Pub Date : 2026-01-08DOI: 10.1016/j.jcp.2026.114665
Andrea Lamperti, Laura De Lorenzis
We propose a novel phase-field model for solute precipitation and dissolution in liquid solutions. Unlike in previous studies with similar scope, in our model the two non-linear coupled governing equations of the problem, which deliver the solute ion concentration and the phase-field variable, are derived in a variationally consistent way starting from a free energy functional of Modica-Mortola type. The phase-field variable is assumed to follow the non-conservative Allen-Cahn evolution law, whereas the solute ion concentration obeys the conservative Cahn-Hilliard equation. We also assess the convergence of the new model to the corresponding sharp-interface model via the method of matched asymptotic expansions, and derive a novel expression of the reaction rate of the sharp-interface model. Through a finite element discretization, we present several numerical examples in one, two and three dimensions.
{"title":"A variationally consistent and asymptotically convergent phase-field model for solute precipitation and dissolution","authors":"Andrea Lamperti, Laura De Lorenzis","doi":"10.1016/j.jcp.2026.114665","DOIUrl":"10.1016/j.jcp.2026.114665","url":null,"abstract":"<div><div>We propose a novel phase-field model for solute precipitation and dissolution in liquid solutions. Unlike in previous studies with similar scope, in our model the two non-linear coupled governing equations of the problem, which deliver the solute ion concentration and the phase-field variable, are derived in a variationally consistent way starting from a free energy functional of Modica-Mortola type. The phase-field variable is assumed to follow the non-conservative Allen-Cahn evolution law, whereas the solute ion concentration obeys the conservative Cahn-Hilliard equation. We also assess the convergence of the new model to the corresponding sharp-interface model via the method of matched asymptotic expansions, and derive a novel expression of the reaction rate of the sharp-interface model. Through a finite element discretization, we present several numerical examples in one, two and three dimensions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114665"},"PeriodicalIF":3.8,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974387","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}
Pub Date : 2026-01-08DOI: 10.1016/j.jcp.2026.114655
Mohammad Motamed , N. Anders Petersson
We propose a marginal likelihood strategy within the Kennedy-O’Hagan (KOH) Bayesian framework, where a Gaussian process (GP) models the discrepancy between a physical system and its simulator. Our approach introduces a novel marginalized likelihood by integrating out the degenerate eigenspace of the covariance matrix, rather than approximating the original likelihood. Unlike approximation methods that compromise accuracy for computational efficiency, our method defines an exact likelihood—distinct from the original but preserving all relevant information. This formulation achieves computational efficiency and stability, even for large datasets where the covariance matrix nears degeneracy. Applied to the characterization of a superconducting quantum device at Lawrence Livermore National Laboratory, the approach enhances the predictive accuracy of the Lindblad master equations for modeling Ramsey measurement data by effectively quantifying uncertainties consistent with the quantum data.
{"title":"Non -degenerate marginal-likelihood calibration with application to quantum characterization","authors":"Mohammad Motamed , N. Anders Petersson","doi":"10.1016/j.jcp.2026.114655","DOIUrl":"10.1016/j.jcp.2026.114655","url":null,"abstract":"<div><div>We propose a marginal likelihood strategy within the Kennedy-O’Hagan (KOH) Bayesian framework, where a Gaussian process (GP) models the discrepancy between a physical system and its simulator. Our approach introduces a novel marginalized likelihood by integrating out the degenerate eigenspace of the covariance matrix, rather than approximating the original likelihood. Unlike approximation methods that compromise accuracy for computational efficiency, our method defines an exact likelihood—distinct from the original but preserving all relevant information. This formulation achieves computational efficiency and stability, even for large datasets where the covariance matrix nears degeneracy. Applied to the characterization of a superconducting quantum device at Lawrence Livermore National Laboratory, the approach enhances the predictive accuracy of the Lindblad master equations for modeling Ramsey measurement data by effectively quantifying uncertainties consistent with the quantum data.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114655"},"PeriodicalIF":3.8,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976096","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}
Pub Date : 2026-01-07DOI: 10.1016/j.jcp.2026.114653
Bonan Xu , Chang Sun , Peixu Guo
The simulation of transcritical flows remains challenging due to strong thermodynamic nonlinearities that induce spurious pressure oscillations in conventional schemes.While primitive-variable formulations offer improved robustness under such conditions, they are always limited by energy conservation errors and the absence of systematic high-order treatments for numerical fluxes. In this paper, we introduce the Central Differential flux with High-Order Dissipation (CDHD), a novel numerical flux solver designed for primitive-variable discretization. This method combines a central flux for advection with a minimal, upwind-biased dissipation term to stabilize the simulation while maintaining formal accuracy. The dissipation term effectively suppresses oscillations and improves stability in transcritical flows. Compared to traditional primitive-variable approaches, CDHD reduces the energy conservation error in two order of magnitude. When incorporated into a hybrid framework with a conservative shock-capturing scheme, the method robustly handles both smooth transcritical phenomena and shock waves. Numerical tests validate the accuracy, stability, and energy-preserving capabilities of CDHD, demonstrating its potential as a reliable tool for complex real-gas flow simulations.
{"title":"A Central Differential flux with high-Order dissipation for robust simulations of transcritical flows","authors":"Bonan Xu , Chang Sun , Peixu Guo","doi":"10.1016/j.jcp.2026.114653","DOIUrl":"10.1016/j.jcp.2026.114653","url":null,"abstract":"<div><div>The simulation of transcritical flows remains challenging due to strong thermodynamic nonlinearities that induce spurious pressure oscillations in conventional schemes.While primitive-variable formulations offer improved robustness under such conditions, they are always limited by energy conservation errors and the absence of systematic high-order treatments for numerical fluxes. In this paper, we introduce the Central Differential flux with High-Order Dissipation (CDHD), a novel numerical flux solver designed for primitive-variable discretization. This method combines a central flux for advection with a minimal, upwind-biased dissipation term to stabilize the simulation while maintaining formal accuracy. The dissipation term effectively suppresses oscillations and improves stability in transcritical flows. Compared to traditional primitive-variable approaches, CDHD reduces the energy conservation error in two order of magnitude. When incorporated into a hybrid framework with a conservative shock-capturing scheme, the method robustly handles both smooth transcritical phenomena and shock waves. Numerical tests validate the accuracy, stability, and energy-preserving capabilities of CDHD, demonstrating its potential as a reliable tool for complex real-gas flow simulations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114653"},"PeriodicalIF":3.8,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923625","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}
Pub Date : 2026-01-07DOI: 10.1016/j.jcp.2026.114651
Aviral Prakash, Ben S. Southworth, Marc L. Klasky
Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. The numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.
{"title":"ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data","authors":"Aviral Prakash, Ben S. Southworth, Marc L. Klasky","doi":"10.1016/j.jcp.2026.114651","DOIUrl":"10.1016/j.jcp.2026.114651","url":null,"abstract":"<div><div>Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. The numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114651"},"PeriodicalIF":3.8,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974389","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}
Pub Date : 2026-01-06DOI: 10.1016/j.jcp.2025.114650
Tianrun Gao , Mingduo Yuan , Lin Fu
In this study, a general smoothed particle-mesh hydrodynamics (SPMH) method is developed for fluid-structure interaction (FSI), particularly for those involving thin structures. The proposed SPMH method obtains improved accuracy in the user-defined mesh domain, which is typically defined near the thin structures. Meanwhile, SPMH can also preserve the free-surface tracking ability of smoothed particle hydrodynamics (SPH). The SPMH integrates SPH and finite-volume method (FVM), for which the weakly compressible SPH and unstructured arbitrary Lagrangian-Eulerian (ALE) FVM are adopted, respectively. The mesh update of the ALE framework is achieved by combining the finite-element method (FEM) with the spring analogy method. For thin structures, a new beam solver degenerated from the three-dimensional shell is developed based on FVM. In SPMH, the data communication between particle and mesh domains is achieved through activated, non-activated particles of SPH particles and interface points on mesh domain edges. To handle the free-surface flow in the mesh domain, the fluid-phase and void cells are identified according to the non-activated SPH particles, and flux calculation at the free-surface region is designed accordingly. A set of challenging FSI cases involving thin structures is simulated using the proposed SPMH method, and SPMH shows higher accuracy than the previous SPH method, particularly for FSI problems in the specified mesh domain.
{"title":"Smoothed particle-mesh hydrodynamics (SPMH) for fluid-structure interactions involving thin structures","authors":"Tianrun Gao , Mingduo Yuan , Lin Fu","doi":"10.1016/j.jcp.2025.114650","DOIUrl":"10.1016/j.jcp.2025.114650","url":null,"abstract":"<div><div>In this study, a general smoothed particle-mesh hydrodynamics (SPMH) method is developed for fluid-structure interaction (FSI), particularly for those involving thin structures. The proposed SPMH method obtains improved accuracy in the user-defined mesh domain, which is typically defined near the thin structures. Meanwhile, SPMH can also preserve the free-surface tracking ability of smoothed particle hydrodynamics (SPH). The SPMH integrates SPH and finite-volume method (FVM), for which the weakly compressible SPH and unstructured arbitrary Lagrangian-Eulerian (ALE) FVM are adopted, respectively. The mesh update of the ALE framework is achieved by combining the finite-element method (FEM) with the spring analogy method. For thin structures, a new beam solver degenerated from the three-dimensional shell is developed based on FVM. In SPMH, the data communication between particle and mesh domains is achieved through activated, non-activated particles of SPH particles and interface points on mesh domain edges. To handle the free-surface flow in the mesh domain, the fluid-phase and void cells are identified according to the non-activated SPH particles, and flux calculation at the free-surface region is designed accordingly. A set of challenging FSI cases involving thin structures is simulated using the proposed SPMH method, and SPMH shows higher accuracy than the previous SPH method, particularly for FSI problems in the specified mesh domain.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114650"},"PeriodicalIF":3.8,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923627","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}
Classical Finite Volume methods for multi-dimensional problems include stabilization (e.g. via a Riemann solver), that is derived by considering several one-dimensional problems in different directions. Such methods therefore ignore a possibly existing balance of contributions coming from different directions, such as the one characterizing multi-dimensional stationary states. Instead of being preserved, they are usually diffused away by such methods. Stationarity preserving methods use a better suited stabilization term that vanishes at the stationary state, allowing the method to preserve it. This work presents a general approach to stationarity preserving Finite Volume methods for nonlinear conservation/balance laws. It is based on a multi-dimensional stationarity preserving quadrature strategy that allows to naturally introduce genuinely multi-dimensional numerical fluxes. The new methods are shown to significantly outperform existing ones even if the latter are of higher order of accuracy and even on non-stationary solutions.
{"title":"Genuinely multi-dimensional stationarity preserving Finite Volume formulation for nonlinear hyperbolic PDEs","authors":"Wasilij Barsukow , Mirco Ciallella , Mario Ricchiuto , Davide Torlo","doi":"10.1016/j.jcp.2025.114633","DOIUrl":"10.1016/j.jcp.2025.114633","url":null,"abstract":"<div><div>Classical Finite Volume methods for multi-dimensional problems include stabilization (e.g. via a Riemann solver), that is derived by considering several one-dimensional problems in different directions. Such methods therefore ignore a possibly existing balance of contributions coming from different directions, such as the one characterizing multi-dimensional stationary states. Instead of being preserved, they are usually diffused away by such methods. Stationarity preserving methods use a better suited stabilization term that vanishes at the stationary state, allowing the method to preserve it. This work presents a general approach to stationarity preserving Finite Volume methods for nonlinear conservation/balance laws. It is based on a multi-dimensional stationarity preserving quadrature strategy that allows to naturally introduce genuinely multi-dimensional numerical fluxes. The new methods are shown to significantly outperform existing ones even if the latter are of higher order of accuracy and even on non-stationary solutions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114633"},"PeriodicalIF":3.8,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974703","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}
Pub Date : 2026-01-06DOI: 10.1016/j.jcp.2026.114664
Ngoc Cuong Nguyen
We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for global approximation of the parametric solution manifold, Galerkin projection of the underlying PDEs onto the RB space for dimensionality reduction, and high-order empirical interpolation for efficient treatment of the nonlinear terms. We propose a class of high-order empirical interpolation methods to derive basis functions and interpolation points by using high-order partial derivatives of the nonlinear terms. We develop error indicator to estimate the interpolation errors and determine parameter points via greedy sampling. Furthermore, we introduce two hyperreduction schemes to construct reduced-order models: one that applies the hyperreduction technique before Newton’s method and another after. The latter scheme significantly reduces hyperreduction errors while maintaining computational efficiency. Numerical results are presented to demonstrate the accuracy and efficiency of our approach.
{"title":"High-order empirical interpolation methods for real-time solution of parametrized nonlinear PDEs","authors":"Ngoc Cuong Nguyen","doi":"10.1016/j.jcp.2026.114664","DOIUrl":"10.1016/j.jcp.2026.114664","url":null,"abstract":"<div><div>We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for global approximation of the parametric solution manifold, Galerkin projection of the underlying PDEs onto the RB space for dimensionality reduction, and high-order empirical interpolation for efficient treatment of the nonlinear terms. We propose a class of high-order empirical interpolation methods to derive basis functions and interpolation points by using high-order partial derivatives of the nonlinear terms. We develop error indicator to estimate the interpolation errors and determine parameter points via greedy sampling. Furthermore, we introduce two hyperreduction schemes to construct reduced-order models: one that applies the hyperreduction technique before Newton’s method and another after. The latter scheme significantly reduces hyperreduction errors while maintaining computational efficiency. Numerical results are presented to demonstrate the accuracy and efficiency of our approach.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114664"},"PeriodicalIF":3.8,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923626","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}
Pub Date : 2026-01-05DOI: 10.1016/j.jcp.2025.114636
Dana Ferranti, Sarah D. Olson
A linear stability analysis of an elastic surface immersed in a viscous fluid is presented. The coupled system is modeled using the method of regularized Stokeslets (MRS), a Lagrangian method for simulating fluid-structure interaction at low Reynolds number. The linearized system is solved in a doubly periodic domain in a 3D fluid. The eigenvalues determine the theoretical critical time step for numerical stability for a forward Euler time integration, which are then verified numerically across several regularization functions, elastic models, and parameter choices. New doubly periodic regularized Stokeslets are presented, allowing for comparison of the stability properties of different regularization functions. The stability results for a common regularization function are approximated by a power law relating the regularization parameter and the surface discretization for two different elastic models. This relationship is empirically shown to hold in the different setting of a finite surface in a bulk fluid.
{"title":"Analysis of the stability of an immersed elastic surface using the method of regularized Stokeslets","authors":"Dana Ferranti, Sarah D. Olson","doi":"10.1016/j.jcp.2025.114636","DOIUrl":"10.1016/j.jcp.2025.114636","url":null,"abstract":"<div><div>A linear stability analysis of an elastic surface immersed in a viscous fluid is presented. The coupled system is modeled using the method of regularized Stokeslets (MRS), a Lagrangian method for simulating fluid-structure interaction at low Reynolds number. The linearized system is solved in a doubly periodic domain in a 3D fluid. The eigenvalues determine the theoretical critical time step for numerical stability for a forward Euler time integration, which are then verified numerically across several regularization functions, elastic models, and parameter choices. New doubly periodic regularized Stokeslets are presented, allowing for comparison of the stability properties of different regularization functions. The stability results for a common regularization function are approximated by a power law relating the regularization parameter and the surface discretization for two different elastic models. This relationship is empirically shown to hold in the different setting of a finite surface in a bulk fluid.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114636"},"PeriodicalIF":3.8,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145974388","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}
Pub Date : 2026-01-05DOI: 10.1016/j.jcp.2026.114652
Lukas Exl , Sebastian Schaffer
We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order B-spline bases, which allow for increased accuracy and smoothness. The method employs a super-potential formulation, which circumvents the need to convolve with a singular kernel. The field is represented with high accuracy as a functional Tucker tensor, leveraging separable expansions on the tensor product domain and trained via a multilinear extension of the extreme learning machine methodology. Unlike conventional grid-based methods, the proposed mesh-free approach allows for continuous field evaluation. Numerical experiments confirm the accuracy and efficiency of the proposed method, demonstrating exponential convergence of the energy and linear computational scaling with respect to the multilinear expansion rank.
{"title":"Higher order stray field computation on tensor product domains","authors":"Lukas Exl , Sebastian Schaffer","doi":"10.1016/j.jcp.2026.114652","DOIUrl":"10.1016/j.jcp.2026.114652","url":null,"abstract":"<div><div>We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order B-spline bases, which allow for increased accuracy and smoothness. The method employs a super-potential formulation, which circumvents the need to convolve with a singular kernel. The field is represented with high accuracy as a functional Tucker tensor, leveraging separable expansions on the tensor product domain and trained via a multilinear extension of the extreme learning machine methodology. Unlike conventional grid-based methods, the proposed mesh-free approach allows for continuous field evaluation. Numerical experiments confirm the accuracy and efficiency of the proposed method, demonstrating exponential convergence of the energy and linear computational scaling with respect to the multilinear expansion rank.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114652"},"PeriodicalIF":3.8,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923624","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}
Pub Date : 2026-01-05DOI: 10.1016/j.jcp.2025.114639
Namkyeong Cho , Junseung Ryu , Hyung Ju Hwang
The recently released Mamba model leverages structured state space models (SSMs), incorporating hardware-efficient designs and selection mechanisms. The Mamba architecture demonstrates strong potential as a replacement for Transformer-based models across various tasks. In this work, we employ Mamba to train neural operators on infinite-dimensional spaces derived from partial differential equations. Using well-established theory on the Rough Path and Reproducing Kernel Hilbert Space (RKHS), we theoretically demonstrate that the SSM-based models can replace Transformer-based models for approximating operators. Our empirical findings further show that Mamba consistently outperforms Transformer models across various tasks while achieving faster inference, highlighting the potential of the Mamba architecture to outperform Transformer-based models in various operator learning tasks.
{"title":"MBNO: Mamba-based neural operators for solving partial differential equations","authors":"Namkyeong Cho , Junseung Ryu , Hyung Ju Hwang","doi":"10.1016/j.jcp.2025.114639","DOIUrl":"10.1016/j.jcp.2025.114639","url":null,"abstract":"<div><div>The recently released Mamba model leverages structured state space models (SSMs), incorporating hardware-efficient designs and selection mechanisms. The Mamba architecture demonstrates strong potential as a replacement for Transformer-based models across various tasks. In this work, we employ Mamba to train neural operators on infinite-dimensional spaces derived from partial differential equations. Using well-established theory on the Rough Path and Reproducing Kernel Hilbert Space (RKHS), we theoretically demonstrate that the SSM-based models can replace Transformer-based models for approximating operators. Our empirical findings further show that Mamba consistently outperforms Transformer models across various tasks while achieving faster inference, highlighting the potential of the Mamba architecture to outperform Transformer-based models in various operator learning tasks.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"550 ","pages":"Article 114639"},"PeriodicalIF":3.8,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923630","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}
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