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

Virginia Polytechnic Institute And State University, Blacksburg VA

Investigators

Abstract

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.