challenging due to the uncertainties in key parameters, such as permeability. To address these challenges, we propose a computational framework by utilizing the novel Ensemble Score Filter (EnSF) to enhance the accuracy of state estimation for two-phase flow systems in porous media. The forward simulation of the two-phase flow model is implemented using a mixed finite element method, which ensures accurate approximation of the pressure, the velocity, and the saturation. The EnSF leverages score-based diffusion models to approximate filtering distributions efficiently, avoiding the computational expense of neural network-based methods. By incorporating a closed-form score approximation and an analytical update mechanism, the EnSF overcomes degeneracy issues and handles high-dimensional nonlinear filtering with minimal computational overhead. Numerical experiments demonstrate the capabilities of EnSF in scenarios with uncertain permeability and incomplete observational data.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"544 ","pages":"Article 114416"},"PeriodicalIF":3.8,"publicationDate":"2025-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334131","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":"Fast-convergence and asymptotic-preserving simulation of neutral particle flows in the plasma edge","authors":"Yifan Wen,&nbsp;Yanbing Zhang,&nbsp;Lei Wu","doi":"10.1016/j.jcp.2025.114428","DOIUrl":"10.1016/j.jcp.2025.114428","url":null,"abstract":"<div><div>The neutral flows in the plasma edge play a pivotal role in the design of nuclear fusion devices such as divertors and pumps. These flows are generally multiscale, encompassing the continuum, slip, transition, and free-molecular flow regimes, thus necessitating the use of gas kinetic equations. Traditional numerical methods, such as the direct simulation Monte Carlo method and the discrete velocity method, are hindered by extensive computation resources when dealing with near-continuum flows. This paper presents a general synthetic iterative scheme to deterministically simulate the neutral flows in plasma edge accurately and efficiently. By alternately solving the kinetic equations and macroscopic synthetic equations, our method substantially decreases the number of iterations, while maintains asymptotic-preserving properties even when the spatial cell size is much larger than the mean free path. Consequently, a significant reduction in the computational cost, particularly in near-continuum flow regimes, is achieved. This advancement provides an efficient computational tool essential for the advancement of next-generation nuclear fusion reactors.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"544 ","pages":"Article 114428"},"PeriodicalIF":3.8,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242542","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 accurate THINC scheme for interface capturing based on homotopy analysis method","authors":"Dezhu Chen ,&nbsp;Shijun Liao ,&nbsp;Bin Xie","doi":"10.1016/j.jcp.2025.114420","DOIUrl":"10.1016/j.jcp.2025.114420","url":null,"abstract":"<div><div>An accurate and robust Tangent Hyperbolic INterface Capturing (THINC) scheme is proposed in the framework of volume of fluid (VOF) method to capture the moving interface on the unstructured grids. In order to determine the interface position, a new iterative algorithm is put forward based on homotopy analysis method (HAM) to solve the high degree univariate polynomial equation, which hardly obtains converged solutions by the previous Newton-Raphson scheme. The so-called THINC/HAM significantly improves the convergence behaviour of interface reconstruction in terms of the maximum iterative residual and percentage of divergent cells, thus enhancing the local volume conservation of volume fraction. Different from Runge-Kutta schemes used in existing THINC methods, VOF equation is then solved by a direct time integral with varying velocity to update the volume fraction at each time step. It requires only one reconstruction step while preserving the numerical accuracy for higher Courant numbers, which substantially benefits the numerical efficiency. Numerical analysis is also carried out to investigate the appropriate values of some critical parameters in this method. As verified in the benchmark tests, the present scheme shows considerable improvements in numerical accuracy and robustness even if a larger time step and distorted unstructured grid are used. Despite of algorithmic simplicity, the solution quality of the present scheme is comparable to most geometric VOF methods, which is highly appealing for practical applications.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"544 ","pages":"Article 114420"},"PeriodicalIF":3.8,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334202","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":"Physically consistent predictive reduced-order modeling by enhancing operator inference with state constraints","authors":"Hyeonghun Kim,&nbsp;Boris Kramer","doi":"10.1016/j.jcp.2025.114418","DOIUrl":"10.1016/j.jcp.2025.114418","url":null,"abstract":"<div><div>Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference—a methodology within scientific machine learning that enables learning from data a low-dimensional representation of a high-dimensional system governed by nonlinear partial differential equations—by embedding such state constraints in the reduced-order model predictions. In the model learning process, we propose a new way to choose regularization hyperparameters based on a key performance indicator. Since embedding state constraints improves the stability of the Operator Inference reduced-order model, we compare the proposed state constraints-embedded Operator Inference with the standard Operator Inference and other stability-enhancing approaches. For an application to char combustion, we demonstrate that the proposed approach yields state predictions superior to the other methods regarding stability and accuracy. It extrapolates over 200 % past the training regime while being computationally efficient and physically consistent.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114418"},"PeriodicalIF":3.8,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145263537","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":"Stable low diffusion flux splitting schemes on unstructured meshes","authors":"Aditya K. Pandare ,&nbsp;Jack R. Edwards","doi":"10.1016/j.jcp.2025.114415","DOIUrl":"10.1016/j.jcp.2025.114415","url":null,"abstract":"<div><div>Shock instabilities are shown to manifest in modern low-diffusion flux-vector splitting (FVS) schemes when used on unstructured meshes, or situations where shocks do not align with the mesh lines. These instabilities occur irrespective of the Mach number of the shock. Three types of dissipative mechanisms that suppress these instabilities are presented. These mechanisms are carefully designed in order to affect only problematic regions of the flux-splittings. The AUSM<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span> and LDFSS schemes are stabilized using the proposed modifications. It is shown that the added dissipation improves the shock behavior of AUSM and LDFSS on unstructured meshes. It is also shown that the AUSM<span><math><msup><mrow></mrow><mo>+</mo></msup></math></span>-up scheme is prone to the “carbuncle” instability, a specific type of shock instability, when used on unstructured meshes. The modifications proposed in this work do not lead to carbuncle instabilities for the problems considered here. Furthermore, the modified schemes are shown to satisfy certain properties that are crucial for accurate shear layer computations, such as stationary contact preservation. Using benchmark problems, it is demonstrated that despite the diffusion added for stabilization, these schemes are not overly diffusive. Due to these advantages, the modified FVS schemes presented here are promising candidates for high-speed compressible flow computations on unstructured meshes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114415"},"PeriodicalIF":3.8,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145263536","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":"Moment-based adaptive time integration for thermal radiation transport","authors":"Ben S. Southworth ,&nbsp;Steven Walton ,&nbsp;Steven B. Roberts ,&nbsp;HyeongKae Park","doi":"10.1016/j.jcp.2025.114417","DOIUrl":"10.1016/j.jcp.2025.114417","url":null,"abstract":"<div><div>In this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to multifrequency TRT, and also introduce a semi-implicit variation that facilitates higher-order integration of TRT, where each stage is implicit in all components except opacities. To appeal to the broad literature on adaptivity with Runge–Kutta methods, we derive new embedded methods for four asymptotic preserving IMEX Runge–Kutta schemes we have found to be robust in our previous work on TRT and radiation hydrodynamics. We then use a moment-based high-order-low-order representation of the transport equations. Due to the high dimensionality, memory is always a concern in simulating TRT. We form error estimates and adaptivity in time purely based on temperature and radiation energy, for a trivial overhead in computational cost and memory usage compared with the base second order integrators. We then test the adaptivity in time on the tophat and Larsen problem, demonstrating the ability of the adaptive algorithm to naturally vary the timestep across 4–5 orders of magnitude, ranging from the dynamical timescales of the streaming regime to the thick diffusion limit.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114417"},"PeriodicalIF":3.8,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145263605","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":"Layer separation deep learning model with auxiliary variables for partial differential equations","authors":"Yaru Liu,&nbsp;Yiqi Gu","doi":"10.1016/j.jcp.2025.114414","DOIUrl":"10.1016/j.jcp.2025.114414","url":null,"abstract":"<div><div>In this paper, we propose a new optimization framework, the layer separation (LySep) model, to improve the deep learning-based methods in solving partial differential equations. Due to the highly non-convex nature of the loss function in deep learning, existing optimization algorithms often converge to suboptimal local minima or suffer from gradient explosion or vanishing, resulting in poor performance. To address these issues, we introduce auxiliary variables to separate the layers of deep neural networks. Specifically, the output and its derivatives of each layer are represented by auxiliary variables, effectively decomposing the deep architecture into a series of shallow architectures. New loss functions with auxiliary variables are established, in which only variables from two neighboring layers are coupled. Corresponding algorithms based on alternating directions are developed, allowing for the optimal update of many variables in closed form. Moreover, we provide theoretical analyses demonstrating the consistency between the LySep model and the original deep model. High-dimensional numerical results validate our theory and demonstrate the advantages of LySep in minimizing loss and reducing solution error.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"543 ","pages":"Article 114414"},"PeriodicalIF":3.8,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145263533","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}