ABSTRACT

Machine learning algorithms have proved to be indispensable to modern industry and society. However, traditional machine learning extracts information from observational data, while ignoring the tremendous amount of information encoded into scientific laws of nature. This research concerns physics-informed machine learning, an emerging area that promises to have a profound and lasting impact in science and engineering, by coding scientific laws directly into machine learning algorithms. This dramatically reduces the data size requirement of these algorithms, and even allows them to extrapolate to domains where there is no data. This project will develop a Bayesian paradigm for physics-informed machine learning, which will include new probabilistic methods with quantified uncertainty, new computation and analysis methods, and new unsupervised algorithms. The results of this research will benefit applications in petroleum engineering, aerospace engineering, materials science, and astronomy being developed by the investigators and their collaborators.

This research will develop a Bayesian paradigm for physics-informed neural networks (PINNs) and physics-informed Gaussian processes (PIGPs). The investigators will develop probabilistic solvers for nonlinear partial differential equations that leverage recent probabilistic solver methods in combination with PINN and PIGP models to solve physics-informed machine learning problems. Training dynamic analysis methods for neural networks with multi-part loss functions will be developed in order to investigate the performance of Bayesian PINNs. The investigators will study Bayesian model averaging for PINN ensembles based on traditional multiple initialization, particle swarms, and variational inference. In addition, new unsupervised methods to combine PINN and PIGP algorithms will be developed to ameliorate the issue of propagating information throughout the physical domain, which is a common failure mode of physics-informed machine learning algorithms. This work will result in Bayesian physics-informed machine learning tools for problems in oil reservoir simulation, computational fluid dynamics, phase-field modeling in microstructure informatics, and radiative transfer in supernova atmospheres, among other multidisciplinary research projects conducted by the investigators and their collaborators at the recently-established Scientific Machine Learning Laboratory of the Texas A&M Institute of Data Science (TAMIDS).

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.

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