arXiv: Computational Physics最新文献_第2页

Eikonal Solution Using Physics-Informed Neural Networks 使用物理信息神经网络的Eikonal解决方案

arXiv: Computational Physics Pub Date : 2020-07-16 DOI: 10.3997/2214-4609.202011041

U. Waheed, E. Haghighat, T. Alkhalifah, Chao Song, Q. Hao

{"title":"Eikonal Solution Using Physics-Informed Neural Networks","authors":"U. Waheed, E. Haghighat, T. Alkhalifah, Chao Song, Q. Hao","doi":"10.3997/2214-4609.202011041","DOIUrl":"https://doi.org/10.3997/2214-4609.202011041","url":null,"abstract":"The eikonal equation is utilized across a wide spectrum of science and engineering disciplines. In seismology, it regulates seismic wave traveltimes needed for applications like source localization, imaging, and inversion. Several numerical algorithms have been developed over the years to solve the eikonal equation. However, they suffer from computational bottleneck when repeated computations are needed for perturbations in the velocity model and/or the source location, particularly in large 3D models. Here, we employ the emerging paradigm of physics-informed neural networks (PINNs) to solve the eikonal equation. By minimizing a loss function formed by imposing the validity of the eikonal equation, we train a neural network to produce traveltimes that are consistent with the underlying partial differential equation. More specifically, to tackle point-source singularity, we use the factored eikonal equation. We observe sufficiently high traveltime accuracy for most applications of interest. We also demonstrate how machine learning techniques like transfer learning and surrogate modeling can be used to massively speed up traveltime computations for updated velocity models and source locations. These properties of the PINN eikonal solver are highly desirable in obtaining an efficient forward modeling engine for seismic inversion applications.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88701816","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: 32

Unified Approach to Enhanced Sampling 增强抽样的统一方法

arXiv: Computational Physics Pub Date : 2020-07-06 DOI: 10.1103/physrevx.10.041034

Michele Invernizzi, P. Piaggi, M. Parrinello

{"title":"Unified Approach to Enhanced Sampling","authors":"Michele Invernizzi, P. Piaggi, M. Parrinello","doi":"10.1103/physrevx.10.041034","DOIUrl":"https://doi.org/10.1103/physrevx.10.041034","url":null,"abstract":"The sampling problem lies at the heart of atomistic simulations and over the years many different enhanced sampling methods have been suggested towards its solution. These methods are often grouped into two broad families. On the one hand methods such as umbrella sampling and metadynamics that build a bias potential based on few order parameters or collective variables. On the other hand, tempering methods such as replica exchange that combine different thermodynamic ensembles in one single expanded ensemble. We instead adopt a unifying perspective, focusing on the target probability distribution sampled by the different methods. This allows us to introduce a new class of collective-variables-based bias potentials that can be used to sample any of the expanded ensembles normally sampled via replica exchange. We also provide a practical implementation, by properly adapting the iterative scheme of the recently developed on-the-fly probability enhanced sampling method [Invernizzi and Parrinello, J. Phys. Chem. Lett. 11.7 (2020)], which was originally introduced for metadynamics-like sampling. The resulting method is very general and can be used to achieve different types of enhanced sampling. It is also reliable and simple to use, since it presents only few and robust external parameters and has a straightforward reweighting scheme. Furthermore, it can be used with any number of parallel replicas. We show the versatility of our approach with applications to multicanonical and multithermal-multibaric simulations, thermodynamic integration, umbrella sampling, and combinations thereof.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86612143","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: 41

Solution of the Monoenergetic Neutron Transport Equation in a Half Space via Singular Eigenfunction Expansion 半空间单能中子输运方程的奇异本征函数展开解

arXiv: Computational Physics Pub Date : 2020-07-05 DOI: 10.13182/T123-33541

B. Ganapol

{"title":"Solution of the Monoenergetic Neutron Transport Equation in a Half Space via Singular Eigenfunction Expansion","authors":"B. Ganapol","doi":"10.13182/T123-33541","DOIUrl":"https://doi.org/10.13182/T123-33541","url":null,"abstract":"The analytical solution of neutron transport equation has fascinated mathematicians and physicists alike since the Milne half-space problem was introduce in 1921 [1]. Numerous numerical solutions exist, but understandably, there are only a few analytical solutions, with the prominent one being the singular eigenfunction expansion (SEE) introduced by Case [2] in 1960. For the half-space, the method, though yielding, an elegant analytical form resulting from half-range completeness, requires numerical evaluation of complicated integrals. In addition, one finds closed form analytical expressions only for the infinite medium and half-space cases. One can find the flux in a slab only iteratively. That is to say, in general one must expend a considerable numerical effort to get highly precise benchmarks from SEE. As a result, investigators have devised alternative methods, such as the CN [3], FN [4] and Greens Function Method (GFM) [5] based on the SEE have been devised. These methods take the SEE at their core and construct a numerical method around the analytical form. The FN method in particular has been most successful in generating highly precise benchmarks. No method yielding a precise numerical solution has yet been based solely on a fundamental discretization until now. Here, we show for the albedo problem with a source on the vacuum boundary of a homogeneous medium, a precise numerical solution is possible via Lagrange interpolation over a discrete set of directions.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91475386","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 assimilation empowered neural network parametrizations for subgrid processes in geophysical flows 数据同化增强了地球物理流中子网格过程的神经网络参数化

arXiv: Computational Physics Pub Date : 2020-06-16 DOI: 10.1103/PHYSREVFLUIDS.6.050501

Suraj Pawar, O. San

{"title":"Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows","authors":"Suraj Pawar, O. San","doi":"10.1103/PHYSREVFLUIDS.6.050501","DOIUrl":"https://doi.org/10.1103/PHYSREVFLUIDS.6.050501","url":null,"abstract":"In the past couple of years, there is a proliferation in the use of machine learning approaches to represent subgrid scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical simulations of these flows. Despite its success for different types of flow, the online deployment of a data-driven closure model can cause instabilities and biases in modeling the overall effect of subgrid scale processes, which in turn leads to inaccurate prediction. To tackle this issue, we exploit the data assimilation technique to correct the physics-based model coupled with the neural network as a surrogate for unresolved flow dynamics in multiscale systems. In particular, we use a set of neural network architectures to learn the correlation between resolved flow variables and the parameterizations of unresolved flow dynamics and formulate a data assimilation approach to correct the hybrid model during their online deployment. We illustrate our framework in a application of the multiscale Lorenz 96 system for which the parameterization model for unresolved scales is exactly known. Our analysis, therefore, comprises a predictive dynamical core empowered by (i) a data-driven closure model for subgrid scale processes, (ii) a data assimilation approach for forecast error correction, and (iii) both data-driven closure and data assimilation procedures. We show significant improvement in the long-term perdition of the underlying chaotic dynamics with our framework compared to using only neural network parameterizations for future prediction. Moreover, we demonstrate that these data-driven parameterization models can handle the non-Gaussian statistics of subgrid scale processes, and effectively improve the accuracy of outer data assimilation workflow loops in a modular non-intrusive way.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84844259","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: 30

Transport coefficients of multi-component mixtures of noble gases based on ab initio potentials: Viscosity and thermal conductivity 基于从头算势的稀有气体多组分混合物输运系数:粘度和导热性

arXiv: Computational Physics Pub Date : 2020-06-15 DOI: 10.1063/5.0016261

F. Sharipov, V. J. Benites

引用次数: 10

Algorithm for generating irreducible site-occupancy configurations 生成不可约场地占用配置的算法

arXiv: Computational Physics Pub Date : 2020-06-11 DOI: 10.1103/physrevb.102.134209

J. Lian, Hong-Yu Wu, Wei‐Qing Huang, Wangyu Hu, Gui‐Fang Huang

{"title":"Algorithm for generating irreducible site-occupancy configurations","authors":"J. Lian, Hong-Yu Wu, Wei‐Qing Huang, Wangyu Hu, Gui‐Fang Huang","doi":"10.1103/physrevb.102.134209","DOIUrl":"https://doi.org/10.1103/physrevb.102.134209","url":null,"abstract":"Generating irreducible site-occupancy configurations by taking advantage of crystal symmetry is a ubiquitous method for accelerating of disordered structure prediction, which plays an important role in condensed matter physics and material science. Here, we present a new algorithm for generating irreducible site-occupancy configurations, that works for arbitrary parent cell with any supercell expansion matrix, and for any number of atom types with arbitrary stoichiometry. The new algorithm identifies the symmetrically equivalent configurations by searching the space group operations of underlying lattice and building the equivalent atomic matrix based on it. Importantly, an integer representation of configurations can greatly accelerate the speed of elimination of duplicate configurations, resulting into a linear scale of run time with the number of irreducible configurations that finally found. Moreover, based on our new algorithm, we write the corresponding code named as disorder in FORTRAN programming language, and the performance test results show that the time efficiency of our disorder code is superior to that of other related codes (supercell, enumlib and SOD).","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89935600","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: 7

Simple and efficient algorithms for training machine learning potentials to force data. 用于训练机器学习潜力以强制数据的简单有效算法。

arXiv: Computational Physics Pub Date : 2020-06-01 DOI: 10.2172/1763572

Justin S. Smith, N. Lubbers, A. Thompson, K. Barros

引用次数: 6

High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard convection Rayleigh- b<s:1>纳德对流的高瑞利数变分多尺度大涡模拟

arXiv: Computational Physics Pub Date : 2020-05-20 DOI: 10.1016/j.mechrescom.2020.103614

David Sondak, Thomas M. Smith, R. Pawlowski, S. Conde, J. Shadid

引用次数: 2

Spectral neural network potentials for binary alloys 二元合金的光谱神经网络电位

arXiv: Computational Physics Pub Date : 2020-05-09 DOI: 10.1063/5.0013208

David Zagaceta, Howard Yanxon, Q. Zhu