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

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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.