检索结果-内蒙古大学图书馆

34th International Conference on High Performance computing (ISC High Performance)

作者： Nichols, Daniel Tomov, Nathalie-Sofia Betancourt, Frank Tomov, Stanimire Wong, Kwai Dongarra, Jack Univ Tennessee Knoxville TN 37996 USA Oak Ridge Natl Lab POB 2009 Oak Ridge TN 37831 USA

ISBN: (纸本)9783030343569;9783030343552

In this paper, we present work towards the development of a new data analytics and machine learning (ML) framework, called MagmaDNN. Our main goal is to provide scalable, high-performance data analytics and ML solutions for scientific applications running on current and upcoming heterogeneous many-core GPU-accelerated architectures. To this end, since many of the functionalities needed are based on standard linear algebra (LA) routines, we designed MagmaDNN to derive its performance power from the MAGMA library. The close integration provides the fundamental (scalable high-performance) LA routines available in MAGMA as a backend to MagmaDNN. We present some design issues for performance and scalability that are specific to ML using Deep Neural Networks (DNN), as well as the MagmaDNN designs towards overcoming them. In particular, MagmaDNN uses well established HPC techniques from the area of dense LA, including task-based parallelization, DAG representations, scheduling, mixed-precision algorithms, asynchronous solvers, and autotuned hyperparameter optimization. We illustrate these techniques and their incorporation and use to outperform other frameworks, currently available.

关键词： Machine learning High-performance DNN data-driven scientific computing

来源：评论

学校读者我要写书评

暂无评论

On Physics-Informed Neural Networks training for coupled hydro-poromechanical problems

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2024年 516卷

作者： Millevoi, Caterina Spiezia, Nicolo Ferronato, Massimiliano Univ Padua Dept Civil Environm & Architectural Engn Padua Italy M3E Srl Padua Italy

The robust and efficient numerical solution of coupled hydro-poromechanical problems is of paramount importance in many application fields, in particular in geomechanics and biomechanics. Even though the solution by means of the Finite Elements Method (FEM) still remains the preferred option, Physics-Informed Neural Networks (PINNs) are rapidly gaining attention as a powerful and promising approach. By involving the residual of the governing PDEs as a constraint in the training, PINNs combine a physics-driven approach together with a data-driven one, leveraging on deep learning techniques. This work focuses on coupled hydro-poromechanical processes, where a PINN-based approach is implemented and investigated in classical benchmarks. An analysis of the influence of the hyper- parameter selection has been performed to study the model sensitivity to PINN architecture and identify the most appropriate one. To take advantage of PINN ability to integrate data and reduce the complexity of the solution of the coupled hydro-poromechanical problem, a "sensor-driven" training is proposed where data are provided at locations inside the domain even to solve a forward problem. The goal is to assess and validate the approach, thus contributing to the foundation of this method in coupled hydro-poromechanics.

关键词： Physics-Informed Neural Networks Coupled hydro-poromechanics data-driven scientific computing Model architecture Sensor-driven training

来源：评论

学校读者我要写书评

暂无评论

DAE-PINN: a physics-informed neural network model for simulating differential algebraic equations with application to power networks

引用

NEURAL computing & APPLICATIONS 2023年第5期35卷 3789-3804页

作者： Moya, Christian Lin, Guang Purdue Univ Dept Math W Lafayette IN 47906 USA Purdue Univ Dept Mech Engn W Lafayette IN 47906 USA

Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. However, deep-learning methods find it very challenging to learn stiff dynamics. In this paper, we develop DAE-PINN, the first effective physics-informed deep-learning framework for learning and simulating the solution trajectories of nonlinear differential-algebraic equations (DAE). DAEs are used to model complex engineering systems, e.g., power networks, and present a "form" of infinite stiffness, which makes learning their solution trajectories challenging. Our DAE-PINN bases its effectiveness on the synergy between implicit Runge-Kutta time-stepping schemes (designed specifically for solving DAEs) and physics-informed neural networks (PINN) (deep neural networks that we train to satisfy the dynamics of the underlying problem). Furthermore, our framework (i) enforces the neural network to satisfy the DAEs as (approximate) hard constraints using a penalty-based method and (ii) enables simulating DAEs for long-time horizons. We showcase the effectiveness and accuracy of DAE-PINN by learning the solution trajectories of a three-bus power network.

关键词： Deep learning data-driven scientific computing Nonlinear differential-algebraic equations Implicit Runge-Kutta

来源：评论

学校读者我要写书评

暂无评论

Revealing the nature of concrete materials using soft computing models

引用

JOURNAL OF BUILDING ENGINEERING 2022年 59卷

作者： Duan, Kangkang Cao, Shuangyin Zou, Zhengbo Huang, Lei He, Zhili Univ British Columbia Dept Civil Engn Vancouver BC Canada Southeast Univ Sch Civil Engn Nanjing Peoples R China

The durability of materials has long been a topic undergoing intense study in civil engineering. This paper used a novel approach to foster current research in two aspects: identifying dominant concrete properties and simulating chloride transport in concrete. Machine learning methods have proven to have remarkable abilities to approximate complex functions, which provides a potential tool for realizing the above ideas. This paper used deep neural networks to identify dominant concrete parameters and simulate the transport process by integrating physical constraints into models. Results showed that deep neural networks combined with physical constraints could effectively identify material properties with high accuracy (relative error <1%) and simulate the aggression of chloride. This study also demonstrated that machine learning models could be interpretable. In addition, this paper also explored the influence of time intervals of detection datasets, the size of datasets, and the noise in datasets (-5%-5%) on the convergence of identification. Results showed that short time intervals and big datasets could accelerate convergence while the noise in datasets had negligible influences on this method. In addition, with exact physical constraints, this method could predict the performance of materials without the assistance of any dataset.

关键词： Concrete Chloride Machine learning Physics-informed neural networks data-driven scientific computing

来源：评论

学校读者我要写书评

暂无评论

NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training

引用

ALGORITHMS 2023年第4期16卷 194-194页

作者： Lu, Binghang Moya, Christian Lin, Guang Purdue Univ Dept Comp Sci W Lafayette IN 47906 USA Purdue Univ Dept Math W Lafayette IN 47906 USA Purdue Univ Sch Mech Engn W Lafayette IN 47906 USA

This paper presents NSGA-PINN, a multi-objective optimization framework for the effective training of physics-informed neural networks (PINNs). The proposed framework uses the non-dominated sorting genetic algorithm (NSGA-II) to enable traditional stochastic gradient optimization algorithms (e.g., ADAM) to escape local minima effectively. Additionally, the NSGA-II algorithm enables satisfying the initial and boundary conditions encoded into the loss function during physics-informed training precisely. We demonstrate the effectiveness of our framework by applying NSGA-PINN to several ordinary and partial differential equation problems. In particular, we show that the proposed framework can handle challenging inverse problems with noisy data.

关键词： machine learning data-driven scientific computing multi-objective optimization

来源：评论

学校读者我要写书评

暂无评论

Wasserstein generative adversarial uncertainty quantification in physics-informed neural networks

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2022年 463卷 1页

作者： Gao, Yihang Ng, Michael K. Univ Hong Kong Dept Math Hong Kong Peoples R China

In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations. By using groupsort activation functions in adversarial network discriminators, network generators are utilized to learn the uncertainty in solutions of partial differential equations observed from the initial/boundary data. Under mild assumptions, we show that the generalization error of the computed generator converges to the approximation error of the network with high probability, when the number of samples are sufficiently taken. According to our established error bound, we also find that our physics-informed WGANs have higher requirement for the capacity of discriminators than that of generators. Numerical results on synthetic examples of partial differential equations are reported to validate our theoretical results and demonstrate how uncertainty quantification can be obtained for solutions of partial differential equations and the distributions of initial/boundary data. However, the quality or the accuracy of the uncertainty quantification theory in all the points in the interior is still the theoretical vacancy, and required for further research.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Wasserstein generative adversarial networks Simi-supervised learning data-driven scientific computing Machine learning Uncertainty quantifications Generalization theory

来源：评论

学校读者我要写书评

暂无评论

Physics-informed neural network method for solving one-dimensional advection equation using PyTorch

引用

ARRAY 2022年 13卷

作者： Vadyala, Shashank Reddy Betgeri, Sai Nethra Betgeri, Naga Parameshwari Louisiana Tech Univ Dept Computat Anal & Modeling Ruston LA 71270 USA Dr BV Raju Inst Technol Dept Business & Adm Medak Telangana India

Numerical solutions to the equation for advection are determined using different finite-difference approximations and physics-informed neural networks (PINNs) under conditions that allow an analytical solution. Their accuracy is examined by comparing them to the analytical solution. We used a machine learning framework like PyTorch to implement PINNs. PINNs approach allows training neural networks while respecting the Partially differential equations (PDEs) as a strong constraint in the optimization as apposed to making them part of the loss function. In standard small-scale circulation simulations, it is shown that the conventional approach incorporates a pseudo diffusive effect that is almost as large as the effect of the turbulent diffusion model;hence the numerical solution is rendered inconsistent with the PDEs. This oscillation causes inaccuracy and computational uncer-tainty. Of all the schemes tested, only the PINNs approximation accurately predicted the outcome. We assume that the PINNs approach can transform the physics simulation area by allowing real-time physics simulation and geometry optimization without costly and time-consuming simulations on large supercomputers.

关键词： data-driven scientific computing Partial differential equations Physics Machine learning Finite element method

来源：评论

学校读者我要写书评

暂无评论

Hybrid FEM-NN models: Combining artificial neural networks with the finite element method

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2021年 446卷 110651-110651页

作者： Mitusch, Sebastian K. Funke, Simon W. Kuchta, Miroslav Simula Res Lab N-1364 Fornebu Norway

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in the optimisation as apposed to making them part of the loss function. The resulting models are discretised in space by the finite element method (FEM). The method applies to both stationary and transient as well as linear/nonlinear PDEs. We describe implementation of the approach as an extension of the existing FEM framework FEniCS and its algorithmic differentiation tool dolfin-adjoint. Through series of examples we demonstrate capabilities of the approach to recover coefficients and missing PDE operators from observations. Further, the proposed method is compared with alternative methodologies, namely, physics informed neural networks and standard PDE-constrained optimisation. Finally, we demonstrate the method on a complex cardiac cell model problem using deep neural networks. (C) 2021 The Authors. Published by Elsevier Inc.

关键词： data-driven scientific computing Partial differential equations Learning unknown physics Machine learning Finite element method

来源：评论

学校读者我要写书评

暂无评论

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2019年 378卷 686-707页

作者： Raissi, M. Perdikaris, P. Karniadakis, G. E. Brown Univ Div Appl Math Providence RI 02912 USA Univ Penn Dept Mech Engn & Appl Mech Philadelphia PA 19104 USA

We introduce physics-informed neural networks - neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge-Kutta time stepping schemes with unlimited number of stages. The effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction-diffusion systems, and the propagation of nonlinear shallow-water waves. (C) 2018 Elsevier Inc. All rights reserved.

关键词： data-driven scientific computing Machine learning Predictive modeling Runge-Kutta methods Nonlinear dynamics

来源：评论

学校读者我要写书评

暂无评论

Sparse identification of truncation errors

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2019年 397卷 108851-108851页

作者： Thaler, Stephan Paehler, Ludger Adams, Nikolaus A. Tech Univ Munich Inst Aerodynam & Fluid Mech D-85748 Garching Germany

This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation errors, for example in the creation of implicit Large Eddy schemes, we introduce the Sparse Identification of Truncation Errors(SITE) framework to automatically identify the terms of the modified differential equation from simulation data. We build on recent advances in the field of data-driven discovery and control of complex systems and combine it with classical work on modified differential equation analysis of Warming, Hyett, Lerat and Peyret. We augment a sparse regression-rooted approach with appropriate preconditioning routines to aid in the identification of the individual modified differential equation terms. The construction of such a custom algorithm pipeline allows attenuating of multicollinearity effects as well as automatic tuning of the sparse regression hyperparameters using the Bayesian information criterion (BIC). As proof of concept, we constrain the analysis to finite difference schemes and leave other numerical schemes open for future inquiry. Test cases include the linear advection equation with a forward-time, backward-space discretization, the Burgers' equation with a MacCormack predictor-corrector scheme and the Korteweg-de Vries equation with a Zabusky and Kruska discretization scheme. Based on variation studies, we derive guidelines for the selection of discretization parameters, preconditioning approaches and sparse regression algorithms. The results showcase highly accurate predictions underlining the promise of SITE for the analysis and optimization of discretization schemes, where analytic derivation of modified differential equations is infeasible. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Sparse regression Truncation error Modified differential equation analysis data-driven scientific computing Preconditioning

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：