Pub Date : 2026-06-01Epub Date: 2026-02-03DOI: 10.1016/j.jcp.2026.114742
Tianyi Hu , Thomas J.R. Hughes , Guglielmo Scovazzi , Hector Gomez
Discontinuity capturing (DC) operators are commonly employed to numerically solve problems involving sharp gradients in the solution. Despite their success, the application of DC operators to the direct van der Waals simulation (DVS) remains challenging. The DVS framework models non-equilibrium phase transitions by admitting interfacial regions in which the derivative of pressure with respect to density is negative. In these regions, we demonstrate that classical DC operators may violate the free energy dissipation law and produce unphysical wave structures. To address this limitation, we propose the phase-field/discontinuity capturing (PF/DC) operator. Numerical results show that PF/DC yields stable and accurate solutions in both bulk fluids and interfacial regions. Finally, we apply the proposed method to simulate cavitating flow over a three-dimensional bluff body, obtaining excellent agreement with experimental data and significant improvements over results produced using classical DC operators.
{"title":"Phase-field/discontinuity capturing operator for direct van der waals simulation (DVS)","authors":"Tianyi Hu , Thomas J.R. Hughes , Guglielmo Scovazzi , Hector Gomez","doi":"10.1016/j.jcp.2026.114742","DOIUrl":"10.1016/j.jcp.2026.114742","url":null,"abstract":"<div><div>Discontinuity capturing (DC) operators are commonly employed to numerically solve problems involving sharp gradients in the solution. Despite their success, the application of DC operators to the direct van der Waals simulation (DVS) remains challenging. The DVS framework models non-equilibrium phase transitions by admitting interfacial regions in which the derivative of pressure with respect to density is negative. In these regions, we demonstrate that classical DC operators may violate the free energy dissipation law and produce unphysical wave structures. To address this limitation, we propose the phase-field/discontinuity capturing (PF/DC) operator. Numerical results show that PF/DC yields stable and accurate solutions in both bulk fluids and interfacial regions. Finally, we apply the proposed method to simulate cavitating flow over a three-dimensional bluff body, obtaining excellent agreement with experimental data and significant improvements over results produced using classical DC operators.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"554 ","pages":"Article 114742"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146147532","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 : 2026-06-01Epub Date: 2026-02-03DOI: 10.1016/j.jcp.2026.114751
Difeng Cai , Paulina Sepúlveda
The appearance of singularities in the function of interest constitutes a fundamental challenge in scientific computing. It can significantly undermine the effectiveness of numerical schemes for function approximation, numerical integration, and the solution of partial differential equations (PDEs), etc. The problem becomes more sophisticated if the location of the singularity is unknown, which is often encountered in solving PDEs. Detecting the singularity is therefore critical for developing efficient adaptive methods to reduce computational costs in various applications. In this paper, we consider singularity detection in a purely data-driven setting. Namely, the input only contains given data, such as the vertex set from a mesh. To handle the raw unlabeled data, we propose a self-supervised learning (SSL) framework for learning the equation that describes the unknown singularity. We show that filtering is critical for obtaining desired detection and propose two filtering options - one based on kernel density estimation, another based on k nearest neighbors - as the pretext task in SSL. We provide numerical examples to illustrate the potential pathological or inaccurate results due to the use of raw data without filtering. The framework can be easily integrated with point cloud reconstruction methods to improve the reconstruction quality and speed for noisy data. Extensive experiments are presented to demonstrate the ability of the proposed approach to deal with input noise, label corruption, and different kinds of singularities such interior and boundary layers, concentric semicircles, multiple disconnected components. Applications to three dimensional noisy point cloud reconstruction are presented with comparison to radial basis function and Poisson surface reconstructions to demonstrate the approximation quality, flexibility, and computational efficiency of the proposed framework. Both visual and quantitative results are reported.
{"title":"Data-driven self-supervised learning for the discovery of solution singularity for partial differential equations","authors":"Difeng Cai , Paulina Sepúlveda","doi":"10.1016/j.jcp.2026.114751","DOIUrl":"10.1016/j.jcp.2026.114751","url":null,"abstract":"<div><div>The appearance of singularities in the function of interest constitutes a fundamental challenge in scientific computing. It can significantly undermine the effectiveness of numerical schemes for function approximation, numerical integration, and the solution of partial differential equations (PDEs), etc. The problem becomes more sophisticated if the location of the singularity is unknown, which is often encountered in solving PDEs. Detecting the singularity is therefore critical for developing efficient adaptive methods to reduce computational costs in various applications. In this paper, we consider singularity detection in a purely data-driven setting. Namely, the input only contains given data, such as the vertex set from a mesh. To handle the raw unlabeled data, we propose a self-supervised learning (SSL) framework for learning the equation that describes the unknown singularity. We show that filtering is critical for obtaining desired detection and propose two filtering options - one based on kernel density estimation, another based on <em>k</em> nearest neighbors - as the pretext task in SSL. We provide numerical examples to illustrate the potential pathological or inaccurate results due to the use of raw data without filtering. The framework can be easily integrated with point cloud reconstruction methods to improve the reconstruction quality and speed for noisy data. Extensive experiments are presented to demonstrate the ability of the proposed approach to deal with input noise, label corruption, and different kinds of singularities such interior and boundary layers, concentric semicircles, multiple disconnected components. Applications to three dimensional noisy point cloud reconstruction are presented with comparison to radial basis function and Poisson surface reconstructions to demonstrate the approximation quality, flexibility, and computational efficiency of the proposed framework. Both visual and quantitative results are reported.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"554 ","pages":"Article 114751"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146147534","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 : 2026-06-01Epub Date: 2026-02-05DOI: 10.1016/j.jcp.2026.114745
Hamidreza Eivazi , Jendrik-Alexander Tröger , Stefan Wittek , Stefan Hartmann , Andreas Rausch
Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, such as uncertainty quantification, remeshing applications, and topology optimization. This limitation has motivated the development of data-driven surrogate models, where microscale computations are substituted by black-box mappings between macroscale quantities. While these approaches offer significant speedups, they typically struggle to incorporate microscale physical constraints, such as the balance of linear momentum. In this contribution, we propose the Equilibrium Neural Operator (EquiNO), a physics-informed PDE surrogate in which equilibrium is hard-enforced by construction. EquiNO achieves this by projecting the solution onto a set of divergence-free basis functions obtained via proper orthogonal decomposition (POD), thereby ensuring satisfaction of equilibrium without relying on penalty terms or multi-objective loss functions. We compare EquiNO with variational physics-informed neural and operator networks that enforce physical constraints only weakly through the loss function, as well as with purely data-driven operator-learning baselines. Our framework, applicable to multiscale FE2 computations, introduces a finite element–operator learning (FE-OL) approach that integrates the finite element (FE) method with operator learning (OL). We apply the proposed methodology to quasi-static problems in solid mechanics and demonstrate that FE-OL yields accurate solutions even when trained on restricted datasets. The results show that EquiNO achieves speedup factors exceeding 8000-fold compared to traditional methods and offers a robust and physically consistent alternative to existing data-driven surrogate models.
{"title":"EquiNO: A physics-informed neural operator for multiscale simulations","authors":"Hamidreza Eivazi , Jendrik-Alexander Tröger , Stefan Wittek , Stefan Hartmann , Andreas Rausch","doi":"10.1016/j.jcp.2026.114745","DOIUrl":"10.1016/j.jcp.2026.114745","url":null,"abstract":"<div><div>Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, such as uncertainty quantification, remeshing applications, and topology optimization. This limitation has motivated the development of data-driven surrogate models, where microscale computations are substituted by black-box mappings between macroscale quantities. While these approaches offer significant speedups, they typically struggle to incorporate microscale physical constraints, such as the balance of linear momentum. In this contribution, we propose the Equilibrium Neural Operator (EquiNO), a physics-informed PDE surrogate in which equilibrium is hard-enforced by construction. EquiNO achieves this by projecting the solution onto a set of divergence-free basis functions obtained via proper orthogonal decomposition (POD), thereby ensuring satisfaction of equilibrium without relying on penalty terms or multi-objective loss functions. We compare EquiNO with variational physics-informed neural and operator networks that enforce physical constraints only weakly through the loss function, as well as with purely data-driven operator-learning baselines. Our framework, applicable to multiscale FE<sup>2</sup> computations, introduces a finite element–operator learning (FE-OL) approach that integrates the finite element (FE) method with operator learning (OL). We apply the proposed methodology to quasi-static problems in solid mechanics and demonstrate that FE-OL yields accurate solutions even when trained on restricted datasets. The results show that EquiNO achieves speedup factors exceeding 8000-fold compared to traditional methods and offers a robust and physically consistent alternative to existing data-driven surrogate models.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"554 ","pages":"Article 114745"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146147537","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 : 2026-06-01Epub Date: 2026-02-07DOI: 10.1016/j.jcp.2026.114760
Pu Gan , Jinxi Li , Fangxin Fang , Xiaofei Wu , Jiang Zhu , Zifa Wang , Mingming Zhu , Xun Zou
Adaptive mesh refinement (AMR) plays an important role in achieving seamless multi-scale simulations within numerical weather prediction (NWP) models. However, the practical implementation of three-dimensional AMR techniques faces significant challenges due to the mesh’s dynamic nature, which requires frequent mesh reconstruction and dynamic topology adjustments-features that are absent in traditional NWP models. Thus, AMR introduces entirely new implementation difficulties in NWP models. In this study, a hybrid deep learning model HyMeshAI is developed, which integrates CNN-based mesh density prediction with ANN-driven nodal positioning through a mesh generation algorithm, achieving an implementation of end-to-end dynamic mesh generation in an AMR atmospheric model. HyMeshAI preserves traditional acceleration benefits that reduce the computational load from higher spatial dimensionality and extended mesh refinement iterations, while also addressing the critical challenges of dynamic AMR. A key limitation of most data-driven artificial intelligence models is their reliance on feature matrices with fixed dimensionality and feature order, which is inherently incompatible with dynamic AMR. HyMeshAI overcomes this constraint by distilling two essential static features of AMR: the mesh point cardinality and the spatial probability distribution of mesh generation. The HyMeshAI’s performance has been estimated in idealized advection and rising bubble scenarios. In the advection test, HyMeshAI achieved a 20%-40% reduction in mesh count and a significant improvement in mesh quality, while maintaining comparable accuracy. In the rising bubble test, HyMeshAI reproduced the key features of buoyancy-driven convection and successfully resolved fine-scale structures, including Kelvin-Helmholtz vortices with a 30%-40% improvement in mesh quality.
{"title":"HyMeshAI: Deep learning enabled three-dimensional adaptive mesh generator for high-resolution atmospheric simulations","authors":"Pu Gan , Jinxi Li , Fangxin Fang , Xiaofei Wu , Jiang Zhu , Zifa Wang , Mingming Zhu , Xun Zou","doi":"10.1016/j.jcp.2026.114760","DOIUrl":"10.1016/j.jcp.2026.114760","url":null,"abstract":"<div><div>Adaptive mesh refinement (AMR) plays an important role in achieving seamless multi-scale simulations within numerical weather prediction (NWP) models. However, the practical implementation of three-dimensional AMR techniques faces significant challenges due to the mesh’s dynamic nature, which requires frequent mesh reconstruction and dynamic topology adjustments-features that are absent in traditional NWP models. Thus, AMR introduces entirely new implementation difficulties in NWP models. In this study, a hybrid deep learning model HyMeshAI is developed, which integrates CNN-based mesh density prediction with ANN-driven nodal positioning through a mesh generation algorithm, achieving an implementation of end-to-end dynamic mesh generation in an AMR atmospheric model. HyMeshAI preserves traditional acceleration benefits that reduce the computational load from higher spatial dimensionality and extended mesh refinement iterations, while also addressing the critical challenges of dynamic AMR. A key limitation of most data-driven artificial intelligence models is their reliance on feature matrices with fixed dimensionality and feature order, which is inherently incompatible with dynamic AMR. HyMeshAI overcomes this constraint by distilling two essential static features of AMR: the mesh point cardinality and the spatial probability distribution of mesh generation. The HyMeshAI’s performance has been estimated in idealized advection and rising bubble scenarios. In the advection test, HyMeshAI achieved a 20%-40% reduction in mesh count and a significant improvement in mesh quality, while maintaining comparable accuracy. In the rising bubble test, HyMeshAI reproduced the key features of buoyancy-driven convection and successfully resolved fine-scale structures, including Kelvin-Helmholtz vortices with a 30%-40% improvement in mesh quality.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"554 ","pages":"Article 114760"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146187232","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}
This paper proposes high-order accurate bound-preserving (BP) finite volume methods on adaptive moving structured meshes for two- and three-dimensional special relativistic hydrodynamics (RHD). The BP property here includes the positivity of rest-mass density and pressure, the subluminal constraint on fluid velocity, as well as the minimum entropy principle established in [1]. The methods are built on the time-dependent coordinate transformation from the computational domain to the physical domain, appropriate discretization of the geometric conservation laws (GCLs), a global Lax-Friedrichs (LF) type numerical flux incorporating the mesh metrics, and the explicit strong-stability-preserving Runge-Kutta time discretizations. Preserving the minimum entropy principle is nontrivial, as the commonly used LF splitting property no longer holds in general. To address this, a weak LF splitting property, compatible with the minimum entropy principle, is introduced. A rigorous BP analysis is conducted based on the weak LF splitting property, the discrete GCLs, and the geometric quasilinearization (GQL) approach in [2, 3]. Finally, various numerical examples in two and three dimensions are presented to validate the high-order accuracy, high resolution, efficiency, and BP property of the proposed methods.
{"title":"High-order accurate bound-preserving adaptive moving mesh finite volume methods for 2D and 3D special relativistic hydrodynamics","authors":"Caiyou Yuan , Zhihao Zhang , Huazhong Tang , Kailiang Wu","doi":"10.1016/j.jcp.2026.114728","DOIUrl":"10.1016/j.jcp.2026.114728","url":null,"abstract":"<div><div>This paper proposes high-order accurate bound-preserving (BP) finite volume methods on adaptive moving structured meshes for two- and three-dimensional special relativistic hydrodynamics (RHD). The BP property here includes the positivity of rest-mass density and pressure, the subluminal constraint on fluid velocity, as well as the minimum entropy principle established in [1]. The methods are built on the time-dependent coordinate transformation from the computational domain to the physical domain, appropriate discretization of the geometric conservation laws (GCLs), a global Lax-Friedrichs (LF) type numerical flux incorporating the mesh metrics, and the explicit strong-stability-preserving Runge-Kutta time discretizations. Preserving the minimum entropy principle is nontrivial, as the commonly used LF splitting property no longer holds in general. To address this, a weak LF splitting property, compatible with the minimum entropy principle, is introduced. A rigorous BP analysis is conducted based on the weak LF splitting property, the discrete GCLs, and the geometric quasilinearization (GQL) approach in [2, 3]. Finally, various numerical examples in two and three dimensions are presented to validate the high-order accuracy, high resolution, efficiency, and BP property of the proposed methods.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"554 ","pages":"Article 114728"},"PeriodicalIF":3.8,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146147538","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 : 2026-05-15Epub Date: 2026-02-02DOI: 10.1016/j.jcp.2026.114726
Amgad Abdrabou, Luis J. Gomez
Analyzing electromagnetic fields in complex, multi-material environments presents substantial computational challenges. To address these, we propose a hybrid numerical method that couples discrete exterior calculus (DEC) with surface integral equations (SIE) in the potential-based formulation of Maxwell’s equations. The technique employs the magnetic vector and electric scalar potentials (A–Φ) under the Lorenz gauge, offering natural compatibility with multi-physics couplings and inherent immunity to low-frequency breakdown. To effectively handle both bounded and unbounded regions, we divide the computational domain: the inhomogeneous interior is discretized using DEC, a coordinate-free framework that preserves topological invariants and enables structure-preserving discretization on unstructured meshes, while the homogeneous exterior is treated using SIEs, which inherently satisfy the radiation condition and eliminate the need for artificial domain truncation. A key contribution of this work is a scalar-component reformulation of the SIEs, which reduces the number of surface integral operators from fourteen to two by expressing the problem in terms of the Cartesian components of the vector potential and their normal derivatives. In the interior DEC domain, each component of A is represented accordingly as a discrete 0-form. This is not a departure from the DEC framework, but rather an adaptation that mirrors established scalar-field treatments within DEC, preserves the underlying geometric structure, and aligns naturally with the scalar-component SIE representation at the interface. The result is a unified formulation in which the potentials remain differential-form quantities in the algebraic sense, yet are discretized component-wise for improved compatibility, numerical conditioning, and computational efficiency. The proposed hybrid method thus offers a physically consistent, structure-preserving, and efficient framework for solving electromagnetic scattering and radiation problems in complex geometries and heterogeneous materials, while avoiding the complexity of conventional vector-potential SIE formulations.
{"title":"A hybrid DEC-SIE framework for potential-based electromagnetic analysis of heterogeneous media","authors":"Amgad Abdrabou, Luis J. Gomez","doi":"10.1016/j.jcp.2026.114726","DOIUrl":"10.1016/j.jcp.2026.114726","url":null,"abstract":"<div><div>Analyzing electromagnetic fields in complex, multi-material environments presents substantial computational challenges. To address these, we propose a hybrid numerical method that couples discrete exterior calculus (DEC) with surface integral equations (SIE) in the potential-based formulation of Maxwell’s equations. The technique employs the magnetic vector and electric scalar potentials (<strong>A</strong>–Φ) under the Lorenz gauge, offering natural compatibility with multi-physics couplings and inherent immunity to low-frequency breakdown. To effectively handle both bounded and unbounded regions, we divide the computational domain: the inhomogeneous interior is discretized using DEC, a coordinate-free framework that preserves topological invariants and enables structure-preserving discretization on unstructured meshes, while the homogeneous exterior is treated using SIEs, which inherently satisfy the radiation condition and eliminate the need for artificial domain truncation. A key contribution of this work is a scalar-component reformulation of the SIEs, which reduces the number of surface integral operators from fourteen to two by expressing the problem in terms of the Cartesian components of the vector potential and their normal derivatives. In the interior DEC domain, each component of <strong>A</strong> is represented accordingly as a discrete 0-form. This is not a departure from the DEC framework, but rather an adaptation that mirrors established scalar-field treatments within DEC, preserves the underlying geometric structure, and aligns naturally with the scalar-component SIE representation at the interface. The result is a unified formulation in which the potentials remain differential-form quantities in the algebraic sense, yet are discretized component-wise for improved compatibility, numerical conditioning, and computational efficiency. The proposed hybrid method thus offers a physically consistent, structure-preserving, and efficient framework for solving electromagnetic scattering and radiation problems in complex geometries and heterogeneous materials, while avoiding the complexity of conventional vector-potential SIE formulations.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114726"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186551","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 : 2026-05-15Epub Date: 2026-01-31DOI: 10.1016/j.jcp.2026.114722
Zequn He, Celia Reina
We present Epistemic Variational Onsager Diffusion Models (EVODMs), a machine learning framework that integrates Onsager’s variational principle with diffusion models to enable thermodynamically consistent learning of free energy and dissipation potentials (and associated evolution equations) from noisy, stochastic data in a robust manner. By further combining the model with Epinets, EVODMs quantify epistemic uncertainty with minimal computational cost. The framework is validated through two examples: (1) the phase transformation of a coiled-coil protein, modeled via a stochastic partial differential equation, and (2) a lattice particle process (the symmetric simple exclusion process) modeled via Kinetic Monte Carlo simulations. In both examples, we aim to discover the thermodynamic potentials that govern their dynamics in the deterministic continuum limit. EVODMs demonstrate a superior accuracy in recovering free energy and dissipation potentials from noisy data, as compared to traditional machine learning frameworks. Meanwhile, the epistemic uncertainty is quantified efficiently via Epinets and knowledge distillation.
{"title":"EVODMs: Variational learning of PDEs for stochastic systems via diffusion models with quantified epistemic uncertainty","authors":"Zequn He, Celia Reina","doi":"10.1016/j.jcp.2026.114722","DOIUrl":"10.1016/j.jcp.2026.114722","url":null,"abstract":"<div><div>We present Epistemic Variational Onsager Diffusion Models (EVODMs), a machine learning framework that integrates Onsager’s variational principle with diffusion models to enable thermodynamically consistent learning of free energy and dissipation potentials (and associated evolution equations) from noisy, stochastic data in a robust manner. By further combining the model with Epinets, EVODMs quantify epistemic uncertainty with minimal computational cost. The framework is validated through two examples: (1) the phase transformation of a coiled-coil protein, modeled via a stochastic partial differential equation, and (2) a lattice particle process (the symmetric simple exclusion process) modeled via Kinetic Monte Carlo simulations. In both examples, we aim to discover the thermodynamic potentials that govern their dynamics in the deterministic continuum limit. EVODMs demonstrate a superior accuracy in recovering free energy and dissipation potentials from noisy data, as compared to traditional machine learning frameworks. Meanwhile, the epistemic uncertainty is quantified efficiently via Epinets and knowledge distillation.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114722"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186474","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 : 2026-05-15Epub Date: 2026-02-02DOI: 10.1016/j.jcp.2026.114707
Óscar Amaro, Chiara Badiali, Bertrand Martinez
This study uses neural networks to improve Monte Carlo (MC) implementations of the Bethe-Heitler process in Particle-In-Cell (PIC) codes. We provide a neural network that is as accurate as pre-calculated tables, and requires a hundred times less memory to store. It is trained to predict Bethe-Heitler pair production cross-sections for atomic numbers 1–50 and photon energies between 1 MeV and 10 GeV in the PIC code OSIRIS. We first validate our approach against a theoretical estimate in a simplified context. We later prove that both approaches have similar performance in a typical relativistic laser-plasma interaction scenario. The large memory decrease accessible with neural networks will enable introducing more advanced cross-section models for Bethe-Heitler pair production and other QED mechanisms in the MC modules of PIC codes.
{"title":"Neural network sampling of Bethe-Heitler process in particle-in-cell codes","authors":"Óscar Amaro, Chiara Badiali, Bertrand Martinez","doi":"10.1016/j.jcp.2026.114707","DOIUrl":"10.1016/j.jcp.2026.114707","url":null,"abstract":"<div><div>This study uses neural networks to improve Monte Carlo (MC) implementations of the Bethe-Heitler process in Particle-In-Cell (PIC) codes. We provide a neural network that is as accurate as pre-calculated tables, and requires a hundred times less memory to store. It is trained to predict Bethe-Heitler pair production cross-sections for atomic numbers 1–50 and photon energies between 1 MeV and 10 GeV in the PIC code <span>OSIRIS</span>. We first validate our approach against a theoretical estimate in a simplified context. We later prove that both approaches have similar performance in a typical relativistic laser-plasma interaction scenario. The large memory decrease accessible with neural networks will enable introducing more advanced cross-section models for Bethe-Heitler pair production and other QED mechanisms in the MC modules of PIC codes.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114707"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186471","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 : 2026-05-15Epub Date: 2026-01-28DOI: 10.1016/j.jcp.2026.114713
Chenhao Si , Ming Yan , Xin Li , Zhihong Xia
We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by Cauchy’s integral theorem. By optimizing the activation parameters, compleX-PINN achieves high accuracy with just a single hidden layer. Empirically, we demonstrate that compleX-PINN solves high-dimensional problems that pose significant challenges for PINNs. Our results show compleX-PINN consistently achieves substantially greater precision, often improving accuracy by an order of magnitude, on these complex tasks.
{"title":"Complex physics-informed neural network","authors":"Chenhao Si , Ming Yan , Xin Li , Zhihong Xia","doi":"10.1016/j.jcp.2026.114713","DOIUrl":"10.1016/j.jcp.2026.114713","url":null,"abstract":"<div><div>We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by Cauchy’s integral theorem. By optimizing the activation parameters, compleX-PINN achieves high accuracy with just a single hidden layer. Empirically, we demonstrate that compleX-PINN solves high-dimensional problems that pose significant challenges for PINNs. Our results show compleX-PINN consistently achieves substantially greater precision, often improving accuracy by an order of magnitude, on these complex tasks.</div></div>","PeriodicalId":352,"journal":{"name":"Journal of Computational Physics","volume":"553 ","pages":"Article 114713"},"PeriodicalIF":3.8,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146098786","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 : 2026-05-15Epub Date: 2026-02-03DOI: 10.1016/j.jcp.2026.114714
Joaquín López
Recent improvements in geometric volume-of-fluid methods, in which the fluid interface is implicitly represented using the volume-of-fluid fraction function, make them an excellent approach for solving complex interfacial dynamics problems. However, mainly due to the complexity involved in implementing them, these methods are typically limited to the use of linear approximations for interface reconstruction and volume-of-fluid fraction advection, especially in three dimensions. This typically produces second-order interface representations, thus making it difficult to achieve interface curvature convergence with grid refinement. This geometric complexity means that the literature contains no evidence of geometric volume-of-fluid methods capable of producing high-order accuracies for interface representation in time-dependent problems with deformed interfaces on arbitrary three-dimensional grids. The current work addresses this gap by presenting a new geometric volume-of-fluid method that uses an iterative least-squares paraboloid fitting to initial piecewise-linear approximations for interface reconstruction and an unsplit flux-based scheme for the advection of the volume-of-fluid fraction on unstructured three-dimensional grids with arbitrary cells, either convex or non-convex. To accurately determine the volume-of-fluid fraction advected out of grid cells, a new method based on local grid refinement and polyhedral approximation is proposed to efficiently compute the intersection between the piecewise reconstructed paraboloidal fluid regions and an arbitrary polyhedron. A detailed assessment of the proposed method is carried out for several commonly used canonical tests and more realistic scenarios, such as the rise of a bubble under gravity in a quiescent liquid, for which the effects of surface tension must be accurately computed. Comparisons with the few results available in the literature show generally favorable results.
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