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

该补助金支持研究生，博士后研究员和初级教师参加将于2023年5月26日至27日在NJIT举行的“应用和计算数学前沿”（FACM）会议。 FACM会议系列的第18次会议将致力于计算波传播和成像领域的最新研究。 波散射和成像问题在各种工程和工业应用中是普遍存在的。例如，这些包括激光器和太阳能电池板等光电设备的设计，隐形技术，医学成像和材料的无损检测（其中使用规定的入射电磁波照射样品并识别裂缝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。会议汇集了一群不同的数学家，统计学家，科学家和工程师，在一个促进参与者之间的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，这些问题要么被确立为应用数学中具有重大意义的领域，要么被确立为具有特殊潜力的新兴研究领域。这些是：（1）逆问题和成像，（2）积分方程和高频方法，（3）光学设计中的最佳传输，以及（4）机器学习在PDE和逆问题中的应用。计算波传播和成像领域在过去二十年中迅速发展，受到工业应用的推动，并受到数学理论和新方法的快速发展的支持，这些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。尽管取得了进展，许多挑战仍然存在，例如，在治疗高频问题与多重散射效应，计算反演有限（稀疏，不完整，或两者兼而有之）的数据，和高维问题，等等。此外，有一个基础理论，可以导致更好地理解新算法的数学基础的强烈需求。FACM 2023提供了一个理想的论坛，以刺激新的战略，以解决这些具有挑战性的问题，通过思想的交叉施肥和新的合作。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的知识价值和更广泛的影响审查标准的支持。

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.