arXiv - MATH - Numerical Analysis最新文献_第3页

Generalizability of Graph Neural Network Force Fields for Predicting Solid-State Properties 用于预测固态特性的图神经网络力场的通用性

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.09931

Shaswat Mohanty, Yifan Wang, Wei Cai

{"title":"Generalizability of Graph Neural Network Force Fields for Predicting Solid-State Properties","authors":"Shaswat Mohanty, Yifan Wang, Wei Cai","doi":"arxiv-2409.09931","DOIUrl":"https://doi.org/arxiv-2409.09931","url":null,"abstract":"Machine-learned force fields (MLFFs) promise to offer a computationally\u0000efficient alternative to ab initio simulations for complex molecular systems.\u0000However, ensuring their generalizability beyond training data is crucial for\u0000their wide application in studying solid materials. This work investigates the\u0000ability of a graph neural network (GNN)-based MLFF, trained on Lennard-Jones\u0000Argon, to describe solid-state phenomena not explicitly included during\u0000training. We assess the MLFF's performance in predicting phonon density of\u0000states (PDOS) for a perfect face-centered cubic (FCC) crystal structure at both\u0000zero and finite temperatures. Additionally, we evaluate vacancy migration rates\u0000and energy barriers in an imperfect crystal using direct molecular dynamics\u0000(MD) simulations and the string method. Notably, vacancy configurations were\u0000absent from the training data. Our results demonstrate the MLFF's capability to\u0000capture essential solid-state properties with good agreement to reference data,\u0000even for unseen configurations. We further discuss data engineering strategies\u0000to enhance the generalizability of MLFFs. The proposed set of benchmark tests\u0000and workflow for evaluating MLFF performance in describing perfect and\u0000imperfect crystals pave the way for reliable application of MLFFs in studying\u0000complex solid-state materials.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Physics-Informed Neural Networks with Trust-Region Sequential Quadratic Programming 采用信任区域顺序二次编程的物理信息神经网络

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.10777

Xiaoran Cheng, Sen Na

{"title":"Physics-Informed Neural Networks with Trust-Region Sequential Quadratic Programming","authors":"Xiaoran Cheng, Sen Na","doi":"arxiv-2409.10777","DOIUrl":"https://doi.org/arxiv-2409.10777","url":null,"abstract":"Physics-Informed Neural Networks (PINNs) represent a significant advancement\u0000in Scientific Machine Learning (SciML), which integrate physical domain\u0000knowledge into an empirical loss function as soft constraints and apply\u0000existing machine learning methods to train the model. However, recent research\u0000has noted that PINNs may fail to learn relatively complex Partial Differential\u0000Equations (PDEs). This paper addresses the failure modes of PINNs by\u0000introducing a novel, hard-constrained deep learning method -- trust-region\u0000Sequential Quadratic Programming (trSQP-PINN). In contrast to directly training\u0000the penalized soft-constrained loss as in PINNs, our method performs a\u0000linear-quadratic approximation of the hard-constrained loss, while leveraging\u0000the soft-constrained loss to adaptively adjust the trust-region radius. We only\u0000trust our model approximations and make updates within the trust region, and\u0000such an updating manner can overcome the ill-conditioning issue of PINNs. We\u0000also address the computational bottleneck of second-order SQP methods by\u0000employing quasi-Newton updates for second-order information, and importantly,\u0000we introduce a simple pretraining step to further enhance training efficiency\u0000of our method. We demonstrate the effectiveness of trSQP-PINN through extensive\u0000experiments. Compared to existing hard-constrained methods for PINNs, such as\u0000penalty methods and augmented Lagrangian methods, trSQP-PINN significantly\u0000improves the accuracy of the learned PDE solutions, achieving up to 1-3 orders\u0000of magnitude lower errors. Additionally, our pretraining step is generally\u0000effective for other hard-constrained methods, and experiments have shown the\u0000robustness of our method against both problem-specific parameters and algorithm\u0000tuning parameters.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"82 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quaternion tensor low rank approximation 四元张量低阶近似值

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.10724

Alaeddine Zahir, Ahmed Ratnani, Khalide Jbilou

引用次数: 0

Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows 带有 LST-DG 预测器和后验子单元 WENO 有限体积限制的时空自适应 ADER-DG 有限元法，用于模拟非稳态可压缩多组分反应流

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.09932

I. S Popov

{"title":"Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell WENO finite-volume limiting for simulation of non-stationary compressible multicomponent reactive flows","authors":"I. S Popov","doi":"arxiv-2409.09932","DOIUrl":"https://doi.org/arxiv-2409.09932","url":null,"abstract":"The space-time adaptive ADER finite element DG method with a posteriori\u0000correction technique of solutions on subcells by the finite-volume ADER-WENO\u0000limiter was used to simulate non-stationary compressible multicomponent\u0000reactive flows. The multicomponent composition of the reacting medium and the\u0000reactions occurring in it were described by expanding the original system of\u0000Euler equations by a system of non-stationary convection-reaction equations.\u0000The use of this method to simulate high stiff problems associated with\u0000reactions occurring in a multicomponent medium requires the use of the adaptive\u0000change in the time step. The solution of the classical problem related to the\u0000formation and propagation of a ZND detonation wave is carried out. It was shown\u0000that the space-time adaptive ADER finite element DG method with a posteriori\u0000correction technique of solutions on subcells by the finite-volume ADER-WENO\u0000limiter can be used to simulate flows without using of splitting in directions\u0000and fractional step methods.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation 带有 LST-DG 预测器和后验子单元 ADER-WENO 有限体积限制的时空自适应 ADER-DG 有限元法用于多维爆轰波模拟

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.09911

I. S. Popov

{"title":"Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation","authors":"I. S. Popov","doi":"arxiv-2409.09911","DOIUrl":"https://doi.org/arxiv-2409.09911","url":null,"abstract":"The space-time adaptive ADER-DG finite element method with LST-DG predictor\u0000and a posteriori sub-cell ADER-WENO finite-volume limiting was used for\u0000simulation of multidimensional reacting flows with detonation waves. The\u0000presented numerical method does not use any ideas of splitting or fractional\u0000time steps methods. The modification of the LST-DG predictor has been\u0000developed, based on a local partition of the time step in cells in which strong\u0000reactivity of the medium is observed. This approach made it possible to obtain\u0000solutions to classical problems of flows with detonation waves and strong\u0000stiffness, without significantly decreasing the time step. The results obtained\u0000show the very high applicability and efficiency of using the ADER-DG-PN method\u0000with a posteriori sub-cell limiting for simulating reactive flows with\u0000detonation waves. The numerical solution shows the correct formation and\u0000propagation of ZND detonation waves. The structure of detonation waves is\u0000resolved by this numerical method with subcell resolution even on coarse\u0000spatial meshes. The smooth components of the numerical solution are correctly\u0000and very accurately reproduced by the numerical method. Non-physical artifacts\u0000of the numerical solution, typical for problems with detonation waves, such as\u0000the propagation of non-physical shock waves and weak detonation fronts ahead of\u0000the main detonation front, did not arise in the results obtained. The results\u0000of simulating rather complex problems associated with the propagation of\u0000detonation waves in significantly inhomogeneous domains are presented, which\u0000show that all the main features of detonation flows are correctly reproduced by\u0000this numerical method. It can be concluded that the space-time adaptive\u0000ADER-DG-PN method with a posteriori sub-cell ADER-WENO finite-volume limiting\u0000is perfectly applicable to simulating complex reacting flows with detonation\u0000waves.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Kernel Descent -- a Novel Optimizer for Variational Quantum Algorithms 核后裔 -- 变量量子算法的新型优化器

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.10257

Lars Simon, Holger Eble, Manuel Radons

引用次数: 0

Space-Time Wave Localisation in Systems of Subwavelength Resonators 亚波长谐振器系统中的时空波定位

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.10100

Habib Ammari, Erik Orvehed Hiltunen, Liora Rueff

引用次数: 0

Arbitrary high order ADER-DG method with local DG predictor for solutions of initial value problems for systems of first-order ordinary differential equations 用局部 DG 预测器解决一阶常微分方程系统初值问题的任意高阶 ADER-DG 方法

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.09933

I. S. Popov

{"title":"Arbitrary high order ADER-DG method with local DG predictor for solutions of initial value problems for systems of first-order ordinary differential equations","authors":"I. S. Popov","doi":"arxiv-2409.09933","DOIUrl":"https://doi.org/arxiv-2409.09933","url":null,"abstract":"An adaptation of the arbitrary high order ADER-DG numerical method with local\u0000DG predictor for solving the IVP for a first-order non-linear ODE system is\u0000proposed. The proposed numerical method is a completely one-step ODE solver\u0000with uniform steps, and is simple in algorithmic and software implementations.\u0000It was shown that the proposed version of the ADER-DG numerical method is\u0000A-stable and L-stable. The ADER-DG numerical method demonstrates\u0000superconvergence with convergence order 2N+1 for the solution at grid nodes,\u0000while the local solution obtained using the local DG predictor has convergence\u0000order N+1. It was demonstrated that an important applied feature of this\u0000implementation of the numerical method is the possibility of using the local\u0000solution as a solution with a subgrid resolution, which makes it possible to\u0000obtain a detailed solution even on very coarse coordinate grids. The scale of\u0000the error of the local solution, when calculating using standard\u0000representations of single or double precision floating point numbers, using\u0000large values of the degree N, practically does not differ from the error of the\u0000solution at the grid nodes. The capabilities of the ADER-DG method for solving\u0000stiff ODE systems characterized by extreme stiffness are demonstrated.\u0000Estimates of the computational costs of the ADER-DG numerical method are\u0000obtained.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds 通过谱子曲面实现非线性有限元模型的无数据非侵入式模型还原

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.10126

Mingwu Li, Thomas Thurnher, Zhenwei Xu, Shobhit Jain

{"title":"Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds","authors":"Mingwu Li, Thomas Thurnher, Zhenwei Xu, Shobhit Jain","doi":"arxiv-2409.10126","DOIUrl":"https://doi.org/arxiv-2409.10126","url":null,"abstract":"The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for\u0000constructing rigorous, low-dimensional reduced-order models (ROMs) of\u0000high-dimensional nonlinear mechanical systems. A direct computation of SSMs\u0000requires explicit knowledge of nonlinear coefficients in the equations of\u0000motion, which limits their applicability to generic finite-element (FE)\u0000solvers. Here, we propose a non-intrusive algorithm for the computation of the\u0000SSMs and the associated ROMs up to arbitrary polynomial orders. This\u0000non-intrusive algorithm only requires system nonlinearity as a black box and\u0000hence, enables SSM-based model reduction via generic finite-element software.\u0000Our expressions and algorithms are valid for systems with up to cubic-order\u0000nonlinearities, including velocity-dependent nonlinear terms, asymmetric\u0000damping, and stiffness matrices, and hence work for a large class of mechanics\u0000problems. We demonstrate the effectiveness of the proposed non-intrusive\u0000approach over a variety of FE examples of increasing complexity, including a\u0000micro-resonator FE model containing more than a million degrees of freedom.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sensitivity analysis with a 3D mixed-dimensional code for DC geoelectrical investigations of landfills: synthetic tests 垃圾填埋场直流地质电学调查三维混合维度代码的灵敏度分析：合成试验

arXiv - MATH - Numerical Analysis Pub Date : 2024-09-16 DOI: arxiv-2409.10326

Lorenzo Panzeri, Alessio Fumagalli, Laura Longoni, Monica Papini, Diego Arosio

{"title":"Sensitivity analysis with a 3D mixed-dimensional code for DC geoelectrical investigations of landfills: synthetic tests","authors":"Lorenzo Panzeri, Alessio Fumagalli, Laura Longoni, Monica Papini, Diego Arosio","doi":"arxiv-2409.10326","DOIUrl":"https://doi.org/arxiv-2409.10326","url":null,"abstract":"Electrical resistivity tomography is a suitable technique for non-invasive\u0000monitoring of municipal solid waste landfills, but accurate sensitivity\u0000analysis is necessary to evaluate the effectiveness and reliability of\u0000geoelectrical investigations and to properly design data acquisition. Commonly,\u0000a thin high-resistivity membrane in placed underneath the waste to prevent\u0000leachate leakage. In the construction of a numerical framework for sensitivity\u0000computation, taking into account the actual dimensions of the electrodes and,\u0000in particular, of the membrane, can lead to extremely high computational costs.\u0000In this work, we present a novel approach for numerically computing sensitivity\u0000effectively by adopting a mixed-dimensional framework, where the membrane is\u0000approximated as a 2D object and the electrodes as 1D objects. The code is first\u0000validated against analytical expressions for simple 4-electrode arrays and a\u0000homogeneous medium. It is then tested in simplified landfill models, where a 2D\u0000box-shaped liner separates the landfill body from the surrounding media, and 48\u0000electrodes are used. The results show that electrodes arranged linearly along\u0000both sides of the perimeter edges of the box-shaped liner are promising for\u0000detecting liner damage, with sensitivity increasing by 2-3 orders of magnitude,\u0000even for damage as small as one-sixth of the electrode spacing in diameter.\u0000Good results are also obtained when simulating an electrical connection between\u0000the landfill and the surrounding media that is not due to liner damage. The\u0000next steps involve evaluating the minimum number of configurations needed to\u0000achieve suitable sensitivity with a manageable field effort and validating the\u0000modeling results with downscaled laboratory tests.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0