CAREER: Understanding Invariant Convolutional Neural Networks through Many Particle Physics

工程和物理科学中的大规模计算，以及新的实验方法，正在产生大量的高维分布式数据，解释，分析和使用这些数据是科学面临的一个基本问题。机器学习算法从这些数据集中提取、内插和外推信息。然而，现代数据的复杂性需要新的算法范式，能够在众多尺度上解析复杂和微妙的模式。该奖项将在开发这些新的机器学习范式方面取得重大进展，重点关注用于分子，材料和药物建模的相互作用体的多尺度系统。更具体地说，该奖项将促进数学，深度学习，许多粒子物理学和数据科学的综合科学和教育计划。在科学上，它将开发基于（小波）散射变换的不变卷积神经网络的数学理论，并试图通过许多粒子系统的透镜来解释这些散射变换的数学特性。这项研究将促进量子多粒子系统的快速模拟，从而为量子化学、材料科学和药物发现开辟新的研究途径。与这些研究工作相协调的是一项计划，旨在增加数据科学中代表性不足的学生的参与。这部分项目的核心是以数据科学为主题的"交替春假"，旨在向本科生介绍数据科学研究，该研究将与密歇根州立大学现有的项目相结合，以最大限度地发挥影响力。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Large scale computing in engineering and the physical sciences, in addition to new experimental methods, are generating massive amounts of high dimensional distributed data, and interpreting, analyzing, and using this data is a fundamental problem facing science. Machine learning algorithms extract, interpolate, and extrapolate information from these data sets. However, the complexity of modern data requires new algorithmic paradigms that are capable of parsing intricate and subtle patterns across numerous scales. This CAREER award will make significant strides in developing these new machine learning paradigms, focusing on multiscale systems of interacting bodies that are used to model molecules, materials, and drugs, amongst others.More specifically, this CAREER award will facilitate an integrated scientific and educational program at the interface of mathematics, deep learning, many particle physics and data science. Scientifically, it will develop a mathematical theory of invariant convolutional neural networks based upon (wavelet) scattering transforms, and seek to interpret the mathematical properties of these scattering transforms through the lens of many particle systems. The research will facilitate fast simulations of quantum many particle systems, thus opening new research avenues in quantum chemistry, materials science and drug discovery. Intertwined with these research efforts is a plan to increase the participation of under-represented students in data science. The centerpiece of this part of the project is a data science themed "alternate spring break," meant to introduce undergraduate students to data science research, which will be integrated with existing programs at Michigan State University to maximize impact.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.