Pub Date : 2026-01-15DOI: 10.1016/j.jcp.2026.114691
Clément Lasuen
In this paper, we propose a finite volume scheme for the grey and multi-group radiative equations. We present it in one space dimension but it can be easily generalized to the two dimensional case using the ideas from Lasuen [1]. This scheme is designed as an upwind scheme where the velocity is modified so as to recover the correct diffusion limit. The resulting scheme is asymptotic preserving, positive under a classical CFL condition and conservative. We also add a reconstruction procedure so as to make it second order consistent. Besides, its computational cost is similar to an explicit scheme.
{"title":"A positive and asymptotic preserving scheme for the multi-group radiative equations","authors":"Clément Lasuen","doi":"10.1016/j.jcp.2026.114691","DOIUrl":"10.1016/j.jcp.2026.114691","url":null,"abstract":"<div><div>In this paper, we propose a finite volume scheme for the grey and multi-group radiative equations. We present it in one space dimension but it can be easily generalized to the two dimensional case using the ideas from Lasuen [1]. This scheme is designed as an upwind scheme where the velocity is modified so as to recover the correct diffusion limit. The resulting scheme is <em>asymptotic preserving</em>, positive under a classical <em>CFL</em> condition and conservative. We also add a reconstruction procedure so as to make it second order consistent. Besides, its computational cost is similar to an explicit scheme.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"552 ","pages":"Article 114691"},"PeriodicalIF":3.8,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025859","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 : 2026-01-14DOI: 10.1016/j.jcp.2026.114672
Youjun Deng, Lingzheng Kong, Gongsheng Tong
Multi-layered structures have attracted increasing attention due to their potential applications in imaging and cloaking. Such structures, which include GPT-vanishing and SC-vanishing configurations, are known to exhibit significant non-uniqueness in inverse problems under low-frequency or slowly oscillating incident fields. Unique recovery in these settings typically requires high-order incident waves, resulting in severe ill-posedness and instability. Motivated by these insights and the hybridization behavior of plasmon modes across interfaces in multi-layered media, we develop a mathematical framework for plasmon hybridization theory in multi-layered structures of general shape based on perturbation theory. Our analysis yields a spectral expansion of the shape sensitivity functional, providing a foundation for highly sensitive shape reconstruction. Numerical simulations are presented to corroborate the theoretical findings and show new plasmon hybridization phenomena.
{"title":"Theory and computation of plasmon hybridization modes for multi-layered complex media","authors":"Youjun Deng, Lingzheng Kong, Gongsheng Tong","doi":"10.1016/j.jcp.2026.114672","DOIUrl":"10.1016/j.jcp.2026.114672","url":null,"abstract":"<div><div>Multi-layered structures have attracted increasing attention due to their potential applications in imaging and cloaking. Such structures, which include GPT-vanishing and SC-vanishing configurations, are known to exhibit significant non-uniqueness in inverse problems under low-frequency or slowly oscillating incident fields. Unique recovery in these settings typically requires high-order incident waves, resulting in severe ill-posedness and instability. Motivated by these insights and the hybridization behavior of plasmon modes across interfaces in multi-layered media, we develop a mathematical framework for plasmon hybridization theory in multi-layered structures of general shape based on perturbation theory. Our analysis yields a spectral expansion of the shape sensitivity functional, providing a foundation for highly sensitive shape reconstruction. Numerical simulations are presented to corroborate the theoretical findings and show new plasmon hybridization phenomena.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114672"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976095","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 : 2026-01-14DOI: 10.1016/j.jcp.2026.114692
Benoit Nennig , Martin Ghienne , Emmanuel Perrey-Debain
A numerical algorithm is proposed to deal with parametric eigenvalue problems involving non-Hermitian matrices and is exploited to find location of defective eigenvalues in the parameter space of non-Hermitian parametric eigenvalue problems. These non-Hermitian degeneracies also called exceptional points (EP) have raised considerable attention in the scientific community as these can have a great impact in a variety of physical problems. The method first requires the computation of high order derivatives of a few selected eigenvalues with respect to each parameter involved. The second step is to recombine these quantities to form new coefficients associated with a partial characteristic polynomial (PCP). By construction, these coefficients are regular functions in a large domain of the parameter space which means that the PCP allows one to recover the selected eigenvalues as well as the localization of high order EPs by simply using standard root-finding algorithms.
The versatility of the proposed approach is tested on several applications, from mass-spring systems to guided acoustic waves with absorbing walls and room acoustics. The scalability of the method to large sparse matrices arising from conventional discretization techniques such as the finite element method is demonstrated. The proposed approach can be extended to a large number of applications where EPs play an important role in quantum mechanics, optics and photonics or in mechanical engineering.
{"title":"Fast recovery of parametric eigenvalues depending on several parameters and location of high order exceptional points","authors":"Benoit Nennig , Martin Ghienne , Emmanuel Perrey-Debain","doi":"10.1016/j.jcp.2026.114692","DOIUrl":"10.1016/j.jcp.2026.114692","url":null,"abstract":"<div><div>A numerical algorithm is proposed to deal with parametric eigenvalue problems involving non-Hermitian matrices and is exploited to find location of defective eigenvalues in the parameter space of non-Hermitian parametric eigenvalue problems. These non-Hermitian degeneracies also called exceptional points (EP) have raised considerable attention in the scientific community as these can have a great impact in a variety of physical problems. The method first requires the computation of high order derivatives of a few selected eigenvalues with respect to each parameter involved. The second step is to recombine these quantities to form new coefficients associated with a partial characteristic polynomial (PCP). By construction, these coefficients are regular functions in a large domain of the parameter space which means that the PCP allows one to recover the selected eigenvalues as well as the localization of high order EPs by simply using standard root-finding algorithms.</div><div>The versatility of the proposed approach is tested on several applications, from mass-spring systems to guided acoustic waves with absorbing walls and room acoustics. The scalability of the method to large sparse matrices arising from conventional discretization techniques such as the finite element method is demonstrated. The proposed approach can be extended to a large number of applications where EPs play an important role in quantum mechanics, optics and photonics or in mechanical engineering.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114692"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035640","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 : 2026-01-14DOI: 10.1016/j.jcp.2026.114684
Rongxin Lu , Jiwei Jia , Young Ju Lee , Zheng Lu , Chen-Song Zhang
In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide range of equations, they often exhibit a suboptimal performance when applied to equations with large local gradients, resulting in substantially localized errors. To address this issue, this paper proposes an adaptive PINN algorithm designed to improve accuracy in such cases. The core idea of the algorithm is to adaptively adjust the distribution of collocation points based on the recovery-type a-posteriori error of the current numerical solution, enabling a better approximation of the true solution. This approach is inspired by the adaptive finite element method. By combining the recovery-type a-posteriori estimator, a gradient-recovery estimator commonly used in the adaptive finite element method (FEM), with PINNs, we introduce the recovery-type a-posteriori estimator enhanced adaptive PINN (R-PINN) and compare its performance with a typical adaptive sampling PINN, failure-informed PINN (FI-PINN), and a typical adaptive weighting PINN, residual-based attention in PINN (RBA-PINN) as a baseline. Our results demonstrate that R-PINN achieves faster convergence with fewer adaptively distributed points and outperforms the other two PINNs in the cases with regions of large errors.
{"title":"R-PINN: Recovery-type a-posteriori estimator enhanced adaptive PINN","authors":"Rongxin Lu , Jiwei Jia , Young Ju Lee , Zheng Lu , Chen-Song Zhang","doi":"10.1016/j.jcp.2026.114684","DOIUrl":"10.1016/j.jcp.2026.114684","url":null,"abstract":"<div><div>In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide range of equations, they often exhibit a suboptimal performance when applied to equations with large local gradients, resulting in substantially localized errors. To address this issue, this paper proposes an adaptive PINN algorithm designed to improve accuracy in such cases. The core idea of the algorithm is to adaptively adjust the distribution of collocation points based on the recovery-type a-posteriori error of the current numerical solution, enabling a better approximation of the true solution. This approach is inspired by the adaptive finite element method. By combining the recovery-type a-posteriori estimator, a gradient-recovery estimator commonly used in the adaptive finite element method (FEM), with PINNs, we introduce the recovery-type a-posteriori estimator enhanced adaptive PINN (R-PINN) and compare its performance with a typical adaptive sampling PINN, failure-informed PINN (FI-PINN), and a typical adaptive weighting PINN, residual-based attention in PINN (RBA-PINN) as a baseline. Our results demonstrate that R-PINN achieves faster convergence with fewer adaptively distributed points and outperforms the other two PINNs in the cases with regions of large errors.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114684"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035681","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 : 2026-01-14DOI: 10.1016/j.jcp.2026.114688
Reese E. Jones , Adrian Buganza Tepole , Jan N. Fuhg
Multi-well potentials are ubiquitous in science, modeling phenomena such as phase transitions, dynamic instabilities, and multimodal behavior across physics, chemistry, and biology. In contrast to non-smooth minimum-of-mixture representations, we propose a differentiable and convex formulation based on a log-sum-exponential (LSE) mixture of input convex neural network (ICNN) modes. This log-sum-exponential input convex neural network (LSE-ICNN) provides a smooth surrogate that retains convexity within basins and allows for gradient-based learning and inference.
A key feature of the LSE-ICNN is its ability to automatically discover both the number of modes and the scale of transitions through sparse regression, enabling adaptive and parsimonious modeling. We demonstrate the versatility of the LSE-ICNN across diverse domains, including mechanochemical phase transformations, microstructural elastic instabilities, conservative biological gene circuits, and variational inference for multimodal probability distributions. These examples highlight the effectiveness of the LSE-ICNN in capturing complex multimodal landscapes while preserving differentiability, making it broadly applicable in data-driven modeling, optimization, and physical simulation.
{"title":"Differentiable neural network representation of multi-well, locally-convex potentials","authors":"Reese E. Jones , Adrian Buganza Tepole , Jan N. Fuhg","doi":"10.1016/j.jcp.2026.114688","DOIUrl":"10.1016/j.jcp.2026.114688","url":null,"abstract":"<div><div>Multi-well potentials are ubiquitous in science, modeling phenomena such as phase transitions, dynamic instabilities, and multimodal behavior across physics, chemistry, and biology. In contrast to non-smooth minimum-of-mixture representations, we propose a differentiable and convex formulation based on a log-sum-exponential (LSE) mixture of input convex neural network (ICNN) modes. This log-sum-exponential input convex neural network (LSE-ICNN) provides a smooth surrogate that retains convexity within basins and allows for gradient-based learning and inference.</div><div>A key feature of the LSE-ICNN is its ability to automatically discover both the number of modes and the scale of transitions through sparse regression, enabling adaptive and parsimonious modeling. We demonstrate the versatility of the LSE-ICNN across diverse domains, including mechanochemical phase transformations, microstructural elastic instabilities, conservative biological gene circuits, and variational inference for multimodal probability distributions. These examples highlight the effectiveness of the LSE-ICNN in capturing complex multimodal landscapes while preserving differentiability, making it broadly applicable in data-driven modeling, optimization, and physical simulation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114688"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145975680","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 : 2026-01-14DOI: 10.1016/j.jcp.2026.114683
James F. Kelly , Felipe A. V. De Bragança Alves , Stephen D. Eckermann , Francis X. Giraldo , P. Alex Reinecke , John T. Emmert
This paper presents and tests a deep-atmosphere, nonhydrostatic dynamical core (DyCore) targeted towards ground-to-thermosphere atmospheric prediction using the spectral element method (SEM) with IMplicit-EXplicit (IMEX) and Horizontally Explicit Vertically Implicit (HEVI) time-integration. Two versions of the DyCore are discussed, each based on a different formulation of the specific internal energy and continuity equations, which, unlike the dynamical cores developed for low-altitude atmospheric applications, are valid for variable composition atmospheres. The first version, which uses a product-rule (PR) form of the continuity and specific internal energy equations, contains an additional pressure dilation term and does not conserve mass. The second version, which does not use the product-rule (no-PR) in the continuity and specific internal energy, contains two terms to represent pressure dilation in the energy equation and conserves mass to machine precision regardless of time truncation error. The pressure gradient and gravitational forces in the momentum balance equation are reformulated to reduce numerical errors at high altitudes. These new equation sets were implemented in two SEM-based atmospheric models: the Nonhydrostatic Unified Model of the Atmosphere (NUMA) and the Navy Environmental Prediction sysTem Utilizing a Nonhydrostatic Engine (NEPTUNE). Numerical results using both a deep-atmosphere and shallow-atmosphere baroclinic instability, a balanced zonal flow, and a high-altitude orographic gravity wave verify the fidelity of the dynamics at low and high altitudes and for constant and variable composition atmospheres. These results are compared to those from existing deep-atmosphere dynamical cores and a Fourier-ray code, indicating that the proposed discretized equation sets are viable DyCore candidates for next-generation ground-to-thermosphere atmospheric models.
{"title":"A nonhydrostatic mass-conserving dynamical core for deep atmospheres of variable composition","authors":"James F. Kelly , Felipe A. V. De Bragança Alves , Stephen D. Eckermann , Francis X. Giraldo , P. Alex Reinecke , John T. Emmert","doi":"10.1016/j.jcp.2026.114683","DOIUrl":"10.1016/j.jcp.2026.114683","url":null,"abstract":"<div><div>This paper presents and tests a deep-atmosphere, nonhydrostatic dynamical core (DyCore) targeted towards ground-to-thermosphere atmospheric prediction using the spectral element method (SEM) with IMplicit-EXplicit (IMEX) and Horizontally Explicit Vertically Implicit (HEVI) time-integration. Two versions of the DyCore are discussed, each based on a different formulation of the specific internal energy and continuity equations, which, unlike the dynamical cores developed for low-altitude atmospheric applications, are valid for variable composition atmospheres. The first version, which uses a product-rule (PR) form of the continuity and specific internal energy equations, contains an additional pressure dilation term and does not conserve mass. The second version, which does not use the product-rule (no-PR) in the continuity and specific internal energy, contains two terms to represent pressure dilation in the energy equation and conserves mass to machine precision regardless of time truncation error. The pressure gradient and gravitational forces in the momentum balance equation are reformulated to reduce numerical errors at high altitudes. These new equation sets were implemented in two SEM-based atmospheric models: the Nonhydrostatic Unified Model of the Atmosphere (NUMA) and the Navy Environmental Prediction sysTem Utilizing a Nonhydrostatic Engine (NEPTUNE). Numerical results using both a deep-atmosphere and shallow-atmosphere baroclinic instability, a balanced zonal flow, and a high-altitude orographic gravity wave verify the fidelity of the dynamics at low and high altitudes and for constant and variable composition atmospheres. These results are compared to those from existing deep-atmosphere dynamical cores and a Fourier-ray code, indicating that the proposed discretized equation sets are viable DyCore candidates for next-generation ground-to-thermosphere atmospheric models.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"552 ","pages":"Article 114683"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025858","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 : 2026-01-14DOI: 10.1016/j.jcp.2026.114687
Madeline M. Peck, Jiajia Waters
Two troubled-cell indicators based on polynomial range estimation methods are used to flag cells that may violate positivity constraints. One method uses interval extension, and the second uses the range enclosure property of the Bernstein polynomial basis. Both methods reduce compute time for the positivity preserver by limiting its application to a subset of cells. The Bernstein polynomial method remains effective as the problem dimensionality increases. Interval extension applied to the internal energy equation permits the use of the troubled-cell indicators for rational functions, though performance suffers compared to directly applying the indicators to polynomial functions.
{"title":"Polynomial range estimation as a troubled-cell indicator for high-order methods","authors":"Madeline M. Peck, Jiajia Waters","doi":"10.1016/j.jcp.2026.114687","DOIUrl":"10.1016/j.jcp.2026.114687","url":null,"abstract":"<div><div>Two troubled-cell indicators based on polynomial range estimation methods are used to flag cells that may violate positivity constraints. One method uses interval extension, and the second uses the range enclosure property of the Bernstein polynomial basis. Both methods reduce compute time for the positivity preserver by limiting its application to a subset of cells. The Bernstein polynomial method remains effective as the problem dimensionality increases. Interval extension applied to the internal energy equation permits the use of the troubled-cell indicators for rational functions, though performance suffers compared to directly applying the indicators to polynomial functions.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114687"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035679","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 : 2026-01-14DOI: 10.1016/j.jcp.2026.114682
Stefan Henneking , Sreeram Venkat , Omar Ghattas
We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.
{"title":"Goal-oriented real-time Bayesian inference for linear autonomous dynamical systems with application to digital twins for tsunami early warning","authors":"Stefan Henneking , Sreeram Venkat , Omar Ghattas","doi":"10.1016/j.jcp.2026.114682","DOIUrl":"10.1016/j.jcp.2026.114682","url":null,"abstract":"<div><div>We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with <span><math><mrow><mi>O</mi><mo>(</mo><msup><mn>10</mn><mn>9</mn></msup><mo>)</mo></mrow></math></span> parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with <span><math><mrow><mi>O</mi><mo>(</mo><msup><mn>10</mn><mn>8</mn></msup><mo>)</mo></mrow></math></span> inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"552 ","pages":"Article 114682"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025848","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 : 2026-01-14DOI: 10.1016/j.jcp.2026.114685
Feng Chen, Yiran Meng, Kegan Li, Chaoran Yang, Jincheng Dai
Physics-Informed Neural Networks (PINNs) and their variants have gained widespread attention as scientific machine learning (SciML) methods for solving Partial Differential Equations (PDEs), but their computational efficiency and accuracy in low-dimensional problems are still lower than that of classical numerical methods, such as Finite Element Method (FEM). This limitation mainly stems from the generalization error of PINNs, whose point-wise loss functional ignores the interactions between neighboring collocation points. To address this challenge, we propose a new Physics-Graph-Informed Neural Networks (abbreviated as PGINNs) framework that combines deep learning with a conservation-consistent nodal network. Compared to traditional PINNs, PGINNs encode two fundamental forms of graph-topological physical information: (1) global node topology operator represented by the sparse incidence matrix, and (2) local edge feature matrix learned through deep neural networks (DNNs). By reconstructing the loss function as a system of algebraic equations learned by the nodal network representation, PGINNs effectively reduce the generalization error while retaining the mesh-free advantage of PINNs. Theoretical analysis shows that the generalization error convergence rate of PGINNs is improved by an order of magnitude compared with that of PINNs. Numerical experiments for complex boundaries and piecewise homogeneous media validate the high accuracy and computational efficiency of the method. This work combines the advantages of both classical numerical analysis and data-driven PDE solvers, establishing a new direction for high-fidelity SciML.
{"title":"Physics-graph-informed neural networks (PGINNs): From local point-wise constraint to global nodal association","authors":"Feng Chen, Yiran Meng, Kegan Li, Chaoran Yang, Jincheng Dai","doi":"10.1016/j.jcp.2026.114685","DOIUrl":"10.1016/j.jcp.2026.114685","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINNs) and their variants have gained widespread attention as scientific machine learning (SciML) methods for solving Partial Differential Equations (PDEs), but their computational efficiency and accuracy in low-dimensional problems are still lower than that of classical numerical methods, such as Finite Element Method (FEM). This limitation mainly stems from the generalization error of PINNs, whose point-wise loss functional ignores the interactions between neighboring collocation points. To address this challenge, we propose a new Physics-Graph-Informed Neural Networks (abbreviated as PGINNs) framework that combines deep learning with a conservation-consistent nodal network. Compared to traditional PINNs, PGINNs encode two fundamental forms of graph-topological physical information: (1) global node topology operator represented by the sparse incidence matrix, and (2) local edge feature matrix learned through deep neural networks (DNNs). By reconstructing the loss function as a system of algebraic equations learned by the nodal network representation, PGINNs effectively reduce the generalization error while retaining the mesh-free advantage of PINNs. Theoretical analysis shows that the generalization error convergence rate of PGINNs is improved by an order of magnitude compared with that of PINNs. Numerical experiments for complex boundaries and piecewise homogeneous media validate the high accuracy and computational efficiency of the method. This work combines the advantages of both classical numerical analysis and data-driven PDE solvers, establishing a new direction for high-fidelity SciML.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114685"},"PeriodicalIF":3.8,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035781","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 : 2026-01-13DOI: 10.1016/j.jcp.2026.114670
Kun Huang , Irene M. Gamba , Chi-Wang Shu
Particle-wave interaction is of fundamental interest in plasma physics, especially in the study of runaway electrons in magnetic confinement fusion. Analogous to the concept of photons and phonons, wave packets in plasma can also be treated as quasi-particles, called plasmons. To model the “mixture” of electrons and plasmons in plasma, a set of “collisional” kinetic equations has been derived, based on weak turbulence limit and the Wentzel-Kramers-Brillouin (WKB) approximation.
There are two main challenges in solving the electron-plasmon kinetic system numerically. Firstly, non-uniform plasma density and magnetic field results in high dimensionality and the presence of multiple time scales. Secondly, a physically reliable numerical solution requires a structure-preserving scheme that enforces the conservation of mass, momentum, and energy.
In this paper, we propose a structure-preserving multiscale solver for particle-wave interaction in non-uniform magnetized plasmas. The solver combines a conservative local discontinuous Galerkin (LDG) scheme for the interaction part with a trajectory averaging method for the plasmon Hamiltonian flow part. Numerical examples for a non-uniform magnetized plasma in an infinitely long symmetric cylinder are presented. It is verified that the LDG scheme rigorously preserves all the conservation laws, and the trajectory averaging method significantly reduces the computational cost.
{"title":"A structure-preserving multiscale solver for particle-wave interaction in non-uniform magnetized plasmas","authors":"Kun Huang , Irene M. Gamba , Chi-Wang Shu","doi":"10.1016/j.jcp.2026.114670","DOIUrl":"10.1016/j.jcp.2026.114670","url":null,"abstract":"<div><div>Particle-wave interaction is of fundamental interest in plasma physics, especially in the study of runaway electrons in magnetic confinement fusion. Analogous to the concept of photons and phonons, wave packets in plasma can also be treated as quasi-particles, called plasmons. To model the “mixture” of electrons and plasmons in plasma, a set of “collisional” kinetic equations has been derived, based on weak turbulence limit and the Wentzel-Kramers-Brillouin (WKB) approximation.</div><div>There are two main challenges in solving the electron-plasmon kinetic system numerically. Firstly, non-uniform plasma density and magnetic field results in high dimensionality and the presence of multiple time scales. Secondly, a physically reliable numerical solution requires a structure-preserving scheme that enforces the conservation of mass, momentum, and energy.</div><div>In this paper, we propose a structure-preserving multiscale solver for particle-wave interaction in non-uniform magnetized plasmas. The solver combines a conservative local discontinuous Galerkin (LDG) scheme for the interaction part with a trajectory averaging method for the plasmon Hamiltonian flow part. Numerical examples for a non-uniform magnetized plasma in an infinitely long symmetric cylinder are presented. It is verified that the LDG scheme rigorously preserves all the conservation laws, and the trajectory averaging method significantly reduces the computational cost.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"551 ","pages":"Article 114670"},"PeriodicalIF":3.8,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976094","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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