Conference: Conference on Frontiers in Applied and Computational Mathematics (FACM 2023): New trends in computational wave propagation and imaging

该基金支持研究生、博士后和初级教师参加将于2023年5月26日至27日在新泽西理工大学举行的“应用与计算数学前沿”（FACM）会议。这是FACM会议系列的第18次会议，将致力于在计算波传播和成像领域有前途的最新研究。波散射和成像问题在各种工程和工业应用中普遍存在。这些包括，例如，光电设备的设计，如激光和太阳能电池板，隐身技术，医学成像和材料的无损检测（其中规定的入射电磁波用于照亮样品并识别裂纹或缺陷的位置和形状）。另一个重要的例子来自微芯片设计，它涉及多层材料中具有挑战性的波传播问题，需要新的数值方法。尽管取得了许多成功，但挑战仍然存在，例如高频问题，复杂介质中的波散射，快速算法的设计以及基于机器学习的新技术的应用等。会议汇集了数学家、统计学家、科学家和工程师等不同群体，在一个促进参与者之间重要互动和交流的环境中展示他们的研究。FACM 2023会议的主题是“计算波传播和成像的新趋势”，并将重点关注几个问题领域，这些问题领域要么是在应用数学中具有重要意义的领域，要么是具有特殊潜力的新兴研究领域。它们是：(1)反问题和成像，(2)积分方程和高频方法，(3)光学设计中的最佳输运，(4)机器学习在PDE和反问题中的应用。在工业应用的推动下，在数学理论和新方法的快速发展的支持下，计算波传播和成像领域在过去二十年中迅速发展，这些新方法源于非线性优化、随机和快速线性求解器以及机器学习/数据科学等方面的进步。尽管取得了进展，但仍然存在许多挑战，例如，在处理具有多重散射效应的高频问题，有限（稀疏，不完整，或两者兼而有之）数据的计算反演以及高维问题等。此外，对基础理论的强烈需求可以使我们更好地理解新算法的数学基础。FACM 2023提供了一个理想的论坛，通过思想的交流和新的合作，激发新的战略来解决这些具有挑战性的问题。该奖项反映了美国国家科学基金会的法定使命，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。

This grant supports the participation of graduate students, postdoctoral fellows, and junior faculty in the conference ``Frontiers in Applied and Computational Mathematics'' (FACM) to be held May 26-27, 2023 at NJIT. This 18th conference in the FACM meeting series will be devoted to promising recent research in the field of computational wave propagation and imaging. Wave scattering and imaging problems are pervasive in a variety of engineering and industrial applications. These include, for instance, the design of optoelectronic devices such as lasers and solar panels, stealth technology, medical imaging, and nondestructive testing of materials (in which a prescribed incident electromagnetic wave is used to illuminate a sample and identify the location and shape of cracks or defects). Another important example comes from microchip design, which involves challenging wave propagation problems in multilayer materials that call for new numerical methods. Despite numerous successes, challenges remain in, e.g., high-frequency problems, wave scattering in complex media, design of fast algorithms, and the application of new techniques based on machine-learning, among others. The conference brings together a diverse group of mathematicians, statisticians, scientists, and engineers to present their research in an environment that promotes significant interaction and cross-fertilization among the participants. The FACM 2023 conference theme is ``New trends in computational wave propagation and imaging,’’ and will focus on several problem areas that have either been established as areas of major significance in applied mathematics, or as emerging research fields with exceptional potential. These are: (1) inverse problems and imaging, (2) integral equation and high-frequency methods, (3) optimal transport in optical design, and (4) applications of machine learning in PDE's and inverse problems. The field of computational wave propagation and imaging has grown rapidly in the past two decades, fueled by industrial applications and supported by rapid development in mathematical theory and novel approaches stemming from advances in, for example, nonlinear optimization, randomized and fast linear solvers, and machine learning/data science. Despite the progress, numerous challenges remain, for instance, in treating high frequency problems with multiple scattering effects, computational inversion with limited (sparse, incomplete, or both) data, and high dimensional problems, among many others. In addition, there is a strong need for fundamental theory that can lead to a better understanding of the mathematical underpinnings of the new algorithms. FACM 2023 presents an ideal forum to stimulate new strategies to tackle these challenging problems through cross-fertilization of ideas and new collaborations.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.