Improving Interpretable Machine Learning for Plasmas: Towards Physical Insight, Data-Driven Models, and Optimal Sensing

磁化等离子体是过热气体和磁场的结合，在我们的宇宙中无处不在，是一些最壮观的自然现象的原因，比如极光。等离子体也被广泛用于工程和工业应用，如空间推进和未来聚变能反应堆的开发。该项目旨在提高我们理解和预测磁化等离子体行为的能力，使用既快速又易于使用的简化模型。特别是，这项调查将探索将机器学习技术与控制磁化等离子体的已知物理定律相结合的方法，这些技术正在彻底改变许多领域，如自动驾驶汽车，寻求利用每种方法的最佳方面。该项目将通过三种方式利用磁化等离子体的物理信息约束来推进数据驱动的建模方法，如机器学习：1)几种新兴的数据分解方法将首次应用于磁化等离子体的数值模拟，并对这些系统进行评估；2)与经典方法相比，基于这些分解的数据驱动非线性模型将用于磁化等离子体的建模，其速度显着提高；3)将评估用于诊断磁化等离子体的传感器优化放置的方法，以提高用于观察等离子体的测量值以及作为建立数据驱动模型的信息源的价值。这三项研究将共同推进低维、非线性和可解释数据驱动方法的有效性，以实现新的物理见解、改进的预测和多尺度磁化等离子体的鲁棒控制。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。

Magnetized plasmas, a combination of superheated gas and magnetic fields, are pervasive in our universe and are responsible for some of the grandest natural phenomena, such as the aurora. Plasmas are also extensively studied for engineering and industrial applications, such as space propulsion and development of future fusion energy reactors. This project aims to improve our ability to understand and predict the behavior of magnetized plasmas using simplified models that are both fast and easy to use. In particular, this investigation will explore methods that combine machine learning techniques that are revolutionizing many fields, like self-driving cars, with the known physical laws that govern magnetized plasmas - seeking to leverage the best aspects of each individual approach.This project will advance data-driven modeling approaches such as machine learning by utilizing physics-informed constraints for magnetized plasmas in three ways: 1) Several emerging data decomposition methods will be applied to numerical simulations of magnetized plasmas for the first time and assessed for these systems; 2) Data-driven nonlinear models based on these decompositions will be tested for modeling magnetized plasmas with significantly increased speed compared to classical approaches; 3) Methods to optimize the placement of sensors to diagnose magnetized plasmas will be evaluated to improve the value of measurements used to both observe plasmas and as the source of information to build data-driven models. Together these three studies will advance the effectiveness of low-dimensional, nonlinear, and interpretable data-driven methods for achieving new physical insight, improved prediction, and robust control of multi-scale magnetized plasmas.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.