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组合，在我们的宇宙中无处不在，是一些最壮观的自然现象的罪魁祸首，比如极光。等离子体还被广泛研究用于工程和工业应用，如空间推进和未来聚变能源反应堆的开发。这个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，这项研究将探索将机器学习技术与管理磁化等离子体的已知物理定律相结合的方法，这些技术正在给许多领域带来革命性的变化，如自动驾驶汽车。该项目将通过利用磁化等离子体的物理信息约束，以三种方式推进数据驱动建模方法，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)基于这些分解的数据驱动非线性模型将被测试用于建模磁化等离子体，与传统方法相比，速度将显著提高；3)将评估优化磁化等离子体诊断传感器位置的方法，以提高用于观测等离子体和作为建立数据驱动模型的信息源的测量的价值。这三项研究将共同推进低维、非线性和可解释的数据驱动方法的有效性，以实现对多尺度磁化等离子体的新的物理洞察、改进的预测和稳健的控制。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。

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.