Collaborative Research: Machine Learning methods for multi-disciplinary multi-scales problems

该项目解决了现代科学研究中两个最紧迫的挑战：(a)在广泛的空间和时间尺度上对自然现象进行建模，以及(b)应用数据科学从大型数据集中发现物理上有意义的关系。它将利用相关和不同学科的知识，通过数据科学将它们联系起来。将研究四个具体问题：云的形成和演化、粒子在随机介质中的运动、受挫磁系统和城市地形的重建。选择这些基准问题是因为它们捕获了多尺度挑战的不同学科方面。最先进的机器学习方法（包括人工神经网络）将用于开发小规模过程的新数学表示。如果成功，该项目将大大提高科学计算的能力，以解决自然科学和社会科学的各种重要问题，并将通过两个研讨会、对5个机构联盟的多次校园访问、高影响力的同行评审出版物和演讲以及十多名博士后和学生的培训等方式广泛传播。该项目将开发、实施和评估一个新的约束优化框架，以发现和测试不同分辨率和尺度的物理现象，包括旨在发现噪声数据下的随机微分方程的新机器学习算法。这将用于训练物理参数化，以解释粗分辨率模型中小规模过程的影响。其核心将是设计一个新的框架来约束人工神经网络，以提供在领域科学中可解释和有意义的解决方案，并且可以直接与微分算子相关联。该项目是美国国家科学基金会“利用数据革命（HDR）大创意”活动的一部分，由HDR和美国国家科学基金会数学与物理科学理事会数学科学部共同支持。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 project addresses two of the most pressing challenges in modern scientific research: (a) modeling natural phenomena across a broad range of space and time scales, and (b) the application of data science to discover physically meaningful relationships from large datasets. It will leverage knowledge from related and disparate disciplines, connecting them through data science. Four specific problems will be studied: cloud formation and evolution, movement of particles through random media, frustrated magnetic systems, and the reconstruction of urban topography. These benchmark problems have been selected as they capture different disciplinary aspects of multi-scale challenges. State-of-the-art methods in machine learning (including Artificial Neural Networks) will be used to develop new mathematical representation for small-scale processes. If successful, this project will substantially increase the capability of scientific computing to address a wide variety of important problems from the natural and social sciences, and will be disseminated widely through a pair of workshops, multiple campus visits across the 5-institution consortium, high impact peer-reviewed publications and presentations and the training of a cadre of more than a dozen post-docs and students.This project will develop, implement and evaluate a new constrained optimization framework to discover and test physical phenomena at different resolutions and scales, including new machine learning algorithms aimed at discovering the stochastic differential equations underlying noisy data. This will be used to train physical parameterizations that account for the effects of small-scale processes in coarse resolution models. Core to this will be the design of a new framework to constrain artificial neural networks to deliver solutions that are interpretable and meaningful in the domain sciences and that can be directly associated with differential operators.This project is part of the National Science Foundation's Harnessing the Data Revolution (HDR) Big Idea activity, and is jointly supported by HDR and the Division of Mathematical Sciences within the NSF Directorate of Mathematical and Physical Sciences.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.