CAREER: Unifying Scientific Knowledge with Machine Learning for Forward, Inverse, and Hybrid Modeling of Scientific Systems

科学的基本目标之一是建立科学系统的数学模型，通过预测系统的行为来解释物理世界的本质。目前基于科学的模型标准，植根于科学理论和方程，在模拟复杂的现实世界系统方面存在一些缺陷。这些缺点的核心是它们的理论科学性，这限制了它们有效地利用没有在理论上得到很好描述的数据。因此，可以从数据中自动提取模式和关系的机器学习方法越来越被视为基于科学的模型的有前途的替代品。然而，仅仅依赖于数据中包含的信息并且与科学理论无关的黑箱机器学习模型在科学问题上取得了有限的成功。相反，在知识引导的机器学习这一新兴领域，人们越来越意识到将科学知识与机器学习统一起来。该项目旨在在三个驱动用例的背景下，在知识引导机器学习方面取得新的进展：流体动力学、气溶胶建模和湖泊建模。该项目的核心目标是为下一代科学和工程领域的劳动力做好准备，包括能够轻松跨越机器学习和科学领域之间学科界限的多元化学生骨干。该项目还将通过三个实际用例以及与行业合作伙伴的合作，对科学和社会产生直接影响。该项目的长期愿景是将知识引导的机器学习建立为一门成熟的研究和教育学科，以促进科学的进步。本项目旨在在知识引导机器学习的三个主要研究任务上取得新的进展：利用科学方程和数据进行正演建模，在基于科学的模型中推断参数的逆建模，以及混合科学-机器学习建模以消除基于科学的模型中的缺陷。该项目将促进知识引导机器学习的变革创新，将各种科学知识纳入机器学习框架，从流体动力学的偏微分方程到气溶胶建模的数值模型和湖泊建模的现象学规则。在正向建模任务中，该项目将在科学指导课程学习中开发一类新的算法，以在训练深度学习模型时利用数据驱动和科学监督之间的相互作用。该项目还将开发新的科学指导的重新采样策略，以便在推理过程中生成科学一致的预测。在逆建模任务中，本项目将带来知识引导逆建模的新公式，利用科学监督（就正演模型的知识而言）来指导基于机器学习的逆模型的训练。在混合建模任务中，本项目将产生一类新的残差校正神经网络，用于增强基于科学的输出中的系统偏差或残差，以及在校正其输出中的残差的同时共同推断基于科学的模型的参数的方法。除了这三个用例之外，在这个项目中开发的方法可以潜在地影响许多科学学科，在这些学科中，科学知识和模型经常被使用。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。

One of the fundamental goals in science is to build mathematical models of scientific systems that can explain the nature of the physical world by predicting the system's behavior. Current standards of science-based models, rooted in scientific theories and equations, suffer from several shortcomings in modeling complex real-world systems. At the core of these shortcomings is their theoretical scientific nature that restricts them from making effective use of data that is not well-described theoretically. Consequently, machine learning methods, that can automatically extract patterns and relationships from data, are increasingly being viewed as promising alternatives to science-based models. However, black-box machine learning models, that solely rely on information contained in data and are agnostic to scientific theories, have met with limited success in scientific problems. Instead, there is a growing realization to unify scientific knowledge with machine learning in the emerging field of knowledge-guided machine learning. This project aims to make novel advances in knowledge-guided machine learning in the context of three driving use-cases: fluid dynamics, aerosol modeling, and lake modeling. A central goal of this project is to prepare the next generation of workforce in science and engineering comprising of a diverse cadre of students who can easily cross disciplinary boundaries between machine learning and scientific fields. This project will also have direct impacts to science and society through the three real-world use-cases and through collaborations with industry partners. The long-term vision of this project is to establish knowledge-guided machine learning as a full-fledged research and education discipline for the advancement of science. This project aims to make novel advances in three primary research tasks of knowledge-guided machine learning: forward modeling with scientific equations and data, inverse modeling for inferring parameters in science-based models, and hybrid-science-machine learning modeling to remove imperfections in science-based models. This project will contribute transformative innovations in knowledge-guided machine learning for incorporating a wide variety of scientific knowledge in machine learning frameworks, from partial differential equations in fluid dynamics to numerical models in aerosol modeling and phenomenological rules in lake modeling. In the task of forward modeling, this project will develop a new class of algorithms in science-guided curriculum learning to exploit the interplay between data-driven and scientific supervision while training deep learning models. This project will also develop novel science-guided resampling strategies for generating scientifically consistent predictions during inference. In the task of inverse modeling, this project will lead to novel formulations of knowledge-guided inverse modeling, where scientific supervision (in terms of knowledge of the forward model) is used to guide the training of machine learning-based inverse models. In the task of hybrid modeling, this project will result in a new class of residual correcting neural networks for augmenting systematic biases or residuals in science-based outputs, and methods to jointly infer parameters of science-based models while correcting for residuals in their outputs. Beyond the three use-cases, the methodologies developed in this project can potentially impact a number of scientific disciplines where scientific knowledge and models are routinely used.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.