Collaborative Research: Randomized Feature Methods for Modeling and Dynamics: Theory and Algorithms

这项研究计划的目标是为高风险决策开发一致的、经过理论验证的机器学习算法。该项目将研究随机特征网络，将其作为高维函数逼近的完全可训练神经网络的一种更简单但同样强大的替代方案。长期目标是开发集成机器学习和动力系统的方法，这是数据科学中针对科学问题的一个具有挑战性的新前沿。该项目还为本科生、研究生和博士后提供了研究培训机会。该项目的主要目标是开发用于数据驱动函数逼近的新算法，目的是使用学习技术进行科学建模和动力学。重点是构建具有复杂性、准确性和/或稳定性保证的随机化算法。严格的算法设计和建模是这个科学计算项目的核心，在这个项目中，我们利用机器学习的进步来增强模拟并提取更好的特征来逼近动态系统。该项目引入了一系列基于随机化特征和自适应阈值程序的新算法，以在不过度拟合的情况下提高精度。通过结合各种结构信息，这有可能避免几个感兴趣的物理问题的维度诅咒。主要测试问题集中在科学模型、高维系统和高维动力系统上。此外，通过了解随机特征模型，我们提供了一条更好地理解神经网络模型的途径。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The objective of this research program is to develop consistent and theoretically validated machine learning algorithms for high-stakes decisions. The project will study randomized feature networks as a simpler but equally powerful alternative to fully-trainable neural networks for high-dimensional function approximation. The long-term goal is to develop methods that integrate machine learning and dynamical systems, a challenging new frontier in data science for scientific problems. This project also provides research training opportunities for undergraduate students, graduate students, and postdoctoral fellows.The main goal of this project is to develop new algorithms for data-driven function approximation, with the goal of using learning techniques for scientific modeling and dynamics. The focus is on the construction of randomized algorithms with complexity, accuracy, and/or stability guarantees. Rigorous algorithmic design and modeling is at the core of this scientific computing project, where we leverage advances in machine learning to augment simulations and extract better features for approximating dynamical systems. This project introduces a family of new algorithms based on randomized features with adaptive thresholding procedures to improve accuracy without overfitting. By incorporating various structural information, this has the potential to avoid the curse-of-dimensionality for several physical problems of interest. The main test problems focus on scientific models, high-dimensional systems, and high-dimensional dynamical systems. In addition, by understanding random feature models, we provide one avenue toward a better understanding of neural network models.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.