Collaborative proposal: Workshop on Numerical Modeling with Neural Networks, Learning, and Multilevel Finite Element Methods

合作提案：神经网络数值建模、学习和多级有限元方法研讨会

• 批准号: 2132710
• 负责人: Ludmil Zikatanov
• 金额: $ 3万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-11-01 至 2022-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2132710&HistoricalAwards=false
• 关键词: Collaborative; proposal; Workshop; Numerical; Modeling

The workshop will focus on the development, investigation, and application of fundamental mathematical theories and advanced modeling techniques using both Artificial Intelligence (AI) tools, such as deep neural networks, and scientific computing techniques, such as multilevel finite element methods. Participation of students, postdocs, junior, and senior researchers in the workshop creates an effective environment for exchange of ideas between researchers working in areas related to machine learning and scientific computing. The overarching goal of this workshop is to bridge these communities with the aim of creating efficient and more robust methods and techniques for the use of AI in mathematical and computational modeling of phenomena in physics, biology, and the social sciences. The workshop will be driven by several factors. The first is the wide range of numerical and mathematical models for real-time interactions at different scales. The second is the combination of numerical tools using classical discretizations with neural network techniques that can handle complex models in physical, biological, and medical research beyond current scientific computing capabilities. The workshop will also include topics in robust linear and nonlinear solvers for different temporal and spatial scales and efficient and interpretable learning processes that provide physics-aware numerical models. Finally, topics on advanced software packages tuned to modern high performance computers will be included. The workshop will be held at Pennsylvania State University, University Park, PA on November 3-5, 2021 (https://jxu60.math.psu.edu).A primary objective of the workshop is to marshal forces to work on the development of newly integrated techniques that properly address the fundamental difficulties of solving multiphysics and multiscale problems. Workshop participants will have the opportunity to present their research related to scientific machine learning and traditional numerical methods, communicate and interact with leading experts from other countries, and initiate potential collaborations. The workshop focuses on key open questions in neural networks, machine learning, and multilevel methods, and is expected to lead to new ideas and collaborations in the development of analytic results and simulation technologies. On a longer-time scale, the design of the workshop will help to enable future advances in interdisciplinary studies of machine learning and traditional scientific computing, which will facilitate progress in many other areas of science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

研讨会将着重于使用人工智能（AI）工具（例如深度神经网络）和科学计算技术（例如多级有限元方法）的基本数学理论和高级建模技术的开发，研究和应用。学生，博士后，初级和高级研究人员的参与为讲习班创造了一个有效的环境，以在与机器学习和科学计算有关的领域工作的研究人员之间进行交流。该研讨会的总体目标是桥接这些社区，目的是为在物理，生物学和社会科学中现象的数学和计算模型中使用AI的使用有效，更强大的方法和技术。研讨会将由几个因素驱动。第一个是在不同尺度上实时相互作用的多种数值和数学模型。第二个是使用经典离散化与神经网络技术的数值工具的组合，这些技术可以处理当前科学计算能力以外的物理，生物学和医学研究中的复杂模型。该研讨会还将在鲁棒线性和非线性求解器中为不同的时间和空间量表以及提供物理意识到的数值模型的有效且可解释的学习过程中的主题。 最后，将包括对现代高性能计算机调整的高级软件包的主题。 研讨会将于2021年11月3日至5日在宾夕法尼亚州宾夕法尼亚州公园宾夕法尼亚州立大学（https://jxu60.math.psu.edu）举行。研讨会的主要目的是授予元帅的力量，以努力解决新型整合技术的开发，这些综合技术的发展构成了解决基本困难的综合型和越来越多组的问题。研讨会参与者将有机会介绍与科学机器学习和传统数值方法有关的研究，与其他国家的领先专家进行交流和互动，并开始潜在的合作。该研讨会着重于神经网络，机器学习和多层次方法中的关键开放问题，并有望在开发分析结果和仿真技术的开发方面带来新的想法和协作。从长期来看，研讨会的设计将有助于在机器学习和传统科学计算的跨学科研究中取得进步，这将促进科学其他许多领域的进步。该奖项反映了NSF的法定任务，并认为通过使用该基金会的知识分子和更广泛影响的评估来评估Criteria的评估。