CAREER: Combining Machine Learning and Physics-based Modeling Approaches for Accelerating Scientific Discovery

机器学习的最新进展使得从复杂数据中捕获空间和时间依赖性成为可能，从而在可获得大规模数据的几个商业应用中取得了巨大成功。鉴于机器学习模型在商业领域的成功，机器学习模型开始在推动不同科学领域的科学发现方面发挥重要作用，这些领域传统上由基于物理的模型主导。由于潜在现象的内在复杂性，当我们目前的知识体系还不能完全理解相关的物理过程时，机器学习模型的使用尤其有前途。然而，机器学习模型的直接应用在现实世界的科学应用中取得了有限的成功，因为许多科学问题的可用数据集远远小于有效训练高级机器学习模型所需的数据集。最近，人们对将机器学习和物理知识结合起来研究科学问题越来越感兴趣。关于该主题的现有方法在孤立的实验中显示出有希望的结果，但在现实世界的科学应用中，由于缺乏训练数据，数据变异性以及不完整或近似的物理信息，它们仍然受到限制。该项目的目标是系统地探索如何将机器学习模型和现有的基于物理的建模方法以协同的方式结合起来，为科学问题建立复杂、非平稳和时空过程的模型。该项目旨在通过四项创新探索机器学习和基于物理的模型的深度耦合，以建模物理系统。首先，将建立一个新的知识引导的机器学习架构，用于捕获物理变量之间的复杂动态和相互作用，这有助于提高模型的预测和泛化性。其次，将研究新的数据驱动逆模型，以发现物理参数，这有助于提高基于物理的模型的性能。第三，将开发新的模型预训练策略，使知识引导的机器学习算法即使在少量观察值下也能有效地工作。这些预训练策略将利用基于物理的模型生成的模拟数据集。还将提出新的技术来指导基于物理的模型的配置，目的是创建新的模拟数据集，以提高预训练的有效性。最后，将创建新的元学习方法，以便在空间和时间上适应知识引导的机器学习模型。所提出的方法将利用物理知识来估计不同物理系统之间的相似性，并促进模型适应。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。

Recent advances in machine learning make it possible to capture spatial and temporal dependencies from complex data, leading to tremendous success in several commercial applications where large-scale data are available. Given their success in commercial domains, machine-learning models are beginning to play an important role in advancing scientific discovery in diverse scientific domains, which are traditionally dominated by physics-based models. The use of machine-learning models is especially promising when relevant physical processes are not completely understood by our current body of knowledge due to the inherent complexity of the underlying phenomenon. However, the direct application of machine-learning models has met with limited success in real-world scientific applications, given that the data sets available for many scientific problems are far smaller than what is needed to effectively train advanced machine-learning models. Recently, there is a growing interest in combining machine learning and physical knowledge for studying scientific problems. Existing methods on this topic have shown promising results in isolated experiments, but they remain limited in real-world scientific applications with scarce training data, data variability, and incomplete or approximate physical information. The goal of this project is to systematically explore ways to combine machine-learning models and existing physics-based modeling approaches in a synergistic manner to model complex, non-stationary, and spatio-temporal processes for scientific problems. This project aims to explore a deep coupling of machine learning and physics-based models for modeling physical systems via four innovations. First, a new knowledge-guided machine-learning architecture will be built for capturing complex dynamics and interactions amongst physical variables, which helps improve the model prediction and generalizability. Second, new data-driven inverse models will be investigated for the discovery of physical parameters, which aids in improving the performance of physics-based models. Third, new model pre-training strategies will be developed to enable knowledge-guided machine-learning algorithms to work effectively even with a small number of observations. These pre-training strategies will leverage simulated data sets generated by physics-based models. New techniques will also be proposed to guide the configuration of physics-based models with the aim to create new simulated data sets for improving the pre-training effectiveness. Finally, new meta-learning approaches will be created for adapting the knowledge-guided machine-learning model over space and time. The proposed methods will leverage physical knowledge to estimate the similarity amongst different physical systems and facilitate model adaptation.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.