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

该研讨会将侧重于基础数学理论和先进建模技术的开发，研究和应用，使用人工智能（AI）工具，如深度神经网络，和科学计算技术，如多级有限元方法。学生，博士后，初级和高级研究人员参加研讨会，为在机器学习和科学计算相关领域工作的研究人员之间交流思想创造了一个有效的环境。本次研讨会的总体目标是为这些社区搭建桥梁，旨在创建有效且更强大的方法和技术，以便在物理学，生物学和社会科学现象的数学和计算建模中使用AI。研讨会将由几个因素驱动。第一个是各种不同规模的实时互动的数值和数学模型。第二个是将使用经典离散化的数值工具与神经网络技术相结合，可以处理超出当前科学计算能力的物理，生物和医学研究中的复杂模型。研讨会还将包括不同时间和空间尺度的鲁棒线性和非线性求解器以及提供物理感知数值模型的高效和可解释的学习过程。 最后，将包括调整到现代高性能计算机的高级软件包的主题。 该研讨会将于2021年11月3日至5日在宾夕法尼亚州大学公园的宾夕法尼亚州立大学举行（jxu60.math.psu.edu）。研讨会的主要目标是集结力量，致力于开发新的集成技术，妥善解决解决多物理场和多尺度问题的基本困难。研讨会的参与者将有机会展示他们与科学机器学习和传统数值方法相关的研究，与来自其他国家的领先专家进行交流和互动，并启动潜在的合作。该研讨会侧重于神经网络，机器学习和多级方法中的关键开放问题，预计将在分析结果和仿真技术的开发方面带来新的想法和合作。从长远来看，该研讨会的设计将有助于推动机器学习和传统科学计算的跨学科研究的未来发展，这将促进许多其他科学领域的进步。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.